tag:blogger.com,1999:blog-58166494865768815402020-10-02T07:55:22.942-07:00Math Ed MattersMathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.comBlogger31125tag:blogger.com,1999:blog-5816649486576881540.post-60368984450503806692016-02-29T10:24:00.000-08:002016-03-01T07:02:13.665-08:00Equity in Mathematics<i>A guest post by Beth Burroughs, Montana State University</i><br /><br />You might have noticed a recent flurry of activity by mathematicians engaged in discussions about the teaching of mathematics. A few examples:<br /><br /><ul><li>The <i>Common Vision</i> project is a joint effort of five organizations in the mathematical sciences (AMATYC, AMS, ASA, MAA and SIAM) focused on modernizing undergraduate programs in the mathematical sciences. The <a href="http://www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf">Phase 1</a> report identified common goals from among those organizations and mapped out plans for the future.</li><br /><br /><li>The Association of Mathematics Teacher Educators is currently writing standards for mathematics teacher preparation for grades K-12--expanding the work of the Mathematical Education of Teachers II (<a href="http://cbmsweb.org/MET2/">CBMS, 2012</a>) by considering <i>entire</i> teacher preparation programs, including mathematical preparation. An initial <a href="http://amte.net/sites/default/files/mtp-standards-draft-jan2016.pdf">draft of that report</a> is currently available for review.</li><br /><br /><li>The MAA Committee on the Teaching of Undergraduate Mathematics (CTUM) is embarking on an ambitious guide for the teaching of undergraduate mathematics. Following an initial meeting in October of 2015, CTUM is galvanizing its team to begin writing guidelines this spring.</li></ul><br />In the face of all this activity, one might ask, “why now?” Why is there so much attention to the teaching of mathematics? The MAA, among other organizations, has consistently paid attention to undergraduate mathematics, so in some sense, why <i>now</i> is the same as why <i>always</i>. One inspiration for the current interest is the <a href="https://www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-executive-report-final_2-13-12.pdf">PCAST report of 2012</a>. This report advocated using active learning approaches in the first two years of college across the STEM disciplines, including mathematics. The report caught the attention of mathematics organizations because it suggested that non-mathematicians in mathematics-intensive disciplines should be involved in mathematics instruction; those of us who study the teaching of mathematics disagree that this strategy is the best way to achieve more expertise in teaching undergraduate level mathematics. Despite this questionable recommendation, the calls to increase retention in STEM majors, to decrease the bottleneck in introductory mathematics classes, and to look for ways to increase active learning in mathematics need our attention.<br /><br />I propose that there is an <i>urgency</i> to the mathematics community’s attention to the teaching of mathematics, and this urgency comes from the way mathematics has become a gatekeeper to access to STEM fields. The practice of mathematics is a human endeavor: Mathematics is understood through human brains and mathematics learning is transmitted through the social setting of schools. And human biases perpetuate biases and inequity in the discipline.<br /><br />Two recent articles shed light on how the way mathematics instructors have been teaching mathematics has visible consequences. One is the address by Professor Danny Martin of the <a href="http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/view/270/169">University of Illinois, Chicago</a>, to the National Council of Teachers of Mathematics (NCTM), published after its delivery in the <i>Journal of Urban Mathematics Education</i> (2015). This address seems to have missed the notice of many mathematicians--on the surface, it is a specific reaction to the NCTM’s policies as expressed through their publication <i>Principles to Actions</i>. But, I’ll suggest that you can listen to Professor Martin’s words with a broad ear and hear the indictment of how those of us who are in mathematics have institutionalized structures that prevent many--specifically poor students and students from minority backgrounds--from engaging in our discipline. Schools--including universities--systematically reinforce disadvantage. Martin goes further, claiming “the hard truth is that the outcomes and inequities lamented over in <i>Principles to Actions</i> and previous documents are precisely the outcomes that our educational system is designed to produce.” Martin highlights our community’s lack of action: “equity-oriented slogans, statements about idealized outcomes, and tweaks to teaching or curricular practices within this system do not change this fact.” The text is <a href="http://ed-osprey.gsu.edu/ojs/index.php/JUME/issue/view/18">here</a>. It deserves your attention.<br /><br />The other article is a <a href="http://www.pnas.org/content/111/23/8410.abstract">meta-analysis published</a> in <i>Proceedings of the National Academy of Sciences</i> on the use of active learning strategies in undergraduate STEM disciplines (Freeman et al., 2014). Its conclusion is that active learning strategies improve student outcomes, and it provides a clear call to mathematicians to change how we teach. The article is <a href="http://www.pnas.org/content/111/23/8410.abstract">here</a>.<br /><br />My guess is you will feel more comfortable reading the Freeman article. You’ll be soothed by the discussion of <i>p</i>-values. I hope you feel distress when you read Martin’s address. The racism and economic disparity in our country is apparent and unacceptable. What responsibility do we bear for this status as mathematicians? It would be easy to dismiss social and economic phenomena as unrelated to our work. We like to think of mathematics as pure and objective, but it isn’t the way we practice it. If we continue to perpetuate teaching strategies that reinforce disadvantage, we’re complicit in societal ills like poverty, racism, and disadvantage. We should not think of equity as something that is somebody else’s responsibility, or that it is a student’s job to advocate for themselves. We should ask, <i>what can I do</i>?<br /><br />I’m committed to these actions:<br /><br /><ul><li>Read more about teaching and learning in mathematics. (You can read blogs sponsored by AMS, MAA, or NCTM; practitioner journals like Mathematics Teacher or PRIMUS; or research journals like Journal of Mathematical Behavior or Journal of Urban Mathematics Education). Don’t look for quick fixes; instead, look for opportunities to make changes that welcome more learners to the discipline.</li><br /><li>Acknowledge the bias in mathematics. Don’t complain about students who are unprepared. Instead, assume that some have had an advantage these students haven’t had, and look for ways to give them an advantage in mathematical thinking and achievement.</li><br /><li>Get involved in the MAA’s--or any organization’s--efforts to improve access in mathematics. The MAA has many links and opportunities in the Teaching and Learning section of its web site. The NCTM is pledging to address the inequities that Professor Martin has highlighted and has invited individuals who are interested in addressing inequity in mathematics to signal their interest by emailing change@nctm.org.</li></ul><br />Changing how we teach or think about teaching is hard. But mathematicians make a career of doing things that are hard, as long as we think they are important. Changing how we teach is important.<br /><br /><b>About the author</b>: Beth Burroughs is Professor and member of the Mathematics Education Research Group in the Department of Mathematical Sciences at Montana State University. She is chair of the MAA Committee on the Mathematical Education of Teachers and serves on the MAA Board of Governors. She a co-PI on the NSF-funded Program Immersion, a collaborative project between George Mason University, Harvey Mudd College, and Montana State University, focused on professional development in mathematical modeling for elementary grades teachers. A 2014-15 U.K. Fulbright scholar, Beth is a former high school mathematics teacher.<br /><br /><br /><b>References</b><br /><br />Conference Board of the Mathematical Sciences (2012). The Mathematical Education of Teachers II. Providence RI and Washington DC: American Mathematical Society and Mathematical Association of America.<br /><br />Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. <i>Proceedings of the National Academy of Sciences</i>, 111(23), 8410-8415.<br /><br />Martin, D.B. (2015). The collective Black and principles to actions. <i>Journal of Urban Mathematics Education</i>, 8(1), 17-23.<br /><br />President’s Council of Advisors on Science and Technology (2012). <i>Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics</i>. Washington, D.C.: Executive Office of the President of the United States.<br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-78326307938153020932016-01-12T13:12:00.001-08:002016-01-12T13:12:28.768-08:00Math AutobiographyWant to know one of my favorite assignments that I have ever given my students? Want to know learn a lot of useful information about your students in a short amount of time?<br /><br />I know it sounds too good to be true, but this one simple assignment could change how you teach your classes and how well you know your audience.<br /><br />Last year after helping lead an inquiry-based learning (IBL) workshop in Portland, I decided to try something new in my own classrooms. One of the other instructors, I wish I could recall who, said he/she started off every class with a math autobiography. That's all I had from my notes, but it sounded interesting so I did some research on it before school started last fall.<br /><br />I went home, Googled “Math Autobiography” and found <a href="http://faculty.fortlewis.edu/wellborn_k/TRS%2092/Math%20Autobiography.doc" target="_blank">this assignment</a> (MS Word document) online written by Kathy Wellborn from <a href="https://www.fortlewis.edu/" target="_blank">Fort Lewis College</a>.<br /><br /><h3>Math Autobiography </h3><b>Purpose of the Assignment </b><br />As your instructor, I want to get to know you as a person and as a student of mathematics. This will help me better meet your needs. It also helps our department as we work to improve our services to students.<br /><br /><b>Content </b><br />Your autobiography should address the four sections listed below. I’ve listed some questions to help guide you, but please don’t just go through and answer each question separately. The questions are just to help get you thinking. Remember the purpose of the paper. Write about the things that will give me a picture of you. The key to writing a good piece is to give lots of detail. See the example below:<br /><br /><i>Not enough detail</i>: I hated math in fourth grade, but it got better in sixth grade.<br /><br /><i>Good detail</i>: I hated math in fourth grade because I had trouble learning my multiplication tables. I was really slow at doing problems, and I was always the last one to finish the timed tests. It was really embarrassing. …<br /><br /><b>Section 1: Introduction </b><br /><br /><ul><li>How would you describe yourself? </li><li>Where are you from? How did you decide to attend Fort Lewis? </li><li>What is your educational background? Did you just graduate from high school? Have you been out of school for a few years? If so, what have you been doing since then? </li><li>General interests: favorite subjects in school, favorite activities or hobbies. </li></ul><b>Section 2: Experience with Math</b><br /><br /><ul><li>What math classes have you taken and when?</li><li>What have your experiences in math classes been like? </li><li>How do you feel about math? </li><li>In what ways have you used math outside of school? </li></ul><b>Section 3: Learning Styles and Habits (specifically for math) </b><br /><br /><ul><li> Do you learn best from reading, listening or doing? </li><li>Do you prefer to work alone or in groups? </li><li>What do you do when you get “stuck”? </li><li>Do you ask for help? From whom? </li><li>Describe some of your study habits. For example: Do you take notes? Are they helpful? Are you organized? Do you procrastinate? Do you read the text? </li></ul><b>Section 4: The Future </b><br /><br /><ul><li>What are your expectations for this course? </li><li>What are your responsibilities as a student in this course? What do you expect from your instructor? </li><li>What are your educational and life goals? </li><li>How does this course fit into your educational goals? </li></ul>It was fantastic! Students took it way more seriously than I could have imagined. Some wrote pages and all wrote enough to get to know them. It made me realize that we don't give our students opportunities to share their math baggage/backgrounds/etc. with us often enough.<br /><br />Students shared everything from horror stories about being shamed in math courses to their excitement about math. Some let you know what they have heard about your class and even fears they may have such as a fear of presenting or working with others. This is good to know in an IBL course, since my students are all expected to work with others and also present problems. I even learned about people who were taking the course "for fun" and others who were in it for the second or third time. It really helped me get to know my students perceived strengths and weaknesses.<br /><br />The first time I did this assignment, I was surprised that almost all of my students said they preferred to work alone and considered themselves introverts. This meant that I had to help them learn how to work together and intentionally help them see the benefits of this type of learning.<br /><br />I kept these autobiographies and looked back on them as the semester passed. I want to create a similar end of course writing assignment and would be happy to share it when I do. If you already have one, please share it.<br /><br />I'll let you try this assignment in your own classrooms and see what you think. Please share your comments on what you learned from this assignment.Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-74298469271920600222015-10-12T09:30:00.000-07:002015-10-12T09:30:00.461-07:00Many Voices Are Greater Than One<div class="separator" style="clear: both; text-align: center;"></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-_NEHuzFk_vs/VgQTIA4RcXI/AAAAAAAAKZQ/qNm3-Mg7u6k/s1600/image.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="248" src="http://3.bp.blogspot.com/-_NEHuzFk_vs/VgQTIA4RcXI/AAAAAAAAKZQ/qNm3-Mg7u6k/s320/image.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Photo credit Stan Yoshinobu</i></td></tr></tbody></table>It turns out that talking to yourself can be a <a href="http://gizmodo.com/5903023/talking-to-yourself-makes-you-smarter" target="_blank">sign of intelligence</a> and <a href="https://www.psychologytoday.com/blog/the-squeaky-wheel/201405/why-you-should-start-talking-yourself" target="_blank">lower stress</a>. The down side is that you don't tend to hear a lot of new ideas. Perhaps it is best to work out ideas by yourself and, once you get stuck, find new ideas by talking to others. Though this is a simple way to describe how discovery happens in a community setting, and describe expectations for students in our classes, it has not always been a common approach to teaching. It was certainly not how we were taught to do mathematics. However, what helped many mathematicians to learn and love mathematics might not work for our students. If you could learn by just being told things, then children would never have to be told twice to brush their teeth or wash their hands. If you have ever seen a tablet or phone screen after an eight year old has used it, you know that the lesson on washing hands doesn’t stick. How do we get mathematics to stick in our students' minds like grime on an eight year old’s hands? In order to make lasting knowledge, you need to get in there, explore, and experiment with everything you see, much like a child at play.<br /><br />It is a shame that so many students never get their hands dirty working <i>with</i> math, but rather most view mathematics as an adversary. A simple measure of this is to ask them “When was the last time math really made sense?” Even good students may have progressed without making sense of any of the ideas that make math so interesting to us. They have had excellent training in finding answers, when faculty think they should have been sense-making instead.<br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-oD7L1ECMm5s/VgL5KorJkdI/AAAAAAAAKYw/9TgpYR613sI/s1600/MathEd%2BMatters%2B3.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="213" src="http://2.bp.blogspot.com/-oD7L1ECMm5s/VgL5KorJkdI/AAAAAAAAKYw/9TgpYR613sI/s320/MathEd%2BMatters%2B3.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i style="font-size: 12.8px;">Photo credit Stan Yoshinobu</i></td></tr></tbody></table>How do we bridge the gap between where we want our students to be and where they are now, while accounting for their lack of preparation in mathematical thinking? The good news is that you can guide your students to build a solid foundation and connect to the most important ideas in education. Key to this approach are the multitude of voices that need to be included in the conversation. If the goal of a class is for students to develop a deep understanding and appreciation of mathematics, then the students' voices are even more necessary than their instructor's. And lasting changes in the lives and minds of our students are exactly what we are trying to achieve as educators. Outside voices are also necessary: the many other like- minded educators, including past, present, and future, and in all disciplines, have to collaborate to decide how to address the ever-changing needs of our students. Faculty at many institutions are already implementing active methods of engaging students and fostering lasting learning.<br /><br />For the last 10 years, the <a href="http://www.inquirybasedlearning.org/" target="_blank">Academy of Inquiry Based Learning</a> has run a workshop to aid mathematics educators in implementing inquiry based learning (IBL). This summer, about 40 faculty, including all three authors, attended a four day workshop in beautiful San Luis Obispo. At the workshop, we worked with experienced faculty to develop materials, and individualized approaches to implementing IBL in our classrooms. This was an immersive experience into the practice and methods of “big tent IBL”, which is a broad and inclusive version of this active learning philosophy. IBL is being implemented in all manner of classes, not just upper level proof-based mathematics courses. In fact, the largest groups of people at the workshop were working on implementing IBL into the sequence of mathematics classes for elementary education majors and intermediate and college algebra.<br /><br />The four day workshop also introduced us to the community of faculty across the country that want nothing more than to help others get the most out of the time spent with their students. It was just enough time to get energized and get to know a lot of great people, as well start thinking about the myriad of ways to implement IBL. Unfortunately, this was not <i>nearly</i> enough time to fully figure out how we would carry out these ideas in our upcoming classes. The workshop wisely includes a year of follow up mentoring with the organizers. As a way to expand on these mentoring conversations, several of us decided to write about our early experiences at <a href="https://noviceiblblog.wordpress.com/" target="_blank">A Novice IBL Blog</a>. Already, blogging has been a wonderful reflective exercise in connecting what we are trying in the classroom to the changes we want for students. Writing posts provides an opportunity to struggle with new pedagogical tools, and learn how to effectively communicate in a new forum. This struggle has helped us each appreciate the difficulties that our students face when grappling with new material.<br /><br />Blogging has also helped us appreciate how difficult it can be to do new things. Especially when the new thing is a fundamental change in how you approach your job. Just as when our students are learning, it’s important to have many voices for ideas and support. Our blog is about support, not just for its authors, but for anyone trying IBL or anything new in the classroom (and not just at the post-secondary level). So, <a href="https://noviceiblblog.wordpress.com/" target="_blank">come visit our blog</a>, participate in the discussions and learn about inquiry based learning along with us.<br /><br />-Liza Cope, David Failing, and Nick Long<br /><br />Liza Cope is an Assistant Professor at Delta State University and can be contacted at lcope@deltastate.edu.<br /><br />David Failing is an Assistant Professor at Quincy University and can be contacted at failida@quincy.edu.<br /><br />Nick Long is an Associate Professor at Stephen F. Austin State University and can be contacted at longne@sfasu.edu.<br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-68655872216899065152015-09-24T06:55:00.000-07:002015-09-24T06:55:41.850-07:00IBL Conference: A New Kid’s Perspective<i>A guest post by Katie Wanek, University of Nebraska at Omaha</i><br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-r1-n0XprzDM/VgMIaVf_ToI/AAAAAAAAKZA/6b4L_bEdGgQ/s1600/MathEd_photo.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="300" src="http://4.bp.blogspot.com/-r1-n0XprzDM/VgMIaVf_ToI/AAAAAAAAKZA/6b4L_bEdGgQ/s400/MathEd_photo.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>The UNO group after the panel presentation.</i></td></tr></tbody></table>This past June, I was given the opportunity to attend the 18th Annual Legacy of R.L. Moore Inquiry-Based Learning Conference in Austin, Texas, along with three of my fellow undergraduates from the University of Nebraska at Omaha (UNO). I was one of only 6 attendees who were still working towards their undergraduate degree, as a majority of the conference attendees were teachers and professors at the collegiate level. Needless to say, I felt very much like the new kid in school where everyone else is already on chapter 8 and I am only on chapter 2. However, although I was much younger than most of the people I interacted with, and much less experienced, everyone I met was not just willing, but seemed excited to share their knowledge. I felt welcomed to share my own ideas and thoughts in sessions, and I was encouraged to actively participate. As it was my second time attending the conference (I attended the conference in Denver last year), I made a lot of comparisons between the two conferences while I was there. I found that there were three main characteristics that stayed constant between the two:<br /><ol><li>Inspiring</li><li>Enlightening, and </li><li>Empowering</li></ol>Inspiring. I left the conference each time inspired by both the session topics and the people I met. Whether it was an idea for a Math Teachers’ Circle, a lesson idea for my future classroom, a method to engage and encourage students, or an activity to try for outreach events, the sessions were always informative, entertaining, and thought-provoking.<br /><br />The people I met at the conference also inspired me. One of my favorite activities at both conferences was the Round-Table Discussion at which I sat with a table of other people passionate about secondary math education. We discussed roadblocks to implementing IBL in a secondary classroom and ways to work around them. People freely shared resources they found to be helpful and we all exchanged e-mails. Within the first week after this past conference, there were multiple emails sent from the other table members with links to sites and Google documents. These people inspired me to be not just an average teacher, but a great teacher who actively searches for ways to help her students and make her classroom and teaching better.<br /><br />Enlightening. I learned a lot about inquiry-based learning and the various techniques that people use to implement it in their classrooms at both conferences. Every year, I learn more and more about inquiry-based learning and what it actually means. I’ve learned that there are tons of different ways to use IBL in classrooms – flipped classrooms, projects, in-class activities, etc. <br /><br />There are also multiple ways to encourage IBL in outreach activities such as with puzzle competitions. One of my favorite sessions at the 2015 Conference was the “IBL and Mathematical Puzzlehunt Competitions” by Steven Clontz and PJ Couch. They talked about puzzlehunt competitions that they have adopted at their respective universities and how puzzles are a great way to spark interest in math.<br /><br />I learned so much at the conferences that my brain was exhausted by the time I got back to Omaha. There was so much to soak in and in a short amount of time.<br /><br />Empowering. Both conferences were empowering. I was empowered with knowledge to implement IBL in my future classrooms. I was empowered with new networks of people to turn to for ideas, techniques, and encouragement. I was empowered with ways to sell IBL to students, parents, and administrators and the data to back-up my claims. Most of all, I was empowered with a can-do attitude and the thought that this is something that is possible and will help students.<br /><br />Although the two conferences had a lot in common, especially with the three main themes I detailed, there were some differences as well. It felt like the 2014 conference had more parallel sessions and there seemed to be a larger focus on hands-on sessions and ready-made ideas to take back to the classroom. The 2015 conference focused more on how to help students be confident in their mathematical ability and how to encourage them to not give up and to keep going. Both of these differences tied back to their respective themes. The 2014 conference theme was “Engaging with Inquiry-Based Learning” and the 2015 conference theme was “Empowering with Inquiry-Based Learning”. When connecting the differences to the themes, the differences make sense. Regardless, both conferences had a lot to offer and I was left with a stronger desire to implement inquiry-based learning into my future classroom after both conferences.<br /><br />Altogether, the conference was an incredible experience and I highly encourage everyone to attend the conference, especially pre-service secondary math teachers who are interested in the idea of inquiry-based learning. For the pre-service teachers and other undergraduates planning on attending a future IBL Conference, my suggestion would be to go in with an open mind, talk to as many people as you can, and participate as actively as you can. It is a wonderful conference that is not only inspiring, enlightening, and empowering, it also focuses on student learning and how to help students deeply understand material. And, whether we are pre-service teachers, new teachers, or teachers who have been in the field for years, anything that will assist student learning is something that we can all get behind.<br /><br /><b>About the author: </b>Katie Wanek is a senior at the University of Nebraska at Omaha where she is a double degree student in Math and Education. She has been the Math Club president for the past three years and also works as Dr. Angie Hodge’s undergraduate assistant. Katie will graduate in May 2016 after which she aims to find a position teaching middle school math where she hopes to incorporate active learning into her classroom.Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-42502148858976890712015-07-01T07:33:00.000-07:002015-07-02T05:39:29.161-07:00Knowing What to Do is not Doing<i>A guest post by Bob Klein, Ohio University</i><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-LarPllUQ7Ag/VZPznjk1AqI/AAAAAAAAKW0/llcrdA8sq5I/s1600/Kleinclass.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="212" src="http://1.bp.blogspot.com/-LarPllUQ7Ag/VZPznjk1AqI/AAAAAAAAKW0/llcrdA8sq5I/s320/Kleinclass.jpg" width="320" /></a></div>In Summer 2014, I attended the <a href="http://iblworkshop.org/home.html" target="_blank">Academy of Inquiry-Based Learning Workshop</a> in Portland that took place prior to <a href="http://www.maa.org/meetings/mathfest" target="_blank">MAA MathFest</a>. While I had always come out relatively well in teaching evaluations, I also have been trying to improve my teaching. For the IBL workshop I redesigned my two fall courses (a capstone math content course for secondary education math majors, and a geometry content course for middle school teachers). Later that semester I redesigned my history of mathematics class to follow an <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">inquiry-based learning</a> (IBL) format. Overall, students were more engaged and I was doing far less “delivery” and much more “data collection” and “decision-making.” When students were working at the board or discussing, my role shifted to listening/observing/evaluating so that I could guide discussion. For a while, I’ve adhered to the mantras in my teaching: “Be less helpful” (DM) and “Never Say Anything a Kid Can Say” (SR). But aside from my work in <a href="http://www.mathcircles.org/" target="_blank">math circles</a>, it hasn’t been until this academic year that I’ve been able to realize those in the classroom.<br /><br />A side effect of this is that I both thought MORE of my students’ abilities and LESS of their mastery at the same time. MORE because they showed me that they could embrace a learning environment that put more on them—this was a matter of willingness to adapt/change what took place in the classroom. But also LESS because I had a much more detailed picture of what they knew and what they were able to do at any given point. The content capstone course for secondary math teachers-to-be contained mostly seniors who have completed college geometry, three semesters of calculus, number theory, discrete mathematics, algebra, statistics, and an elective. It may just be this lot, but I’m worried about their abilities as they move forward next year to teaching. Worried especially that we may have promoted them through “the system” of courses without an accurate read on their mastery of the content of those courses. That said, I think I caused those students to be worried about their mastery of content because I asked them to PERFORM that content in rather public ways and subject to peer criticism. This is cause for hope and also a good basis for me to make further refinements to the running of the curriculum.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-EHQxBBLgEC4/VZPzvFvxSzI/AAAAAAAAKW8/wAk63JzPh7I/s1600/Kleinclass2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="186" src="http://3.bp.blogspot.com/-EHQxBBLgEC4/VZPzvFvxSzI/AAAAAAAAKW8/wAk63JzPh7I/s320/Kleinclass2.jpg" width="320" /></a></div>The other course I redesigned for fall was a geometry content course for future middle school teachers. The sophomore level course is significantly different from the capstone course and I think students here were challenged and pushed though in different ways from the capstone course. I was able to push the geometry students to see mathematics itself (as a practice) differently. They began the course trying to convince me that the “(I do)→(we do)→(you do)” formula of exercises (not problems) was what math was all about. By the end of the semester they were asking each other, “How would you defend that?” and digging deeper. I think I probably needed two semesters with them to achieve my stated goals for the course so I might need to be more realistic or more specific about the syllabus goals.<br /><br />History of mathematics was the hardest to redesign for me. The course enrolls mostly middle-level education majors though secondary math education majors and a few STEM majors also enroll. As such, the group has a wide range of backgrounds and it cannot be a course that focuses in large part on proofs (without significant support) though we do cover some demonstrative mathematics. To adopt an IBL approach, I carefully chose a focus area (in this case Egyptian Mathematics) and we spent a long time engaging in problems and discussions centered on Egyptian techniques. We then spent some time working on Mesopotamian, Greek, and European mathematics (as well as other topics). Having a “big focus” for the course (almost an area of expertise for the students) made IBL techniques of problems and board work something that challenged the disparate backgrounds of the students equally and stimulated discussion about the deep ideas behind mathematics, including the assumptions, leanings, and contextual influences thereof.<br /><br />All in all, though, this was very eye-opening for me. As an educational researcher (rather than a research mathematician), I KNEW what I was supposed to be doing, but the IBL workshop and community gave me the support and courage necessary to try it and to stick with it, especially in those first few weeks when I was still in the mode of ‘selling the approach’ to the students. The mass of existence proofs for the model, backed up with the leadership team’s smiles and insistence that this was a flexible set of practices rather than orthodoxy, were especially helpful. <br /><br />One upshot of this work has been my nomination and eventual <a href="http://www.ohio-forum.com/2015/05/klein-makes-math-fun-named-presidential-teacher/" target="_blank">awarding of the Presidential Teacher Award at Ohio University</a>. I was selected as one of only two faculty on my campus to receive the award after a thorough process involving a teaching portfolio, multiple observations of my teaching throughout the year, and interviews by the selection committee of me and my chair. It was truly humbling and nourishes my belief that the IBL approach is making a difference that is visible to students and beyond. I’m eager to engage in further discussions about approaches that worked for others, and welcome others to contact me at the address below.<br /><br /><i>The reflections above are from Bob Klein, PhD, Associate Professor and Undergraduate Chair, Department of Mathematics, Ohio University, Athens, Ohio USA. <a href="mailto:kleinr@ohio.edu">kleinr@ohio.edu</a></i><br /><br /><h4>References</h4>[1] Meyer, Dan. <a href="http://blog.mrmeyer.com/2009/asilomar-4-be-less-helpful/" target="_blank">http://blog.mrmeyer.com/2009/asilomar-4-be-less-helpful/</a>.<br /><br />[2] Reinhart, Steven. (2000). Never Say Anything a Kid Can Say. <i>Mathematics Teaching in the Middle School</i>. Vol 5, No 8, pp. 54-57.<br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-38606460694421866322015-04-09T10:48:00.005-07:002015-04-09T10:48:52.505-07:00Calculating Community: The Running EquationHow does one do something they perceive to be so difficult that they never thought they would even consider doing it? How does one go from being a non-athlete to running 100 miles at elevation? And, how does this have anything to do with mathematics? I challenge you to read this blog post and replace “running” with “mathematics” for most people.<br /><br />In my free time, I run. I run a lot. In fact, my new favorite race to run is the 50-miler, but I have completed three 100-mile events. One of these 100-mile events I completed in under 24 hours.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-1bRL2IW6foM/VSa6QWl9xsI/AAAAAAAAKU4/vXyQmSuWiYQ/s1600/Picture2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-1bRL2IW6foM/VSa6QWl9xsI/AAAAAAAAKU4/vXyQmSuWiYQ/s1600/Picture2.jpg" height="223" width="320" /></a></div>Was I born a runner? No, in fact I was a scrawny girl with chicken legs who would do anything to get out of gym class. Running used to make me cry. It was hard and it hurt. But, I was curious. Why did so many people run and say they loved running? In January 2009, I set out on a mission to find out what this running hype was all about. I trained for my first half marathon (13.1 miles) diligently for 4 months. I followed a training program to the nth degree, ran my race, and found my new hobby. The next day I signed up for a full marathon, 26.2 miles. I again trained and still liked running after completing it. Everyone I talked to told me that after running it I would never want to do another one, but instead I was looking for my next race shortly after I finished my first one. I didn’t want to tell anyone, but I wasn’t all that tired by the end of the race. I was hungry, but not tired. What was going on here?<br /><br />I had thought I hated running because it was difficult, but I did my homework and ended up liking the feeling of success. With each step of the way I thirsted for more, even though others told me it would be “too hard.”<br /><br />For a few years, I was able to fill this thirst with trying to run faster, but then I moved to Omaha. Here is where I found the ultra running community – the Ph.D. program of running.<br /><br />26.2 miles was enough “difficulty” for me for years and I even thought it was insanity to run anything over that distance. Who does that for fun?!?! Not only is an ultra marathon anything over 26.2 miles, but they are often ran on dirt trails following flags on a course that may or may not be well marked. However, they do feed you multiple times along the way and I like food. Think of an aid station as a semester break in grad school. It means you have survived another semester. You get to rest, eat, recover, and forget the pain for a while. Then you go back for more with each leg of the journey providing new challenges and opportunities for growth.<br /><br />How does one survive such madness? My answer to surviving both mathematics classes/programs and ultra running events is one and the same: community. When people are brought together to complete a task that at the time seems impossible, there’s something special that develops. Here are a few tips I have for creating that community that comes with embarking on a hard task.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-5JfDiCHZdck/VSa5nG48ELI/AAAAAAAAKUs/oBBZqGOwGOg/s1600/Picture1.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://2.bp.blogspot.com/-5JfDiCHZdck/VSa5nG48ELI/AAAAAAAAKUs/oBBZqGOwGOg/s1600/Picture1.png" height="270" width="330" /></a></div><strong>The buddy system:</strong> Find people to train/work with who inspire you to do more than you think you can. This does not always mean finding people who are better than you. I would say that this should people of varying abilities. For instance, I have three training partners who come to mind when I think of the types of people who help me go beyond my “limits.” <br /><br />First, there is my friend, Steve Stender. He is fast. He is very fast. He’s also the person I have ran more miles with than anyone I know. By being a friend and getting to know me as a person and as a runner, I value what he has to say. He shows me on a regular basis that I can go faster than I think I can and longer than I think I can with good company. He also has flat out told me to “go out and win something.” This being told to a non-athlete is something I am still not even sure if I believe. However, I have won races now and don’t think I would have even tried without Steve. He would be the friend encouraging you to get an A+ on an exam instead of just passing it.<br /><br />Second, there is my friend, Kim Moore. She is tough as nails. She challenges me to go beyond my comfort zone. Somehow this lady has gotten me to run outside in the cold all winter and to run in the dark. I hate the cold and am scared of the dark. She would be the friend who encourages you to take the hard instructor or the difficult class. These things make us stronger, even though they may be painful at the time.<br /><br />The third “type” of running friend I have is similar to my friend, Eric Schelker. He is someone who I mentor/train. He couldn’t run two miles when we met a year and a half ago, but now he is training for his first marathon. There’s something about helping someone and knowing they are looking up to you that makes you not want to quit. This also helps me want to do well and be a good role model. This would be the friend who you have to “teach” while working together, but in return you then understand the material better.<br /><br /><strong>Regular meetings:</strong> This one is rather simple. Once you have a core group of people to train/work with you, meet regularly. This helps develop friendships and holds you accountable for doing your training/work. Don’t forget to make these meetings fun! Our running group meeting at a local bar on Tuesdays that has 50 cent tacos. We run 3-10 miles and hang out afterwards eating cheap tacos. My calculus classes meet daily before class to finish homework in a casual setting.<br /><br /><strong>Talk to strangers:</strong> Whether there are newcomers in your group or you are seeking out a group, don’t be afraid to make new friends. Everyone feels awkward talking to new people, but you may just meet a life long friend or future colleague by talking to strangers. <br /><br /><strong>Cave into peer pressure:</strong> Before you know it you will be running crazy distances (with these people who were once strangers) or taking crazy hard math classes. Sometimes peer pressure is a good thing!!<br /><br /><strong>Impossible go</strong><strong>al:</strong> Lastly, don’t be afraid to set a seemingly impossible goal for yourself. Break that goal into baby steps and conquer it with the help of your new friends.<br /><br />For more details watch my TEDx talk at: <a href="https://www.youtube.com/watch?v=W6JG9-MWCKA">https://www.youtube.com/watch?v=W6JG9-MWCKA</a>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-37983447505338476432015-01-27T08:20:00.000-08:002015-01-27T12:47:42.041-08:00Setting the StageWhenever I’m teaching via <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">inquiry-based learning</a> (IBL), it is important to get student buy-in. I often refer to this as “marketing IBL”. My typical approach to marketing involves having a dialogue with my students, where I ask them leading questions in the hope that at the end of our discussion the students will have told me that something like IBL is exactly what we should be doing.<br /><br />In the past, I would just wing it on day one and it’s been different every time. However, I’ve had lots of people ask me to describe exactly what I do and I also thought it would be a good exercise for me to sit down and think carefully about the activity. So, in the fall of 2014, I created some slides to guide the activity, which I am now calling "Setting the Stage". Since then I have shortened the activity and made some improvements. The current version of the activity is inspired by <a href="http://theronhitchman.github.io/" target="_blank">TJ Hitchman</a>, <a href="http://www.ma.utexas.edu/users/starbird/" target="_blank">Mike Starbird</a>, and <a href="https://twitter.com/thewordninja_bk" target="_blank">Brian Katz</a>.<br /><br />The main idea is that I want to get students thinking about why we there and what we should really be striving to get out of the course. In addition, it helps students understand why I take an IBL approach in my classes. Below is an outline of the the activity.<br /><br /><h2>Directions to the Students</h2><ul><li>Get in groups of size 3–4.</li><li>Group members should introduce themselves.</li><li>For each of the questions that follow, I will ask you to: <ol><li>Think about a possible answer on your own.</li><li>Discuss your answers with the rest of your group.</li><li>Share a summary of each group’s discussion.</li></ol></li></ul><br /><h2>Questions</h2><ol><li>What are the goals of a university education?</li><li>How does a person learn something new?</li><li>What do you reasonably expect to remember from your courses in 20 years?</li><li>What is the value of making mistakes in the learning process?</li><li>How do we create a safe environment where risk taking is encouraged and productive failure is valued?</li></ol>Each time I’ve run the activity, the responses are slightly different. The responses to the first two questions are usually what you would expect. Question 3 always generates great discussions. The idea of "productive failure" naturally arises when discussing question 4 and I provide them with this language sometime while discussing this question. Listening to the students’ responses to question 4 is awesome. It’s really nice to get the students establishing the necessary culture of the class without me having to tell them what to do.<br />After we are done discussing the 5 questions, I elaborate on the importance of productive failure and inform that I will often tag things in class with the hashtag #pf in an attempt to emphasize its value. I also provide them with the following quote from <a href="http://www.ma.utexas.edu/users/starbird/" target="_blank">Mike Starbird</a>:<br /><blockquote>“Any creative endeavor is built on the ash heap of failure.” </blockquote>I wrap up the activity by conveying some claims I make about education and stating some of my goals as a teacher.<br /><br /><h2>Claims</h2><ul><li>An education must prepare a student to ask and explore questions in contexts that do not yet exist. That is, we need individuals capable of tackling problems they have never encountered and to ask questions no one has yet thought of.</li><li>If we really want students to be independent, inquisitive, & persistent, then we need to provide them with the means to acquire these skills.</li></ul><br /><h2>Lofty Goals</h2><ul><li>Transition students from consumers to producers!</li><li>I want to provide the opportunity for a transformative experience.</li><li>I want to change my students’ lives!</li></ul><br />Below is the Spring 2015 version of the slides that accompany the activity.<br /><br /><div><script async="" class="speakerdeck-embed" data-id="4591c4107e8b013259f02ed1d5d39548" data-ratio="1.33333333333333" src="//speakerdeck.com/assets/embed.js"></script></div><br />You can always find the current version of the LaTeX source at my GitHub repo located <a href="https://github.com/dcernst/MiscTeachingMaterials" target="_blank">here</a>. Note that I’m using the <a href="https://github.com/matze/mtheme" target="_blank">beamer m theme</a> for the slides, which require the <a href="https://github.com/mozilla/Fira" target="_blank">Mozilla Fira fonts</a> by default. Feel fee to steal, modify, and improve. And please let me know if do.<br /><br />Note: This post originally appeared on <a href="http://danaernst.com/setting-the-stage/" target="_new">Dana’s personal blog</a>.<br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-75607605108791096162015-01-08T08:14:00.002-08:002015-01-08T08:14:57.665-08:00The Twin Pillars of IBL<i>By Dana C. Ernst</i><br /><br />As regular readers of this blog know, I am passionate about <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">inquiry-based learning</a> (IBL) and the <a href="http://legacyrlmoore.org/method.html" target="_blank">Moore method</a> for teaching mathematics. This educational paradigm has had a profound impact on my life as a teacher. Actually, scratch that. It has had a profound impact on my life!<br /><br />When I started teaching, I mimicked experiences I had as a student. I tried to emulate my favorite teachers. Because it was all I really knew, I lectured. And this seemed to work out just fine. By standard metrics, I was an excellent teacher. Glowing student and peer evaluations, as well as reoccurring teaching awards, indicated that I was effectively doing my job. However, two observations made me reconsider how well I was really doing. Namely, many of my students seemed to: (i) heavily depend on me to be successful, and (ii) retain only some of what I had taught them. In the words of <a href="http://www.calpoly.edu/~dretsek/" target="_blank">Dylan Retsek</a>:<br /><br /><div style="text-align: center;"><i>"Things my students claim that I taught them masterfully, they don’t know."</i></div><br />Inspired by a desire to address these concerns, I began transitioning away from direct-instruction towards a more student-centered approach. The goals and philosophy behind IBL resonate deeply with my ideals, which is why I have embraced this paradigm.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-2G2hlLr7LRY/VK2YZdnSrAI/AAAAAAAAKSw/dWtOrt_4roM/s1600/037.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-2G2hlLr7LRY/VK2YZdnSrAI/AAAAAAAAKSw/dWtOrt_4roM/s1600/037.JPG" height="240" width="320" /></a></div>While there is variation in practice, IBL courses typically provide students with experiences that differ from traditional lecture-based courses. In many mathematics classrooms, doing mathematics means following the rules dictated by the teacher and knowing mathematics means remembering and applying these rules. However, an IBL approach challenges students to create/discover mathematics. According to the <a href="http://www.inquirybasedlearning.org/" target="_blank">Academy of Inquiry-Based Learning</a>, IBL is a method of teaching that engages students in sense-making activities. Students are given tasks requiring them to conjecture, experiment, explore, and solve problems. Rather than showing facts or a clear, smooth path to a solution, the instructor guides students via well-crafted problems through an adventure in mathematical discovery.<br /><br />I believe that there are two essential elements to IBL. First, students should (as much as possible) be responsible for guiding the acquisition of knowledge, including the pace at which this happens, and second, they should be responsible for validating the ideas presented. That is, students should not be looking to the instructor as the sole authority. In most IBL courses, student-led presentations and small group work form the backbone of the course. In general, the majority of class time is spent on these types of student-centered activities, which provide ample opportunity to discuss and critique ideas that arise from a group problem or student-presented solution.<br /><br />One guiding principle of IBL is the following question:<br /><br /><div style="text-align: center;"><i>Where do I draw the line between content I must impart to my students versus the content they can produce independently? </i></div><br />While instructors might give a mini-lecture to introduce or summarize the day's work, the instructor's main role is not lecturing, but rather to foster a safe environment, facilitate discussion, and redirect as necessary. In an IBL course, instructor and students have joint responsibility for the depth and progress of the course.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-dS7rH4asTFQ/VK2YoEL0xiI/AAAAAAAAKS4/MzO8zQwdgRQ/s1600/0241_ernst_math_class_11052013.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-dS7rH4asTFQ/VK2YoEL0xiI/AAAAAAAAKS4/MzO8zQwdgRQ/s1600/0241_ernst_math_class_11052013.jpg" height="320" style="cursor: move;" width="213" /></a></div>A <a href="http://www.colorado.edu/eer/research/steminquiry.html" target="_blank">research group</a> from the University of Colorado Boulder lead by <a href="http://www.colorado.edu/eer/people/" target="_blank">Sandra Laursen</a> has conducted a comprehensive study of student outcomes in IBL undergraduate mathematics courses while linking these outcomes to students’ and instructors’ experiences of IBL. This quasi-experimental, longitudinal study examined over 100 courses at four different campuses over a period that spanned two years. The courses examined self-identified as IBL versus non-IBL. Classroom observation was used to verify that IBL classes were indeed different from those designated as non-IBL sections of the same course. The following is a list of characteristics that the IBL sections shared:<br /><br /><ul><li>Students solve challenging problems alone or in groups; share solutions; analyze, critique & refine their solutions </li><li>Class time is used for these student-centered activities </li><li>Students play a leadership role </li><li>Activities change often </li><li>Course is driven by a carefully built sequence of problems or proofs, rather than a textbook</li><li>Pace is set by students' progress through this sequence </li><li>Course goals usually emphasize thinking skills & communication; content “coverage” is less central </li><li>Instructor serves as "guide on the side" not "sage on the stage"—manager, monitor, summarizer, cheerleader </li></ul><br />On average over 60% of IBL class time was spent on student-centered activities including student-led presentations, discussion, and small-group work. In contrast, in non-IBL courses, 87% of class time was devoted to students' listening to an instructor talk. In addition, the IBL sections were rated more highly for a supportive classroom environment and students conveyed that engaging in meaningful mathematical tasks while collaborating was as essential to their learning.<br /><br />Below is a brief summary of some of the outcomes of Laursen et al.'s work:<br /><br /><ul><li>After an IBL or comparative course, IBL students reported higher learning gains than their non-IBL peers, across cognitive, affective, and collaborative domains of learning. </li><li>IBL students’ attitudes and beliefs changed pre- to post-course in ways that are known to be more supportive of learning, compared to students who took the non-IBL sections. </li><li>In later courses, students who had taken an IBL course earned grades as good or better than those of students who took non-IBL sections, despite having "covered" less material. </li><li>On a research-based test of students' ability to evaluate proofs, IBL students showed evidence of greater skill in recognizing valid and invalid arguments and of the use of more expert-like reasoning in making such evaluations. The volunteer sample consisted of only high-ability students; no instructors gave the test to all students during class time. </li><li>Non-IBL courses show a marked gender gap: across the board, women reported lower learning gains and less supportive attitudes than did men (effect size 0.4-0.5). Women’s confidence and sense of mastery of mathematics, and their interest in continued study of math, was lower. This difference appears to be primarily affective, not due to real differences in women’s mathematical preparation or achievement. </li><li>This gender gap was erased in IBL classes: women’s learning gains were equal to men’s, and their confidence and intent to persist similar. IBL approaches leveled the playing field for women, fixing a course that is problematic for women yet with no harm to men. </li><li>When sorted by prior achievement, the grades of most students (IBL and non-IBL alike) dropped in subsequent courses as course work became more difficult. But grades of initially low-achieving students who had taken the IBL course rose 0.3-0.4 grade points, unlike their low-achieving, non-IBL peers, and unlike their higher-achieving classmates. </li></ul><br />This work determined that there are two "twin pillars" of IBL that may explain the student outcomes, namely (i) deep engagement in rich mathematics and (ii) opportunities to collaborate. Here, deep engagement refers to individual and group effort in tackling meaningful problem-solving tasks that are not merely "busy work." Collaboration is a key component as students learn from explaining their ideas and trying to understand others. According to Laursen et al.:<br /><br /><div style="text-align: center;"><i>"The twin pillars reinforced each other: after struggling with a problem individually, students were well prepared to contribute meaningfully during class, and interested in the solutions that others proposed. Collaboration in turn motivated them to complete the individual work. It also made class enjoyable, encouraged clear thinking, and built communication skills."</i></div><br />IBL is not a magic bullet, but the experiences that I have had watching students transform into independent learners is why I am so passionate about it. I want students to have life-changing experiences! Learning the content of mathematics is just a bonus.<br /><br />One of my principal goals is to make my students independent of me. I want them to experience the unmistakable feeling that comes when one really understands something thoroughly. In the words of <a href="http://www2.kenyon.edu/Depts/Math/schumacherc/public_html/Professional/Research/Zero/guide.pdf" target="_blank">Carol Schumacher</a>:<br /><br /><div style="text-align: center;"><i>"When one can distinguish between really knowing something and merely knowing about something, that individual will be on his/her way to becoming an independent learner."</i></div><br />I’m not terribly picky about the particular flavor of IBL or active learning one chooses to employ, but it is becoming increasingly clear to me that if we want to produce life-long independent learners, then the twin pillars need to form the foundation for the pedagogical approach we choose to take.<br /><br /><b>References</b><br /><br />[1] Laursen, S. L., Hassi, M.-L., Kogan, M., & Weston, T. J. (2014). <a href="http://www.nctm.org/publications/article.aspx?id=42527" target="_blank">Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution study</a>. <i>Journal of Research in Mathematics Education</i>, 45(4), 406-418.<br /><br />[2] Kogan, M., & Laursen, S. L. (2014). <a href="http://link.springer.com/article/10.1007/s10755-013-9269-9" target="_blank">Assessing long-term effects of inquiry-based learning: A case study from college mathematics</a>. <i> Innovative Higher Education</i>, 39(3), 183-199. DOI 10.1007/s10755-013-9269-9.<br /><br />[3] Laursen, S. L. (2013). From innovation to implementation: Multi-institution pedagogical reform in undergraduate mathematics. In D. King, B. Loch, L. Rylands (Eds.), <i>Proceedings of the 9th DELTA conference on the teaching and learning of undergraduate mathematics and statistics</i>, Kiama, New South Wales, Australia, 24-29 November 2013. Sydney: University of Western Sydney, School of Computing, Engineering and Mathematics, on behalf of the International Delta Steering Committee.<br /><br /><div style="text-align: left;">[4] Assessment & Evaluation Center for Inquiry-Based Learning in Mathematics (2011). <i><a href="http://www.colorado.edu/eer/research/documents/IBLmathReportALL_050211.pdf" target="_blank">Evaluation of the IBL Mathematics Project: Student and Instructor Outcomes of Inquiry-Based Learning in College Mathematics</a></i>. (Report to the Educational Advancement Foundation and the IBL Mathematics Centers) Boulder, CO: University of Colorado, Ethnography & Evaluation Research.</div><br />Further resources can be found <a href="http://www.colorado.edu/eer/research/steminquiry.html" target="_blank">here</a>.<br /><br />Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-55427651651012030892014-11-06T06:18:00.000-08:002014-11-06T13:52:47.713-08:00Math Teachers’ Circles: What Makes a Good One?<i>by Angie Hodge</i><br /><i><br /></i> <br /><div class="MsoNormal"><a href="http://www.mathteacherscircle.org/" target="_blank">Math Teachers’ Circles</a> (MTCs) bring together middle school math teachers and professional mathematicians to enrich the teachers’ experience of mathematical problem solving and to build mathematical community. Free math club-like events, MTCs give teachers the chance to have fun doing math three or four times per semester.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><a href="http://www.mathteacherscircle.org/about/our-mission/" target="_blank">MTCs strive</a> to:<o:p></o:p></div><div class="MsoNormal"></div><ol><li>increase the confidence of middle school math teachers in their problem-solving ability;</li><li>deepen teachers’ content knowledge through exploring mathematically rich problems and developing an arsenal of techniques for solving unfamiliar and challenging problems;</li><li>form long-term professional relationships between teachers and mathematicians through regular, highly interactive meetings; and</li><li>provide support for teachers who want to bring richer mathematical experiences to their students.</li></ol><div class="separator" style="clear: both; text-align: center;"></div><div class="MsoNormal">Teams interested in starting a Math Teachers’ Circle in their area should contact AIM at <a href="mailto:circles@aimath.org" target="_blank">circles@aimath.org</a>. Six teams of four or five teachers attended workshops on <a href="http://www.mathteacherscircle.org/upcoming-workshops/start-a-circle/" target="_blank">How to Run a Math Teachers’ Circle</a><span class="MsoHyperlink"> in 2014</span>. At the 2014 workshop in Washington, D.C., the teams were asked to answer two questions:</div><ol><li>What makes a good Math Teachers’ Circle session? </li><li>What makes a good Math Teachers’ Circle problem?</li></ol><div class="MsoNormal">Workshoppers were asked to brainstorm with a focus on "quantity versus quality," and they came up with quite a list. Just perusing it gives even someone unfamiliar with MTCs a pretty good idea of what they’re all about:</div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><b>What makes a good Math Teachers' Circle session?</b></div><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="MsoNormal">Snack break<o:p></o:p></div><div class="MsoNormal">Good snacks<o:p></o:p></div><div class="MsoNormal">Engaging problems<o:p></o:p></div><div class="MsoNormal">Aha! Moment<o:p></o:p></div><div class="MsoNormal">Leader ready to scaffold/backfill/support<o:p></o:p></div><div class="MsoNormal">Leader ready to give next challenge<o:p></o:p></div><div class="MsoNormal">Focus on math<o:p></o:p></div><div class="MsoNormal">Out of comfort zone<o:p></o:p></div><div class="MsoNormal">All participants feel comfortable with math and other participants<o:p></o:p></div><div class="MsoNormal">Safe environment for failure<o:p></o:p></div><div class="MsoNormal">Discussion and collaboration<o:p></o:p></div><div class="MsoNormal">Entertaining/enjoyable<o:p></o:p></div><div class="MsoNormal">Buy-in for participants<o:p></o:p></div><div class="MsoNormal">Community<o:p></o:p></div><div class="MsoNormal">Group of common professionals<o:p></o:p></div><div class="MsoNormal">Relaxed, non-threatening atmosphere<o:p></o:p></div><div class="MsoNormal">Classroom connections without focus on classroom<o:p></o:p></div><div class="MsoNormal">Interesting presentation of problems<o:p></o:p></div><div class="MsoNormal">All levels of mathematics<o:p></o:p></div><div class="MsoNormal">Overplanning<o:p></o:p></div><div class="MsoNormal">All participants are involved<o:p></o:p></div><div class="MsoNormal">Generate enthusiasm<o:p></o:p></div><div class="MsoNormal">Participants explain and present<o:p></o:p></div><div class="MsoNormal">Variety of participant backgrounds</div>Pacing good <table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-aEjpS1FnXBo/VFpvhb522uI/AAAAAAAAKKU/_-Iqikl0mXg/s1600/14690049463_eed8fedf85_z.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-aEjpS1FnXBo/VFpvhb522uI/AAAAAAAAKKU/_-Iqikl0mXg/s1600/14690049463_eed8fedf85_z.jpg" width="350" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Participants in the workshop in Washington, D.C. (photo Hana Silverstein)</i></td></tr></tbody></table><o:p></o:p> <div class="MsoNormal">Memorable<o:p></o:p></div><div class="MsoNormal">Wine<o:p></o:p></div><div class="MsoNormal">No whine<o:p></o:p></div><div class="MsoNormal">Different presenter personalities<o:p></o:p></div><div class="MsoNormal">Appropriate amount of room<o:p></o:p></div><div class="MsoNormal">Good number of participants<o:p></o:p></div><div class="MsoNormal">Humor/laughter<o:p></o:p></div><div class="MsoNormal">Make friends<o:p></o:p></div><div class="MsoNormal">Noncompetitive<o:p></o:p></div><div class="MsoNormal">Supportive<o:p></o:p></div><div class="MsoNormal">Multiple strategies<o:p></o:p></div><div class="MsoNormal">Include failure<o:p></o:p></div><div class="MsoNormal">Hook<o:p></o:p></div><div class="MsoNormal">Not lecture-y</div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal">Celebrate discovery<o:p></o:p></div><div class="MsoNormal">Good flow<o:p></o:p></div><div class="MsoNormal">Participants sharing discoveries<o:p></o:p></div><div class="MsoNormal">End loving/wanting more<o:p></o:p><br />SWAG (Sell your MTC by advertising it!)</div><div class="MsoNormal">Climate of respect<o:p></o:p></div><div class="MsoNormal">Knowledgeable leaders<o:p></o:p></div><div class="MsoNormal">Focus<o:p></o:p></div><div class="MsoNormal">Critiquing mathematics/solutions (safe for people)<o:p></o:p></div><div class="MsoNormal">Providing resources to learn more<o:p></o:p></div><div class="MsoNormal">Inter-workshop closure, info, etc.<o:p></o:p></div><div class="MsoNormal">Leader's love of math is transmitted<o:p></o:p></div><div class="MsoNormal">Plenty of time<o:p></o:p></div><div class="MsoNormal">Time flies<o:p></o:p></div><div class="MsoNormal">T-shirts<o:p></o:p></div><div class="MsoNormal">Time to explore<o:p></o:p></div><div class="MsoNormal">Time to fail before seeing solution<o:p></o:p></div><div class="MsoNormal">Good entry/exit<o:p></o:p></div><div class="MsoNormal">Freedom to digress/follow tangents/not too fixed a goal<o:p></o:p></div><div class="MsoNormal">Individualized closure<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><b>What makes a good Math Teachers' Circle problem?</b></div><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="MsoNormal">Hands on<o:p></o:p></div><div class="MsoNormal">Engaging<o:p></o:p></div><div class="MsoNormal">Knobbifiable (problems can be made harder or easier)<o:p></o:p></div><div class="MsoNormal">Low-level entry<o:p></o:p></div><div class="MsoNormal">Multisensory/multimodal<o:p></o:p></div><div class="MsoNormal">Mystery<o:p></o:p></div><div class="MsoNormal">Leads to more questions<o:p></o:p></div><div class="MsoNormal">Out of the box<o:p></o:p></div><div class="MsoNormal">Initially simple<o:p></o:p></div><div class="MsoNormal">Folkloric<o:p></o:p></div><div class="MsoNormal">Variety of strategy and/or tactics<o:p></o:p></div><div class="MsoNormal">Minimal lecture<o:p></o:p></div><div class="MsoNormal">Lets participants get to board<o:p></o:p></div><div class="MsoNormal">Novelty to participants<o:p></o:p></div><div class="MsoNormal">Not textbook<o:p></o:p></div><div class="MsoNormal">Good lead-in<o:p></o:p></div><div class="MsoNormal">More than an hour to solve<o:p></o:p></div><div class="MsoNormal">Interesting to different groups<o:p></o:p></div><div class="MsoNormal">Some element of fun<o:p></o:p></div><div class="MsoNormal">Joy of math<o:p></o:p></div><div class="MsoNormal">Physical/"crafty" <table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-O2bweZEN9XE/VFpvpCfQ1RI/AAAAAAAAKKc/M9xVAmA_il4/s1600/14493359457_99fd94b429_z.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-O2bweZEN9XE/VFpvpCfQ1RI/AAAAAAAAKKc/M9xVAmA_il4/s1600/14493359457_99fd94b429_z.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>The list in its original form (photo Hana Silverstein)</i></td></tr></tbody></table><o:p></o:p></div><div class="MsoNormal">Abstract/thoughtful<o:p></o:p></div><div class="MsoNormal">Has a hook<o:p></o:p></div><div class="MsoNormal">Clear parameters<o:p></o:p></div><div class="MsoNormal">Real world<o:p></o:p></div><div class="MsoNormal">Not too intimidating<o:p></o:p></div><div class="MsoNormal">Challenging<o:p></o:p></div><div class="MsoNormal">Easy to generate data<o:p></o:p></div><div class="MsoNormal">Strategies embedded<o:p></o:p></div><div class="MsoNormal">Associated with a lesson<o:p></o:p></div><div class="MsoNormal">Moral to the story<o:p></o:p></div><div class="MsoNormal">Cognitive dissonance<o:p></o:p></div><div class="MsoNormal">Surprise<o:p></o:p></div><div class="MsoNormal">Some closure<o:p></o:p></div><div class="MsoNormal">Some open endedness<o:p></o:p></div><div class="MsoNormal">Group or individual<o:p></o:p></div><div class="MsoNormal">Multilayered problems<o:p></o:p></div><div class="MsoNormal">Opportunities for discussion<o:p></o:p></div><div class="MsoNormal">Little intro prep/setup<o:p></o:p></div><div class="MsoNormal">Patterns<o:p></o:p></div><div class="MsoNormal">Connections within mathematics<o:p></o:p></div><div class="MsoNormal">Multiple pathways<o:p></o:p></div><div class="MsoNormal">Gives participants something to bring home<o:p></o:p></div><div class="MsoNormal">Reasoning/argumentation<o:p></o:p></div><div class="MsoNormal">Memorable problems<o:p></o:p></div><div class="MsoNormal">Spatial<o:p></o:p></div><div class="MsoNormal">Games<o:p></o:p></div><div class="MsoNormal">Intro fun<o:p></o:p></div><div class="MsoNormal">Not too much tedium<o:p></o:p></div><div class="MsoNormal">Aha! moment<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div class="MsoNormal">For the MTC veterans out there, do the items on the lists above square with your experience of what makes a good Math Teachers’ Circle? <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Note: This exercise was given as a way to create closure for the How to Run a Math Teachers’ Circle workshop. Participants had been working problems in MTC sessions all week and this gave them a chance to reflect on the experience. I think this exercise of thinking about good problems and a good class session could also be used in other mathematics courses. Imagine your own classes generating lists about what makes a good student, a good teacher, a good exam, a good problem set, etc. The possibilities are endless! Happy list generating!!! <o:p></o:p></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-45381589815317262322014-09-12T07:29:00.000-07:002014-09-12T07:33:23.221-07:00A First-timer’s Experience with IBL<em>a guest post by Ellie Kennedy</em><br /><em></em><em><br /></em>Prior to the spring of 2013, I taught my discrete mathematics course via a traditional lecture style. I used to bore myself with those lectures. Counting principles seemed like a topic that students could develop on their own with maybe just a little problem-solving help. With induction I felt like I was lecturing and showing the students the same examples over and over and it wasn't sinking in. I needed to try something new and fresh, and <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">inquiry-based learning (IBL)</a> seemed like a method that might work for me. So, last spring when I taught discrete math, I used a modified <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">Moore method</a>. I'd like to share my experience as a first-timer and some of what I learned.<br /><br /><a href="http://www.math.lamar.edu/faculty/mahavier/mahavier.aspx" target="_blank">Ted Mahavier</a> started me off with a set of notes, and <a href="http://danaernst.com/" target="_blank">Dana Ernst</a> helped me sort out the logistics of the course. I was so thankful to have such great resources. Students would read definitions and theorems in the note packet and work on problems at home and then present the problems in class. In a traditional Moore method classroom, students are not allowed to collaborate, but I encouraged students to work together.<br /><br />The counting and graph theory parts of Ted's notes were fantastic, but I did modify them a bit to fit the topics taught in our course. Ted's notes focused on strong induction and our course has a weak induction focus. This was not a difficult change to make to the notes. Ted's notes did not have anything on recursion, so I wrote an entire section myself. I was surprised how challenging it is to write IBL notes! I found it hard to build questions leading to the main idea when, to me, the main idea was an algorithm to solve recurrence relations. It made me realize how much I personally rely on knowing how and why an algorithm works but not the history of how it was developed in the first place. Very eye-opening for me.<br /><br />I used the <a href="http://danaernst.com/felt-tip-pens/" target="_blank">felt tip pen idea</a> that Dana has written about, and it was a true success. While in class with other students presenting, the students would use only felt tip pens to mark up the work they had done at home. This allowed them to produce a solution set of sorts, and it made my grading super easy. I did not grade for correctness. I graded only on the math they produced at home (non-felt tip pen work). This method also allowed students to constantly <a href="http://files.eric.ed.gov/fulltext/EJ815370.pdf" target="_blank">self-assess, which can be an effective learning tool</a>. The students felt it was easier to do homework when they didn't have to worry about getting it right at that very moment. They found they could just concentrate on the math that way.<br /><br />I tried to make the class a comfortable place where students could make mistakes freely and without embarrassment. I made a list of "dos" and "don'ts" so the students were aware of some positive ways of pointing out that they thought someone was wrong. The first time a student did a problem wrong, I made a big deal out of it (in a positive way). I thanked the student for having the guts to put up something that was wrong. Then the class discussed what parts were correct and I had the students work on the problem for another night and we came back to it the next day. I always pointed out the learning experience that came from each mistake that was made. A student commented in my end-of-semester evaluations that I "showed respect for the students and encouraged [the students] to fail early and often (this is a good thing)." Mission accomplished!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-DepNej-H5vc/VBL3TP3rO3I/AAAAAAAAKEo/dh7SmQ7mfxA/s1600/6918107833_dbc1e04e85_b.jpg" imageanchor="1" style="clear: left; float: left; margin-right: .5em;"><img border="0" src="http://3.bp.blogspot.com/-DepNej-H5vc/VBL3TP3rO3I/AAAAAAAAKEo/dh7SmQ7mfxA/s1600/6918107833_dbc1e04e85_b.jpg" height="214" width="320" /></a></div>One of my students struggled to switch to this new learning environment all semester. It is an adjustment for most students, but he never quite got it. During an exam review I realized he was always trying to jump to the end result without any thought of how to get there. I suggested that he write down a list of steps for each type of problem. "Like a map," he said. This comment made me realize an analogy that helped me understand what my students were going through.<br /><br /> In a traditional lecture-style course we start with a city and then tell the students what road to take to get the next town. We expect them to repeat the same route we just showed them. Yet in an IBL class we give the students the cities and states and then tell them to find their own roads and build their own map. Creating our own paths makes it much easier to remember how to get there the next time.<br /><br />The number one thing that I learned from this new experience (other than that IBL is amazing and really does contribute to deeper student understanding) is that it is important to understand that being confused is not just okay but a really good feeling to embrace in mathematics.<br /><br />When I first started going through Ted's notes, I found problems where I didn't understand the question. I realized that this was purposeful, intended to promote conversation. Confusion leads to questions, and it is in those questions that true understanding and learning occurs.<br /><br />This current technological age pushes us to find the answer FAST. Even I am guilty of just "Googling it." It is challenging for students to work on a problem or question for an extended period of time. They don't understand that some questions go unanswered for centuries and that is normal for us mathematicians to keep trying. I feel that as educators we need to let our students know that as long as they get the important parts before the exam, it is okay (and fun) to be confused and search for an answer for decades or years. Let's encourage the struggle and show our students that struggling in math is really exciting! Hopefully students can realize the incredibly rewarding feeling of solving something after much thought and time! Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-46611238598076098702014-08-01T05:30:00.000-07:002014-08-01T05:34:08.485-07:00Teaching Math to Non-Math Teachers<div><i>by Angie Hodge</i></div><div><br /></div>I know how to sell freshman calculus students on math and, in particular, on math taught using inquiry-based learning (IBL). Undergraduate math majors also buy into IBL pretty easily. They like math no matter how it is taught.<br /><br />The same cannot be said of my students this summer. I've taught graduate courses to secondary mathematics teachers before, and my summer students were teachers, too. They were mostly elementary teachers, though, elementary teachers who had enrolled in a two-year master’s program focused on learning middle school math deeply. They recognized weakness in their mathematical preparation and wanted to learn math better for the benefit of their students.<br /><div><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-sz4dVGF36Zk/U8U-KhobhJI/AAAAAAAAJ5Y/hSJcK6qwM6w/s1600/M2C2June30CervantesHopper.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-sz4dVGF36Zk/U8U-KhobhJI/AAAAAAAAJ5Y/hSJcK6qwM6w/s1600/M2C2June30CervantesHopper.jpg" height="275" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: left;"><i>photo credit Lindsay Augustyn</i></td></tr></tbody></table>This is very brave of these teachers. To recognize that you are not the best at something is one thing, but to face that fear head on and enter into a master’s program focusing entirely on your fear takes courage. <br /><br />I spent five days (8 a.m.-5 p.m.) in the last couple of weeks with 29 teachers who were taking their first math course in a math master’s program for teachers. During these five days, I witnessed the teachers undergo amazing transformations in both attitude toward math and knowledge of it. And I learned a lot, too.<br /><br />Here are some reflections on the lessons learned over the five-day period. The course was taught in partnership with two middle school math teachers, one elementary school teacher, and two grading assistants. When I say "we" or "the instructional team" that is who I am referring to.<br /><br /><b>Day 1: Be firm and friendly</b><br />We all tried to be firm, but friendly on Day 1. Setting the tone for an entire master's program is a big task, and our instructional team didn't take this lightly. We spent lots of time discussing the importance of working together, having a positive attitude, knowing the importance of productive failure, taking chances, thinking outside the box, and learning to communicate in a mathematically correct manner. We dug right into the mathematics and the mathematical habits of mind. On Day 1, the teachers were "good students," but they were still very timid. They made lots of negative comments about math and moaned when asked to justify the "whys" rather than just memorizing rules. Despite the moans, we kept pushing: friendly but firm. <br /><br /><b>Day 2: Persevere (pep talks are a must!)</b><br />"Ugh" is all I have to say about the first hour of this day! Imagine being swarmed as you walk into your classroom by 15-20 upset people, all of them near tears. "Tough it out," I told myself. "Things will get better for you as an instructor if you persevere as you want the teachers to persevere." </div><div><br />Teachers wanted to quit. Teachers were really not happy about math or the amount of time it took to think about the homework problems. They did not understand why an answer wasn’t good enough and why they had to "show us" their thinking process.<br /><br />For all the tears and griping we somehow pulled together and even bonded as a team/class on Day 2. How? There was a lot of pep talking. We talked about productive failure. We talked about the importance of struggling. We cheered for progress. We gave praise for positive attitudes. We rallied and threw energy around like it was going out of style. <br /><br /><b>Day 3: The calm before the storm</b><br />Day 3 was one of our best days and one of the days when we saw the teachers grow the most. Teachers who were barely talking earlier were taking risks to present (but only if they knew they were correct) and were talking more to the instructional team and to their group members. Although it worried us (the instructional team) that some groups weren't talking as much as we had hoped, some were working really well. We debated switching up the groups and decided to try it for Day 4. We didn’t have to do much on Day 3 other than teach and continue to compliment progress, positive attitudes, and good work ethic.<br /><br /><b>Day 4: Beware of your first "hit" of hard material</b><br />We switched up the groups. Maybe not the best idea on the hardest day of class. Fractions!!! Need I say more? :) Wow. At the end of this day I truly wanted to cry. Our evaluations were lower than usual (still pretty decent, but we all strive for perfection). The teachers were frustrated. We were frustrated. How could we use this as a teachable moment to help them persevere? <br /><br /><b>Day 5: Make every moment a teachable moment</b><br />We started Day 5 as we started every day, talking about the evaluations. We discussed evaluations daily to make sure the teachers knew that we heard their voices. We commented on why we were or were not changing things based upon the feedback they gave us. We used negative comments about confusion as a teachable moment. We talked about what it meant to be confused and how it was part of the learning process. We also discussed the importance of speaking up if you are confused or stuck. We stressed the team aspect of the course again and emphasized that even though it was hard we were here to learn together. Since these were teachers, we were able to do this in an IBL manner, asking the teachers how they would respond to students who were confused but did not tell them this until after the fact. This discussion set the stage for a new tone. No matter how clear you think you are with your expectations and no matter how approachable you think you are, you need to remember that your students come pre-programmed to try to get the correct answer quickly. "Unprogramming" this takes time. Be a broken record about this and praise your students when they finally believe you!<br /><br />Boom! (as Dana Ernst would say) On Day 5 I saw remarkable growth in nearly every single teacher. They made it over many mental hurdles and they realized they made it. Somehow making it past that tough hurdle on Day 4, they had become a team. We let the teachers sit anywhere they wanted to on Day 5. Some sat with their original groups and some paired up with new people they met from switching. Some sat in pairs, some sat in triples. Honestly, I didn’t care how big the groups were. What was important was that everyone had found someone whose learning style complemented his or her own. The day could not have gone better. The teachers did some really tough problems really well (even showing multiple solution paths). They were even asking each other to "prove it" and asking why things worked. Teachers wanted to know when they would get to see the team again. Right then it was clear that the connections made were ones that would extend beyond the one course.<br /><br />Somehow, 29 individual teachers (and the instructional team) went from strangers to a team in five days. We all problem solved together and bonded—IBL Style. Boom.</div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-4283040502077396462014-07-11T08:52:00.000-07:002014-07-11T08:54:25.604-07:00Service-Learning and Making a Difference<i>a guest post by <a href="http://www.math-cs.gordon.edu/~kcrisman/" target="_blank">Karl-Dieter Crisman</a></i><br /><i><br /></i> <br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-MhWl3OYYwP8/U7_Xa5-cl2I/AAAAAAAAJ44/pM52dN6uoFc/s1600/AGH3Math-1060777.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-MhWl3OYYwP8/U7_Xa5-cl2I/AAAAAAAAJ44/pM52dN6uoFc/s1600/AGH3Math-1060777.jpg" width="350" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Crisman at the 17th Annual Legacy of R. L. Moore—Inquiry-Based </i><br /><i>Learning Conference (photo Kirk Tuck/EAF)</i></td></tr></tbody></table>When I teach a new course, or return to a course after a number of years, one of the most exciting parts is to start with that clean slate. What new text can I choose? Is there a topic I can create my own materials for, to "do it right"? Is there some unifying project I can use to help give my students a broader vision of what the course really is about?<br /><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Over the past few decades, in many disciplines the answer to that last question has been to incorporate a service-learning component of some kind. At some institutions, this is even being mandated in various ways. And the words sound nice: <i>Service</i> seems useful, and we certainly want <i>learning</i>. But what is service-learning, and what does it have to do with math?<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">At its core, service-learning involves students participating in some useful service to the community, but in such a way that the service is <i>itself</i> a learning experience directly related to the content of the course. As an example, having students volunteer at a food bank would be service, and having them write a research paper about distribution of government and private largesse would be learning; students working at the food bank and then incorporating that experience as part of a research paper on the topic would be service-learning.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">In addition to "feeling right" for many instructors, there is a growing research literature about benefits of service-learning in a wide range of disciplines. However, many readers of this blog will probably echo Charles Hadlock, the editor of the <a href="http://www.maa.org/publications/maa-reviews/mathematics-in-service-to-the-community" target="_blank">MAA's book on this subject</a>: "Unfortunately, the mathematical sciences are sometimes perceived as having a more difficult task to incorporate service activities in the curriculum." Campus Compact, a major clearinghouse, has only two syllabi for math on its <a href="http://www.compact.org/category/syllabi/math/" target="_blank" title="Campus Compact website">website</a>. In one survey of attitudes<span class="MsoFootnoteReference"><!--[if !supportFootnotes]--><span class="MsoFootnoteReference"><span style="font-family: "Cambria","serif"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;">[*]</span></span><!--[endif]--></span>, an anonymous math professor says, "I can think of no service projects in the community that will enhance student learning of the abstract reasoning skills they should be learning in mathematics."<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">It is true that there is not the same body of plug-in activities as there may be in many other disciplines, and a paucity of resources, published online or in print. But in fact there are many such activities, appropriate for a wide variety of courses. A representative recent sampling I am personally acquainted with includes:<o:p></o:p></div><div class="MsoNormal"><br /><ul><li>Analyzing energy use and sustainability practices on campus (quantitative reasoning)</li><li>Assessing volunteer versus state-provided aid in a local fire (intro statistics)</li><li>Helping local American Diabetes Association focus fundraising (finite math)</li><li>Tutoring high school precalculus students (calculus)</li><li>Creating math fun fair games (upper-level math and math ed)</li><li>Designing a new layout for a food pantry (upper-level modeling)</li><li>Providing feedback on cash flow for a local non-profit (upper-level modeling)</li><li>Analyzing (scrubbed) freshman orientation data (upper-level math/stats)</li><li>Running a math camp for middle-schoolers (graduate students)</li></ul><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-n6lN1qBE54Q/U7_9kiF2xJI/AAAAAAAAJ5I/X27ubmTE2ho/s1600/aprilschoolvacationweek2012+019.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-n6lN1qBE54Q/U7_9kiF2xJI/AAAAAAAAJ5I/X27ubmTE2ho/s1600/aprilschoolvacationweek2012+019.jpg" width="355" /></a></td></tr><tr><td class="tr-caption"><div style="text-align: center;"><i>A math game event is service; what are your ideas for turning this </i><br /><i><i>into service-learning?</i></i></div><i></i></td></tr></tbody></table>If any of these ideas intrigue you or get you thinking about your own ideas, there are several great resources to examine. I would personally recommend Hadlock's MAA book, which gathers many more wonderful ideas together, and the <a href="http://www.tandfonline.com/toc/upri20/23/6" target="_blank">recent special issue of <i>PRIMUS</i></a> on the topic (disclosure: I am a co-editor). I have gathered presentations from a contributed paper session at the Joint Meetings as well on a <a href="http://www.math-cs.gordon.edu/~kcrisman/SLTalks/" target="_blank">very minimalist website</a>, and other journals in statistics, math ed, and service have related articles on occasion.</div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">There are caveats, of course. First, it is unwise to attempt a project without some administrative support. Hopefully your campus has an office of community engagement or something similar to help find a community partner, and to assist in interacting with them, setting realistic goals, and so forth. Similarly, you will want to know that you have at least tacit approval to try this from your own department, at least as a pilot—especially if it is required of all students in a given course. It helped a lot for me to have both forms of support at <a href="http://www.gordon.edu/" target="_blank">Gordon College</a> from the start. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Third, read case studies and guides. From writing syllabi to managing students to meaningful evaluation, it is well worth planning things out carefully first. That said, I can't think of any example where the first offering went so smoothly that it didn't require mid-course correction, so the potential mentor will need to be open to last-minute changes.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Finally, as one may note from the list of sample projects, there is a big need for more tested ideas, particularly in proof-based courses (think abstract algebra), or those where directly using techniques for modeling for partners would not be appropriate for beginners (like an intro differential equations course). If you have an idea, do not be shy! Try it out, and then write about it for some venue (an article in <a href="http://digital.ipcprintservices.com/publication/?i=27730&p=18" target="_blank">the December 2009/January 2010 issue of <i>MAA FOCUS</i></a> was an inspiration to me).<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I'd like to thank Dana and Angie for giving me this opportunity. Math ed does matter to those in the university context, and it's about so much more than targeted pedagogical strategies; the values we express in teaching do come home to roost in our students, in more ways than we can realize. And this can make a difference not only in the lives of those served, but also in many deep ways in the lives of our students.</div><div><!--[if !supportFootnotes]--><br clear="all" /><hr align="left" size="1" width="33%" /><!--[endif]--> <br /><div id="ftn1"><div class="MsoFootnoteText"><span class="MsoFootnoteReference"><!--[if !supportFootnotes]--><span class="MsoFootnoteReference"><span style="font-family: "Cambria","serif"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "MS Mincho"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;">[*]</span></span><!--[endif]--></span>See the first article in <a href="http://ginsberg.umich.edu/mjcsl/content/volume-09-2002" target="_blank">volume 9 (2002)</a>of the <i>Michigan Journal for Community Service Learning</i>.<o:p></o:p></div></div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-33035489543541079542014-06-23T10:55:00.000-07:002014-06-23T10:55:24.406-07:00Fear is the mind-killer<i>by Dana Ernst</i><br /><br /><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"></div></div>My favorite conference of the year, the <a href="http://legacyrlmoore.org/events.html">Legacy of R. L. Moore — IBL Conference</a>, kicked off last Thursday. The day began for me with an introduction to IBL mini-workshop facilitated by <a href="http://www.ma.utexas.edu/users/starbird/">Michael Starbird</a>. For our first activity, Starbird had the participants discuss in small groups the following question.<br /><div style="text-align: center;"><br /><i>What do you want your students to keep from their education?</i><br /><i><br /></i><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-_m5UwuQW9MM/U6hfWFlwMMI/AAAAAAAAJ1c/BPJw3__QcfY/s1600/IMG_0425.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-_m5UwuQW9MM/U6hfWFlwMMI/AAAAAAAAJ1c/BPJw3__QcfY/s1600/IMG_0425.JPG" height="245" width="400" /></a></div><br /></div>After a few minutes of brainstorming, groups shared their ideas. Here’s the list we generated (I’m paraphrasing):<br /><ul><li>Love of learning</li><li>Persistence/perseverance</li><li>Ability to teach yourself</li><li>Ability to communicate verbally and in writing</li><li>Independence</li><li>Self-awareness</li><li>Self-direction</li><li>Ability to collaborate</li><li>Curiosity</li><li>Confidence</li><li>Receptivity to different perspectives</li><li>Appreciation of failure</li><li>Lack of fear</li></ul>Do you notice anything interesting about the items on this list? None of them has anything to do with mathematics! Moreover, as one participant keenly observed, one of the major obstacles to most of the items on the list is related to the final item: namely, fear. <br /><br />Upon hearing this, I was immediately reminded of a quote from one of my favorite sci-fi books, <i>Dune</i>.<br /><br /><div style="text-align: center;"><i>Fear is the mind-killer.</i></div><br />This line is part of the <a href="http://en.wikipedia.org/wiki/Bene_Gesserit#Litany_against_fear">litany against fear</a>, which is an incantation used throughout Frank Herbert’s Dune universe by the Bene Gesserit to focus their minds and calm themselves in times of peril. Here is the full litany:<br /><br /><div style="margin-left: 1em;"><i>I must not fear.<br />Fear is the mind-killer.<br />Fear is the little-death that brings total obliteration.<br />I will face my fear.<br />I will permit it to pass over me and through me.<br />And when it has gone past I will turn the inner eye to see its path.<br />Where the fear has gone there will be nothing.<br />Only I will remain.</i></div><br />I believe (and there is <a href="http://www.colorado.edu/eer/research/steminquiry.html">plenty of evidence</a> to support this) that <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html">inquiry-based learning</a> (IBL) provides an optimal framework for students to develop the skills on the list above. Yet, it stands to reason that this method will expose our students’ weaknesses in these areas. Some manifestation of fear is often an obstruction to individuals addressing their weaknesses. As instructors, how can we help students minimize the fear that blocks their development? <br /><br />It might be time for me to add the litany against fear to my syllabi.Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com4tag:blogger.com,1999:blog-5816649486576881540.post-19101461021307305682014-05-22T05:15:00.000-07:002014-05-22T05:15:51.432-07:00Hooking the Student<i>a guest post by Jeff Rushall</i><br /><i><br /></i><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-PgHpfFB_TyY/U30GsxF1oLI/AAAAAAAAJrw/okVfGEtxsFU/s1600/pic1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-PgHpfFB_TyY/U30GsxF1oLI/AAAAAAAAJrw/okVfGEtxsFU/s1600/pic1.png" height="240" /></a></div><div class="MsoNormal">Six years ago, I told my chair that our <a href="http://nau.edu/cefns/natsci/math/" target="_blank">Department of Mathematics and Statistics</a> here at <a href="http://nau.edu/" target="_blank">Northern Arizona University</a> needed something new to inspire our majors. I suggested a “Brown Bag Seminar,” structured much like what many of us encountered while in college: a one-hour lunchtime colloquium targeting undergraduates. I chose several topics that I felt would “hook” students, including <a href="http://en.wikipedia.org/wiki/Cantor_set" target="_blank">Cantor sets</a>, <a href="http://en.wikipedia.org/wiki/Magic_square" target="_blank">magic squares</a>, and <a href="http://en.wikipedia.org/wiki/Latin_square" target="_blank">Latin squares</a>. The brown bag seminars began in the fall of 2008, with expectations—at least on my part—very high. The rooms, times, and topics were set. The advertising flyers were posted. I was convinced that the combination of my wit and charm together with some sexy mathematical content would be a huge hit. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I was very wrong. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">The audiences were small; after an opening crowd of 18, the attendance numbers slowly dwindled to single digits by the end of that fall semester. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Down but not out, and still convinced that the basic idea was a good one, I went straight to the main source of my inspiration: my students. I sat down with three of my favorite students (to protect the innocent, I’ll call them Kathryn, Charlie, and Natalie) and picked their brains about how to organize my vision (in retrospect, this was the best idea I’d had in years!). These and other students made the following suggestions: <o:p></o:p></div><div class="MsoNormal"><br /></div><ul style="margin-top: 0in;" type="disc"><li class="MsoNormal">Hold the seminar on a Friday afternoon. </li></ul><ul style="margin-top: 0in;" type="disc"><li class="MsoNormal">Give the gathering a snappier name. </li></ul><ul style="margin-top: 0in;" type="disc"><li class="MsoNormal">Limit the talks to about 30 minutes. </li></ul><ul style="margin-top: 0in;" type="disc"><li class="MsoNormal">Expose the audience to more than just math to entice their attendance, such as…</li></ul><ul style="margin-top: 0in;" type="disc"><li class="MsoNormal">Interview a faculty member each week. </li></ul><div class="MsoNormal">We retooled, and in January of 2009, <a href="http://oak.ucc.nau.edu/jws8/FAMUSflyer.pdf" target="_blank">FAMUS</a> (the Friday Afternoon Mathematics Undergraduate Seminar) was born. Today, 11 semesters later, FAMUS is thriving. Our weekly gathering hosts an average of 35 audience members, and although several faculty and graduate students attend each week, the majority of attendees are undergraduates. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Selecting talk topics for FAMUS is without question the easiest aspect of organizing and running FAMUS. The proper balance of talks on mathematics (ranging from the <a href="http://en.wikipedia.org/wiki/Tower_of_Hanoi" target="_blank">Tower of Hanoi</a> to <a href="http://en.wikipedia.org/wiki/Euler_brick" target="_blank">Euler bricks</a> to the <a href="http://en.wikipedia.org/wiki/St._Petersburg_paradox" target="_blank">St. Petersburg paradox</a>), on mathematicians (<a href="http://en.wikipedia.org/wiki/David_Hilbert" target="_blank">Hilbert</a>, <a href="http://en.wikipedia.org/wiki/Srinivasa_Ramanujan" target="_blank">Ramanujan</a>, <a href="http://en.wikipedia.org/wiki/Paul_Erd%C5%91s" target="_blank">Erdös</a>, to name but three), on mathematics education (flipped classrooms, the mathematics “common core” of Ireland, etc.) and various math-themed topics (AP Calculus exams, summer projects/trips/activities of our faculty, international teaching opportunities in mathematics) seems to keep things fresh. And nearly all FAMUS talks end with open questions, designed to encourage students to ponder the possibility of beginning some sort of undergraduate research or independent study project. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-vEa88W2lL1M/U30G4tkExmI/AAAAAAAAJr4/IDmqc0vf0Co/s1600/pic2.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://2.bp.blogspot.com/-vEa88W2lL1M/U30G4tkExmI/AAAAAAAAJr4/IDmqc0vf0Co/s1600/pic2.png" height="340" /></a></div><div class="MsoNormal">But for many students, the highlight of FAMUS is the weekly interview of a faculty member. Structured à la the interviews on the popular <i><a href="http://en.wikipedia.org/wiki/Inside_the_Actors_Studio" target="_blank">Inside the Actors Studio</a></i> series on the Bravo Network, the list of 16 questions remains the same each week. These questions and responses paint a broad portrait of the guest faculty member, and this is followed by a closing open-question-and-answer session that can last up to 30 minutes. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">During the last 5.5 years, FAMUS audiences have ranged from a low of 15 (a dreadful weather day) to 71 (a former NAU graduate student and current research fellow at Harvard was the guest speaker). The 133 FAMUS gatherings have been evenly split: one third featured undergraduate presenters, one third have been given by fellow faculty and graduate student talks, and one third have been my own talks. </div><div class="MsoNormal"><br /></div><div class="MsoNormal">FAMUS does take time: planning and setting up the semester schedule, acquiring appropriate snacks (coffee and cookies are for our departmental faculty seminars; we serve popcorn, chocolate, and student-friendly beverages like Mountain Dew), and promoting and advertising has its share of twists. And yes, preparing appropriate and entertaining talks is not a quick process. But the results speak for themselves. Of course, injecting some humor into FAMUS talks helps. For instance, our recent semester-ending FAMUS featured a slide containing just some of the cartoon images that have appeared in past presentations (can you spot the picture of one of the usual authors of this blog?). <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-vVyOatP3rbE/U30HAgt1BaI/AAAAAAAAJsA/EaSBcrPJpi8/s1600/pic3.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-vVyOatP3rbE/U30HAgt1BaI/AAAAAAAAJsA/EaSBcrPJpi8/s1600/pic3.png" height="320" width="258" /></a></div><div class="MsoNormal">Have we hooked students? Yes. Do all of our majors attend FAMUS? Not remotely! But students who regularly show up at FAMUS each Friday generally refer to FAMUS as their favorite part of the week. In fact, regular attendees at FAMUS help to advertise, set up, clean up, and they do so happily, even late on a Friday afternoon. And FAMUS is influencing our student population: We are attracting current math majors at our weekly gathering, while at the same time enticing prospective math majors and minors, and promoting undergraduate research, all while simultaneously advertising careers in mathematics, most notably opportunities to attend graduate school in mathematics, statistics, and mathematics education. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Kathryn, Charlie, and Natalie helped us start something special here in our department in the spring of 2009. Notably, none of these three students were mathematics majors when they began their undergraduate careers at NAU, but FAMUS worked its magic on each of them, as they all graduated with undergraduate degrees in mathematics. All three chose to pursue graduate careers in mathematics, and all are at various stages of Ph.D. programs at rather different locations (Kathryn at <a href="http://www.brynmawr.edu/" target="_blank">Bryn Mawr</a>, Charlie at the <a href="http://umt.edu/" target="_blank">University of Montana</a>, and Natalie at the <a href="http://colorado.edu/" target="_blank">University of Colorado at Boulder</a>). <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I cannot say that every department needs something like FAMUS, and I do not claim that what we have created is something that can be duplicated in a like manner at other institutions. But I can say that FAMUS has become engrained in our department culture. Perhaps most importantly, FAMUS has provided our students with something that they perhaps didn’t even know that they wanted or needed: an activity that helps to foster a sense of community among our undergraduate majors, and a place to become exposed to the cool kind of math that hooked many of us as we began our own march towards careers in mathematics. </div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-39302228145438803902014-05-05T15:03:00.000-07:002014-05-08T05:51:46.300-07:00Love Math?<div class="Body1"><span style="font-family: inherit;"><i>by Angie Hodge</i></span></div><div class="Body1"><span style="font-family: inherit;"><br /></span></div><div class="Body1"><span style="font-family: inherit;">This year Mathematics Awareness Month made me realize how in love I am with math. I became a teacher because I loved to teach, but recently I discovered I am equally in love with </span><i style="font-family: inherit;">math</i><span style="font-family: inherit;">.</span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">How do we as mathematicians and mathematics educators help others to discover this passion (and in a timely manner, so that students take more mathematics courses)?<o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">I will be the first to admit that Mathematics Awareness Month has never had a lot of meaning to me until this year. So what was so different about this time around? Well, this year I said yes to something (and often more than one something) math-related each week in April. The funny thing is I didn't even realize I had done this until about halfway through the month.<o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">Each event could be a blog post in and of itself, but here are the highlights. Feel free to provide feedback on which events you would like to hear more about in future blogs. We love suggestions!<o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-JZ6dWL1xmss/U2t9dltufcI/AAAAAAAAJpk/a_lzILpf_Nw/s1600/image+(5).jpeg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-JZ6dWL1xmss/U2t9dltufcI/AAAAAAAAJpk/a_lzILpf_Nw/s1600/image+(5).jpeg" height="239" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; color: #222222; font-family: arial, sans-serif; text-align: start;"><i>Dr. Betty Love leading a "Meet the Professor" series <br />talk on operations research.</i></span></td></tr></tbody></table><span style="font-family: inherit;">At the <a href="http://www.unomaha.edu/" target="_blank">University of Nebraska Omaha</a> (UNO), we kicked off Mathematics Awareness Month by getting to know one of our math professors, <a href="http://www.unomaha.edu/math/people/love/" target="_blank">Dr. Betty Love</a>, through a "<a href="http://www.unomaha.edu/math/colloquia.php" target="_blank">Meet Your Professor</a>" talk. Students got to learn about a UNO math professor both professionally and personally. <o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">The <a href="http://www.unomaha.edu/math/index.php" target="_blank">UNO mathematics department</a> also hosted two speakers, <a href="https://www.math.ohiou.edu/people/directory/rklein" target="_blank">Dr. Bob Klein</a> and <a href="http://www.vmi.edu/content.aspx?id=4294974313" target="_blank">Dr. Randy Cone</a>. They each gave a "<a href="http://www.unomaha.edu/math/colloquia.php" target="_blank">Cool Math Talk</a>" for students and a "<a href="http://www.mathteacherscircle.org/" target="_blank">Math Teachers' Circle</a>" session for local math teachers. All of these sessions both actively engaged and challenged the audiences. <o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">I also spent four days at the <a href="http://www.nctm.org/neworleans/" target="_blank">National Council of Teachers of Mathematics national conference</a>. The week was filled with ideas to bring into the classroom for both university students and K-12 students. I held a gallery workshop on "<a href="http://nctm.confex.com/nctm/2014AM/webprogram/Session25204.html" target="_blank">Hands-on, Minds-on Calculus</a>." In this workshop, teachers had a chance to try both unguided and guided activities that I do with my own calculus students. This included a game where they worked in groups to match differential equations to slope fields. <o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">Mathematics Awareness Month for me was capped off with a five-day visit to the <a href="http://www.colorado.edu/math/" target="_blank">University of Colorado at Boulder</a> to discuss ways to engage students in the learning of calculus. <o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">Wow, that was a lot of extra-curricular math for one month. Instead of being exhausted from it, though, I was surprisingly re-energized! <o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">This made me think back to my calculus students. For each of our guest speakers at UNO, I had several students who went to both talks (even the one for practicing teachers). For Dr. Klein’s talk, many of the students had spent an hour in the math help room before class, over an hour in class, an hour in Dr. Klein's "Cool Math Talk," and two hours at the Math Teachers' Circle. Then it hit me. They love math. They may not know it yet, but who spends that much time doing anything unless they enjoy it? It also hit me that, you know what? I, too, love math! <o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">There are a few questions that come to mind when I think about this. What was it that held my students attention through so many hours of math events? What was it that made me want to set up and attend these math events? What can we do to help others "fall in love" with math? Here's one thought I had (and I look forward to hearing yours).</span></div><div class="Body1"><span style="font-family: inherit;"><br /></span></div><div class="Body1"><span style="font-family: inherit;">What did all of these events have in common? They all involved the audience. Dr. Love used mathematical humor and real life applications to keep the audience members engaged. Dr. Klein was on his toes modifying his sessions to fit his audience. Dr. Cone got the audience engaged in an IBL style competition to lead into each new portion of his talk. <o:p></o:p></span></div><div class="Body1"><br /></div><div class="Body1"><span style="font-family: inherit;">So, what do you do to help others discover a passion for math?</span></div><div class="Body1"><span style="font-family: inherit;"><br /></span></div><div class="Body1"><span style="font-family: inherit;">Share your favorite story or technique with us! </span><span style="font-family: Cambria, serif;"><o:p></o:p></span></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-16091424402374967502014-04-01T08:05:00.000-07:002014-04-01T08:06:46.049-07:00Encouraging Students to Tinker<i>by Dana Ernst</i><br /><br />A few days ago I was in my office working on a research problem related to the combinatorics of <a href="http://en.wikipedia.org/wiki/Coxeter_group" target="_blank">Coxeter groups</a>. I’ve been thinking about this problem off and on for a few years and haven’t made any real progress in quite some time. The last time I worked on the problem, I was feeling pretty discouraged. On this particular day, however, I was just enjoying the process and feeling blessed that part of my career includes hunting for and occasionally discovering new mathematics. Someone actually pays me to put my head in the clouds and do mathematics.<br /><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">It had been a while since I worked on the problem, so I started by reviewing all the things I had tried previously. I thought, “now what?” I couldn’t think of anything new to try that I thought had any chance of actually working. At this point, I was reminded of a recent post by <a href="http://www.moebiusnoodles.com/" target="_blank"><i>Moebius Noodles</i></a>, titled "<a href="http://www.moebiusnoodles.com/2014/03/make-mistakes-on-purpose/" target="_blank">Make Mistakes on Purpose</a>," that contains a wonderful quote by the author <a href="http://en.wikipedia.org/wiki/Neil_Gaiman" target="_blank">Neil Gaiman</a>.</div><blockquote class="tr_bq"><i>Make interesting mistakes, make amazing mistakes, make glorious and fantastic mistakes.</i></blockquote><div class="MsoNormal">This quote comes at the very end of Gaiman’s excellent keynote address from the 2012 commencement at the <a href="http://www.uarts.edu/" target="_blank">University of the Arts</a> in Philadelphia. (I’ve included the whole address below.)<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">So, I set myself the task I trying to come up with clever mistakes. I intentionally followed what I expected to be dead ends. An hour later, I had several new insights. I still haven’t cracked the problem, but for the first time in a while I felt like I had made some headway.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">This experience reminded me of something I’ve been pondering for a while in regards to teaching. How do we encourage students to tinker with mathematics? As a culture, it seems we are afraid of making mistakes. This seems especially bad when it comes to how most students approach mathematics. But making and then reflecting on mistakes is a huge part of learning. Just think about learning to walk or riding a bike. Babies are brave enough to take a first step even though they have no idea what will happen. My kids fell down a lot while learning to walk. But they kept trying. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I want my students to approach mathematics in the same way. Try stuff, see what happens, and if necessary, try again. But many of them resist tinkering. Too many students have been programmed to think that all problems are solvable, that there is exactly one way to approach each problem, and that if they can’t solve a problem in five minutes or less, they must be doing something wrong. But these are myths, and we must find ways to remove the misconceptions. The first step is to encourage risk taking.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">A few months ago, Stan Yoshinobu addressed this topic over on <a href="http://theiblblog.blogspot.com/" target="_blank"><i>The IBL Blog</i></a> in a post titled "<a href="http://theiblblog.blogspot.com/2014/01/destigmatizing-mistakes.html" target="_blank">Destigmatizing Mistakes</a>." I encourage you to read his whole post, but here is a highlight:</div><blockquote class="tr_bq"><i>Productive mistakes and experimentation are necessary ingredients of curiosity and creativity. A person cannot develop dispositions to seek new ideas and create new ways of thinking without being willing to make mistakes and experiment. Instructors can provide frequent, engaging in-class activities that dispel negative connotations of mistakes, and simultaneously elevate them to their rightful place as a necessary component in the process of learning.</i></blockquote><div class="MsoNormal">Here are a few related questions I have:</div><div class="MsoNormal"></div><ul><li><span style="text-indent: -0.25in;">How do we encourage students to tinker with mathematics?</span></li><li><span style="font-family: Symbol; text-indent: -0.25in;"><span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><span style="text-indent: -0.25in;">How do we destigmatize mistakes in the mathematics classroom?</span></li><li><span style="text-indent: -0.25in;">How do we encourage and/or reward risk taking?</span></li><li><span style="text-indent: -0.25in;">What are the obstacles to addressing the items above and how do we remove these obstacles?</span></li></ul><br /><div class="MsoNormal">I have some ideas about how to tackle these issues, but I’m curious what ideas you might have. I’m hoping for a fruitful dialogue in the comments. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Here is Gaiman’s keynote address in its entirety. Trust me, it’s worth 20 minutes of your time.<o:p></o:p><br /><div style="text-align: center;"><br /></div></div><div style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/ikAb-NYkseI" width="420"></iframe></div><div class="MsoNormal"><br /></div><div class="MsoNormal">You can find the transcript for his speech <a href="http://www.uarts.edu/neil-gaiman-keynote-address-2012" target="_blank">here</a>.</div><div><div><div class="msocomtxt" id="_com_1" language="JavaScript"><!--[if !supportAnnotations]--></div><!--[endif]--></div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com8tag:blogger.com,1999:blog-5816649486576881540.post-18478958643445770202014-02-20T08:44:00.000-08:002014-02-20T08:44:59.436-08:00Engaging in Inquiry-Based Learning<div class="MsoNormal"><i>by Dana Ernst, Angie Hodge, and TJ Hitchman</i></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Do you like teaching? Do you like learning about teaching? Is STEMath teaching your specialty? Do you want new ideas to engage students in your classrooms? Do you ever wonder how you can make outreach activities more hands-on? <o:p></o:p></div><br /><div class="MsoNormal"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-GzI7AfqGiAo/UwYDUY06k0I/AAAAAAAAJYA/LugfG7tgpy8/s1600/5842400867_b4a33edbde_n.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-GzI7AfqGiAo/UwYDUY06k0I/AAAAAAAAJYA/LugfG7tgpy8/s1600/5842400867_b4a33edbde_n.jpg" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>It was all smiles at the 14th Legacy of R. L. Moore <br />Conference in 2011.</i></td></tr></tbody></table>Well, wonder no more. This year’s <a href="http://legacyrlmoore.org/events.html" target="_blank">Legacy of R. L. Moore and Inquiry-Based Learning Conference</a> promises to be your dream destination summer “math-cation.” As the name suggests, the Moore Conference is devoted to inquiry-based learning (IBL), as well as the bequest of <a href="http://en.wikipedia.org/wiki/Robert_Lee_Moore" target="_blank">R. L. Moore</a>, for whom the <a href="http://legacyrlmoore.org/method.html" target="_blank">Moore Method</a>is named. The <a href="http://eduadvance.org/" target="_blank">Educational Advancement Foundation</a>, the <a href="http://www.maa.org/" target="_blank">Mathematical Association of America</a>, and the <a href="http://www.inquirybasedlearning.org/" target="_blank">Academy of Inquiry-Based Learning</a>generously subsidize the conference. If you are unfamiliar with IBL, check out our previous post, "<a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">What the Heck is IBL?</a>" In general, the IBL community is an energetic group of mathematicians and mathematics educators who are passionate about the ways that students can actively explore and discover mathematics.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">This year’s conference theme is “Engaging in Inquiry-Based Learning,” and it promises to be one of the most interactive conferences to date. The theme was chosen to encourage people to share their IBL ideas with others in an active manner. Everyone at the conference will get to experience IBL while learning about IBL. Pretty cool! <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Whether one is new to IBL or has been trying IBL for years, there will be something for everyone at the conference. The excellent folks from the <a href="http://www.artofmathematics.org/" target="_blank">Discovering the Art of Mathematics</a> project will kick off the conference with an engaging demonstration of IBL that will be educational to all IBL’ers. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Looking to take your IBL practice to the next level? Bill McKenna will host a grant writing workshop prior to the conference kickoff to help you learn to support your IBL ideas. The best part is that the cost is included in the conference fee. All you have to do is register! <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Help us create the rest of the conference by submitting your abstracts for the parallel sessions. We have several categories to fit your needs and a general IBL session if you think your talk isn’t like the others. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><a href="http://legacyrlmoore.org/Reports/201406/call_papers.html" target="_blank"><span style="font-size: 16.0pt;">Call for Papers</span></a><span style="font-size: 16.0pt;"><o:p></o:p></span></div><div class="MsoNormal">The theme is intended to encourage abstracts and proposals that focus on ACTIVE participation of attendees during the parallel sessions. We are interested in sessions about any aspect of IBL, but especially encourage submissions to the following special sessions:<o:p></o:p></div><br /><ul><li><b>My Favorite IBL Activity:</b> Share your favorite IBL activity or group of activities with the participants.</li><li><b>IBL Outreach:</b> Share how you use IBL in outreach activities such as Math Teachers’ Circles, Math Student Circles, math clubs, and math camps. </li><li><b>IBL Professional Development:</b> Share how you educate others in the preK-16 educational community about IBL. </li><li><b>Nuts & Bolts:</b> Share your most successful (or not so successful) approaches to engaging students, grading, assessment, and marketing in an IBL classroom. </li><li><b>General IBL:</b> Share other engaging IBL topics that do not fit into any of the above sessions.</li></ul><div class="MsoNormal"><br /></div><div class="MsoNormal">Sessions will be a bit longer than in the past to account for the focus on active participation. Specifically, sessions will be 30 minutes in duration (25 minutes for presentation and 5 minutes reserved for questions). <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">To submit a proposal for a talk or workshop session, send the following information to Angie Hodge (<a href="file:///C:/Users/kmerow/Desktop/amhodge@unomaha.edu">amhodge@unomaha.edu</a>), TJ Hitchman (<a href="mailto:theron.hitchman@uni.edu">theron.hitchman@uni.edu</a>), and Norma Flores (<a href="mailto:nflores@edu-adv-foundation.org">nflores@edu-adv-foundation.org</a>) with the subject line “Legacy 2014 Abstract Submission.”<o:p></o:p></div><div class="MsoNormal"><br /></div><div align="center"><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;"> <tbody><tr style="height: 135.65pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;"> <td style="border: solid windowtext 1.0pt; height: 135.65pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 293.5pt;" valign="top" width="391"><div class="MsoNormal">Name:<o:p></o:p></div><div class="MsoNormal">Affiliation:<o:p></o:p></div><div class="MsoNormal">Title of talk or presentation:<o:p></o:p></div><div class="MsoNormal">Abstract (200 words or less): <o:p></o:p></div><div class="MsoNormal">Email:<o:p></o:p></div><div class="MsoNormal">Preferred Session:<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Description of how the proposed session will be active or engaging for the participants (50 words or less):<o:p></o:p></div></td> </tr></tbody></table></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><a href="http://legacyrlmoore.org/events" target="_blank">Registration</a>is also open and is very affordable! When else can you get registration, most meals, AND hotel for under $200? What a steal!!! <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">The 17<sup>th</sup> Annual Legacy of R. L. Moore and Inquiry-Based Learning Conference takes place on June 19-21, 2014 at the Sheraton Downtown in Denver, CO. Come learn and share about IBL!</div><div><div><div class="msocomtxt" id="_com_1" language="JavaScript"><!--[if !supportAnnotations]--></div><!--[endif]--></div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-72577061267369577952014-01-10T06:00:00.000-08:002014-01-10T06:00:00.053-08:00Math Ed Mania at the JMM<i>by Dana Ernst and Angie Hodge</i><br /><br /><a href="http://www.flickr.com/photos/maaorg/8366922088/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" title="2013 JMM Exhibit Hall Opening by Mathematical Association of America, on Flickr"><img alt="2013 JMM Exhibit Hall Opening" src="http://farm9.staticflickr.com/8088/8366922088_18a4596a54_n.jpg" height="204" width="320" /></a>In our <a href="http://maamathedmatters.blogspot.com/2013/12/the-jmm-whats-mathematics-education-got.html" target="_blank">previous post</a>, we highlighted numerous talks and events with an <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">inquiry-based learning</a> theme that will be taking place at the upcoming <a href="http://jointmathematicsmeetings.org/jmm" target="_blank">Joint Mathematics Meetings</a> in Baltimore.<br /><br />However, there are lots of mathematics education-focused sessions that we didn’t mention. Of course, you can browse the <a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program.html" target="_blank">JMM Program</a>, but this can be overwhelming since there are so many awesome things going on. In this short post, we thought we would share a few items from the program that caught our eye.<br /><br />Nearly all of the <a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_maacp.html" target="_blank">MAA Contributed Paper Sessions</a> are math education flavored and it seems like there are going to be some fantastic sessions. The one we are the most excited about is “Flipping the Classroom,” which has a whopping four parts.<br /><div><br /></div><div><b>Flipping the Classroom</b><br /><div class="MsoListParagraphCxSpFirst"></div><ul><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_friday.html#2160:MCPMAXE1" target="_blank">Part I</a>: Friday January 17, 2014, 8:00 a.m.-10:55 a.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_friday.html#2160:MCPMAXE2" target="_blank">Part II</a>: Friday January 17, 2014, 1:00 p.m.-5:55 p.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_saturday.html#2160:MCPMAXE3" target="_blank">Part III</a>: Saturday January 18, 2014, 8:00 a.m.-10:55 a.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_saturday.html#2160:MCPMAXE4" target="_blank">Part IV</a>: Saturday January 18, 2014, 1:00 p.m.-2:35 p.m.</li></ul><br />Inverted pedagogy (i.e., flipping) has been a hot topic the past few years and we are interested in learning more about its benefits and pitfalls. It’s also a topic we hope to discuss in future <i>Math Ed Matters</i> posts. <a href="http://faculty.gvsu.edu/talbertr/Robert_Talbert,_PhD/Welcome.html" target="_blank">Robert Talbert</a> has been an evangelist for both inverted pedagogy and peer instruction and has agreed to give four talks at the JMM! Robert is a great speaker and we encourage you to check out at least one of his talks.<br /><ul><li><a href="http://jointmathematicsmeetings.org/amsmtgs/2160_abstracts/1096-e1-1597.pdf" target="_blank">"A different type of math": Addressing student difficulties with proof by flipping the transition-to-proof course</a></li><li><a href="http://jointmathematicsmeetings.org/amsmtgs/2160_abstracts/1096-f1-1579.pdf" target="_blank">Peer instruction in linear algebra</a></li><li><a href="http://jointmathematicsmeetings.org/amsmtgs/2160_abstracts/1096-l1-1566.pdf" target="_blank">Inverting the transition-to-proof course</a></li><li><a href="http://jointmathematicsmeetings.org/amsmtgs/2160_abstracts/1096-m5-1584.pdf" target="_blank">Technology as a tool for self-regulated learning in an inverted calculus class</a></li></ul><br />No matter what approach one may take to teaching, assessment is something that all teachers are concerned—and likely struggle—with. Thankfully, there are two sessions devoted entirely to this topic.<br /><br /><b>Assessing Student Learning: Alternative Approaches</b><br /><ul><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_wednesday.html#2160:MCPBUTB5" target="_blank">Part I</a>: Wednesday January 15, 2014, 8:00 a.m.-10:55 a.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_wednesday.html#2160:MCPBUTB6" target="_blank">Part II</a>: Wednesday January 15, 2014, 2:15 p.m.-5:50 p.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_thursday.html#2160:MCPBUTB7" target="_blank">Part III</a>: Thursday January 16, 2014, 8:00 a.m.-11:55 a.m.</li></ul><b><br /></b><b>Assessment of Proof Writing Throughout the Mathematics Major</b><br /><ul><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_thursday.html#2160:MCPCOOC1" target="_blank">One Session</a>: Thursday January 16, 2014, 8:00 a.m.-9:15 a.m.</li></ul><br />Two courses that are “hot topics” in their design and pedagogy at the moment are “Introduction to Proofs” and “Linear Algebra.” If you are teaching one of these courses in the near future, you will want to check out one of these sessions.<br /><br /><b>Bridging the Gap: Designing an Introduction to Proofs Course</b><br /><ul><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_thursday.html#2160:MCPMABD1" target="_blank">One Session</a>: Thursday January 16, 2014, 7:40 a.m.-11:55 a.m.</li></ul><b></b><br /><b>Innovative and Effective Ways to Teach Linear Algebra</b><br /><ul><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_friday.html#2160:MCPSTRF1" target="_blank">Part I</a>: Friday January 17, 2014, 8:00 a.m.-10:55 a.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_friday.html#2160:MCPSTRF2" target="_blank">Part II</a>: Friday January 17, 2014, 1:00 p.m.-2:55 p.m.</li></ul><div class="MsoNormal"><br />The AMS also has three sessions on mathematics education that grabbed our attention. Learn about general math education, the Common Core, and even math outreach. With many departments wanting to help the community, the two-part session on outreach sounds very timely! <o:p></o:p></div><br /><b>AMS Session on Mathematics Education</b><br /><ul><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_thursday.html#2160:AMSCP18" target="_blank">One Session</a>: Thursday January 16, 2014, 1:00 p.m.-3:55 p.m.</li></ul><div><br /></div><b>AMS Special Session on The Changing Education of Preservice Teachers in Light of the Common Core </b><br /><ul><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_ss52.html#title" target="_blank">Part I</a>: Wednesday January 15, 2014, 8:00 a.m.-10:50 a.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_ss52.html#title" target="_blank">Part II</a>: Wednesday January 15, 2014, 2:15 p.m.-6:05 p.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_ss52.html#title" target="_blank">Part III</a>: Thursday January 16, 2014, 8:00 a.m.-11:50 a.m</li></ul><div><br /></div><b>AMS Special Session on Outreach for Mathematically Talented Youth</b><br /><ul><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_ss45.html#title" target="_blank">Part I</a>: Friday January 17, 2014, 1:00 p.m.-5:50 p.m.</li><li><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program_ss45.html#title" target="_blank">Part II</a>: Saturday January 18, 2014, 8:00 a.m.-10:50 a.m.</li></ul><div><br /></div>We hope to see y’all at the JMM!!! If you see us, please stop and chat. <br /><br />What sessions are you looking forward to attending?<br /><div><div><div class="msocomtxt" id="_com_2" language="JavaScript"><!--[if !supportAnnotations]--></div><!--[endif]--></div></div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com1tag:blogger.com,1999:blog-5816649486576881540.post-68777731046234926042014-01-06T10:21:00.000-08:002014-01-06T10:21:21.842-08:00What's So Good about IBL Anyway?<i>a guest post by <a href="http://math.mit.edu/wim/about/sr.html" target="_blank">Susan Ruff</a></i><br /><i><br /></i> <br /><div class="MsoNormal">I recently came across a striking article: “<a href="http://www.tandfonline.com/doi/abs/10.1207/s15326985ep4102_1#.UnzpIvnkslJ">Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching</a>.” This title is followed by an equally provocative abstract: “…Although unguided or minimally guided instructional approaches are very popular and intuitively appealing,…these approaches ignore…evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process…” And the paper ends with more than two solid pages of supporting literature.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">In the body of the paper, Kirschner et al. make many good points, which appear to be well supported by research and theory; for example, that <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">IBL</a> and similar pedagogies may be too challenging for the <i>weakest</i> students, that students benefit from scaffolding and other guidance, and that performance on tests doesn’t necessarily improve as a result of IBL. But the paper seems to be primarily a straw man argument: It makes valid points, but these points do not support the claim that IBL is a “failure.” Those of us who teach with IBL know from experience that it has real benefits that are not measured by test scores, and that test scores improve in some cases.<br /><br />Thus, I take the paper as a challenge to those of us who see value in inquiry-based learning to more clearly articulate that value and the factors that contribute to it, so research can be designed to tease out the beneficial aspects of IBL. This paper prompted me to do a quick search of the literature to see what is known about the benefits of IBL. Not surprisingly, it’s complicated. <br /><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><div class="MsoNormal">One of the challenges with past research is articulated well by both <a href="http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2923.2000.00749.x/abstract" target="_blank">Norman & Schmidt (2000)</a> and <a href="http://onlinelibrary.wiley.com/doi/10.1002/j.2168-9830.2004.tb00809.x/abstract" target="_blank">Prince (2004)</a>: The many different forms of IBL are characterized by various variables, such as the amount and type of guidance, whether work is student directed and/or student paced, the percent of class time that is student led, and even the <a href="http://maamathedmatters.blogspot.com/2013/07/personality-matters.html" target="_blank">personality of the instructor</a>. These variables have different, possibly negative, and likely interacting, effects on student learning, so lumping all of the variables together under the single name “IBL” naturally gives muddy research results. To obtain more meaningful results, Norman & Schmidt call for multivariate analysis that captures all possible variables and interactions.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Fortunately, the exciting <a href="http://www.colorado.edu/eer/research/documents/IBLmathReportALL_050211.pdf" target="_blank">recent study by Laursen et al.</a> has begun to tease out some of these variables. They found, for example, that student-reported gains (e.g., in confidence and math thinking) correlated with some class practices, including peer interactions, student-instructor interactions, and the extent to which the class was student directed and student-paced. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">But which of these variables contribute most to an IBL classroom’s success? For example, is it more important for an IBL classroom to have peer interactions or to be student directed? Prince notes that cooperative learning has much more robust research support than does student-directed work: Cooperative learning not only improves test scores, but also improves interpersonal skills, student attitudes, retention in academic programs, and more. But student-directed and student-paced work can have a slight negative effect on test scores. Could past muddy results for test scores in IBL research be due in part to student-directed work? Could Laursen et al.’s student-reported gains be explained entirely by the benefits due to cooperative learning? Is it even possible to gather sufficient data to tease out the interactions among these variables? <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Perhaps if we can tease out which variables most contribute to the benefits we know IBL can provide, not only can we more easily respond to skeptics but, more importantly, we can craft our classes to even better serve our students.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">So, what’s so good about IBL, anyway? And what variables do you hypothesize are most important to that success?<o:p></o:p></div><div class="MsoNormal"><br /></div><hr /><div class="MsoNormal" style="margin-left: .5in; text-indent: -.5in;">Kirschner, P. A., Sweller, J., & Clark, R.E., (2006). “<a href="http://www.tandfonline.com/doi/abs/10.1207/s15326985ep4102_1#.UnzpIvnkslJ" target="_blank">Why Minimal Guidance DuringInstruction Does Not Work: An Analysis of the Failure of Constructivist,Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching</a>,” Educational Psycologist, 41(2): 75-86. <br /><o:p></o:p></div><div class="MsoNormal" style="margin-left: .5in; text-indent: -.5in;">Laursen, S., Hassi, M., Kogan, M., Hunter, A., & Weston, T., (2011). <a href="http://www.colorado.edu/eer/research/documents/IBLmathReportALL_050211.pdf" target="_blank">Evaluation of theIBL Mathematics Project: Student and Instructor Outcomes of Inquiry-BasedLearning in College Mathematics: A Report Prepared for the EducationalAdvancement Foundation and the IBL Mathematics Centers</a>. Assessment & Evaluation Center for Inquiry-Based Learning in Mathematics.<br /><o:p></o:p></div><div class="MsoNormal" style="margin-left: .5in; text-indent: -.5in;">Norman, G.R., & Schmidt, H. G., (2000). “<a href="http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2923.2000.00749.x/abstract" target="_blank">Effectiveness of problem-based learningcurricula: theory, practice and paper darts</a>,” Medical Education, 34(9):721-728.<br /><o:p></o:p></div><div class="MsoNormal"></div><div class="MsoNormal" style="margin-left: .5in; text-indent: -.5in;">Prince, M., (2004). “<a href="http://onlinelibrary.wiley.com/doi/10.1002/j.2168-9830.2004.tb00809.x/abstract" target="_blank">Does Active Learning Work? A Review of the Research</a>,” Journal of Engineering Education, 93(3): 223-231.<br /><o:p></o:p></div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com1tag:blogger.com,1999:blog-5816649486576881540.post-13222098050229082442013-12-16T06:00:00.000-08:002013-12-16T06:04:29.156-08:00The JMM: What's Mathematics Education Got to Do with It?<i>by Dana Ernst and Angie Hodge</i><br /><br />In just a few weeks, thousands of mathematicians and mathematics educators will descend on Baltimore for the <a href="http://jointmathematicsmeetings.org/jmm" target="_blank">2014 Joint Mathematics Meetings</a>. The JMM is a joint venture between the <a href="http://www.ams.org/home/page" target="_blank">American Mathematical Society</a> and the <a href="http://www.maa.org/" target="_blank">Mathematical Association of America</a>. Held each January, the JMM is the largest annual mathematics meeting in the world—attendance in 2013 was an incredible 6600! This year’s JMM takes place January 15-18 at the Baltimore Convention Center.<br /><br /><a href="http://www.flickr.com/photos/maaorg/8366922816/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" title="Around 2013 JMM by Mathematical Association of America, on Flickr"><img alt="Around 2013 JMM" src="http://farm9.staticflickr.com/8050/8366922816_c2921d9333.jpg" width="410" /></a>If you’ve attended the JMM before, you know how incredible of an experience it can be. If you’ve never been, we highly encourage you to attend. A quick glance at the <a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_program.html" target="_blank">conference program</a> makes it clear that there is something for everyone. In fact, the number of opportunities is a bit overwhelming. <br /><br />The handy <a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/2160_scheduler" target="_blank">JMM Personal Scheduler</a> makes managing your time at the JMM much easier, but you still have to decide what talks and sessions you want to attend. Each year, there are numerous mathematics education and scholarship of teaching and learning related events to partake in (more than you could possibly attend)—and this year is no exception. <br /><br />If you are having trouble deciding what talks to go to at the JMM and if you have an interest in math education, we are here to help. Below is just a sample of some of the offerings that caught our eye. Our list has a definite bias towards topics involving <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html" target="_blank">inquiry-based learning</a>. The <a href="http://www.legacyrlmoore.org/" target="_blank">Legacy of R. L. Moore</a> has compiled a similar <a href="http://www.legacyrlmoore.org/Reports/201401_JMM/sample_list_ibltalks.pdf" target="_blank">list</a>.<br /><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;"><b><u>Wednesday January 15, 2014 </u></b><br /><b><u><br /></u></b></div>8:40am <i>A Modified-Moore Method in Precalculus</i><br /><b>Brad Bailey</b>, University of North Georgia<br />Room 339, Baltimore Convention Center<br /><br />9:40am <i>The Sound of Mathematics: Pythagorean Music and Beyond</i><br /><div><b>Randall E. Cone</b>, Virginia Military Institute<br />Room 338, Baltimore Convention Center</div><div><br />10:00am <i>Collaborative Assessments</i> </div><div><b>Brian Katz</b>, Augustana College<br />Room 340, Baltimore Convention Center</div><div><br />3:00pm <i>Using Inquiry-Based Learning in Courses for Prospective Elementary Teachers</i> </div><div><b>Stan Yoshinobu</b>, Cal Poly San Luis Obispo<br />Room 347, Baltimore Convention Center</div><div><div style="background-position: initial initial; background-repeat: initial initial; margin-bottom: 0.1in;"><br />3:20pm <i>Effective Thinking and Mathematics</i><br /><b>Michael Starbird</b>, University of Texas at Austin<br />Ballrooms I & II 4th Floor, Baltimore Convention Center<br /><br />4:15pm <i>Two sets of Moore-Method Analysis notes and two websites that support them</i><br /><b>William T. Mahavier</b>, Lamar University<br />Room 349, Baltimore Convention Center</div>4:55pm <i>Gently Introducing IBL in Advanced Calculus</i> </div><div><b>Robert W. Vallin</b>, Slippery Rock University<br />Room 349, Baltimore Convention Center</div><div><br /><b><u>Thursday January 16, 2014 </u></b><br /><b><u><br /></u></b>9:00 – 11:50am <i>MAA Invited Paper Session on Mathematics and Effective Thinking, I</i> </div><div><b>Edward Burger</b>, Southwestern University;<br /><b>J. Michael Pearson</b>, MAA;<br /><b>Stan Yoshinobu</b>, Cal Poly San Luis Obispo;<br /><b>Jodi Cotten</b>, Westchester Community College, Valhalla, NY;<br /><b>Sandra Laursen</b>, University of Colorado Boulder;<br /><b>David Bressoud</b>, Macalester College<br />Room 307, Baltimore Convention Center</div><div><br /></div><div>9:20am <i>Developing Reinvention Materials in Ring Theory: Analysis of Student's Mathematical Activity</i> </div><div><b>John Paul Cook</b>, University of Science and Arts of Oklahoma<br /><b>Brian Katz</b>, Augustana College<br /><b>Milos Savic</b>, University of Oklahoma<br />Room 341, Baltimore Convention Center</div><div><br /></div><div>10:30am <i>An IBL Approach to Advanced Calculus that Incorporates Proficiency</i> </div><div><b>Scott Beaver</b>, Western Oregon University<br />Room 348, Baltimore Convention Center</div><div><br /></div><div>10:40am <i>Successes and Failures of Inquiry-Based Learning in an Introduction to Proofs Course</i> </div><div><b>Rachel Esselstein</b>, California State Univ. Monterey Bay<br />Room 339, Baltimore Convention Center</div><div><br />10:40am Holistic, <i>Diagnostic Grading Rubric for Student Presentations in an IBL Geometry Course</i></div><div><b>Nina Juliana White</b>, University of Michigan</div><div>Room 340, Baltimore Convention Center</div><div><br />11:00am <i>How Important is the Final Answer? Using Inquiry-Based Learning in an Introductory Proofs Course</i> </div><div><b>Susan Crook</b>, Loras College<br />Room 339, Baltimore Convention Center</div><div><br />11:20am <i>Using an Inquiry-Based Learning Approach in Introduction to Proofs and Advanced Calculus Course </i></div><div><b>Jim Fulmer and Tom McMillan</b>, University of Arkansas at Little Rock<br />Room 339, Baltimore Convention Center</div><div><br />1:00 – 4:00pm <i>MAA Invited Paper Session on Mathematics and Effective Thinking, II </i></div><div><b>Paul Zorn</b>, St. Olaf College;<br /><b>Katherine Socha</b>, Math for America;<br /><b>Deborah J. Bergstrand</b>, Swarthmore College;<br /><b>Carol Schumacher</b>, Kenyon College;<br /><b>Francis Edward Su</b>, Harvey Mudd College<br />Room 307, Baltimore Convention Center</div><div><br /><u><b>Friday, January 17, 2014</b></u><br /><u><b><br /></b></u>8:45am <i>An Inquiry-Based Approach to Teaching Parameterization</i> </div><div><b>Fabiana Cardetti</b>, University of Connecticut;<br /><b>Nicole DeMatteo</b>, Providence College;<br /><b> Jonathan Dollar</b>, Emory University;<br /><b>Gabriel Feinberg</b>, Haverford College<br />Room 348, Baltimore Convention Center<br /><br />1:00pm <i>Group Work & Modified Moore Method in Flipping Calculus 1</i> </div><div><b>Karen Bliss</b>, Quinnipiac University<br />Room 337, Baltimore Convention Center<br /><br />2:40pm <i>Flipping Intermediate Algebra</i> </div><div><b>Jacqueline A. Jensen-Vallin</b>, Slippery Rock University<br />Room 337, Baltimore Convention Center<u><b><br /></b></u><u><b><br /></b></u><u><b>Saturday, January 18, 2014</b></u><br /><br />1:45pm - 1:55pm <i>Creating a Duel-Credit/Dual Enrollment "OnRamps" Precalculus Course to Enhance the College Readiness of High School and Community College Students</i> <br /><b> Mark Daniels</b>, University of Texas at Austin<br />Room 347, Baltimore Convention Center<br /><br />2:00pm <i>How About a Free Set of IBL Calculus Notes that Covers all of Calculus I, II and III?</i> </div><div><b>William T. Mahavier</b>, Lamar University<br />Room 340, Baltimore Convention Center<br /><br />2:30pm <i>Inquiry-Based Problem Solving Strategies through Interactive Approaches for Engaging Students in Mathematics</i><br /><b> Padmanabhan Seshaiyer and Jennifer Suh</b>, George Mason University<br />Room 314, Baltimore Convention Center<br /><br />3:00pm <i>Resources to Aid the Transition into an IBL Mathematics Course</i> </div><div><b>Gabriel Feinberg</b>, Haverford College;<br /><b>Lily An</b>, Williams College;<br /><b>Victoria Lewis</b>, California State University Sacramento;<br /><b>Fabiana Cardetti</b>, University of Connecticut<br />Room 347, Baltimore Convention Center</div><div><br /></div><div>3:15pm <i>Inquiry-Based Learning and Hybrid Inquiry-Based Learning in College Geometry</i> </div><div><b>Ali S. Shaqlaih</b>, University of North Texas at Dallas<br />Room 347, Baltimore Convention Center<br /><br /><div style="background: #ffffff; margin-bottom: 0.1in;">In addition to the sessions listed above, we also encourage you to visit the <span style="color: blue;"><span lang="zxx"><u><a href="http://eduadvance.org/" target="_blank">Educational Advancement Foundation</a></u></span></span>'s booth. The EAF aims to strengthen mathematics education through fostering critical thinking and problem solving by ensuring all students have an inquiry-based learning (IBL) experience in mathematics. Why visit the EAF booth? <span style="color: blue;"><span lang="zxx"><u><a href="http://jointmathematicsmeetings.org/meetings/national/jmm2014/jmm2014-eaf.mp3" target="_blank">Listen to a short podcast</a></u></span></span> as Mike Breen (AMS Public Awareness Officer) speaks with Tina Straley (former MAA Executive Director), Stan Yoshinobu (California Poly, San Luis Obispo), and Michael Starbird (University of Texas at Austin).<br /><br />If you are interested in undergraduate mathematics education, it’s likely because you care about students. It's not related to mathematics education, but we’d like to encourage you to go to the <span style="color: blue;"><span lang="zxx"><u><a href="http://www.maa.org/programs/students/undergraduate-research/jmm-poster-session" target="_blank">Undergraduate Poster Session</a></u></span></span>, which takes place on Friday, January 17, 4:30-5:30pm. One of the best ways to support students at the JMM is by attending the poster session. We hope to see you there!</div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-48642934989648536832013-10-30T08:01:00.000-07:002013-10-30T08:01:30.867-07:00Group Work: Be Predictably Unpredictable<div class="MsoNormal"><i>By Angie Hodge</i><br /><i><br /></i><span style="font-family: inherit;">Group work. It’s the Hodge-IBL method. Even though I did not enjoy group work as a student until graduate school, it fits my teaching style. My classroom is social. We all learn together. We all learn from one another. With tables, whiteboards around the room, and a lot of chatter, we get math done.<o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: inherit;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-o-vzhsZ4nHw/Um_vgTBMV0I/AAAAAAAAIzE/ecmxgR_6iRQ/s1600/group+work.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-o-vzhsZ4nHw/Um_vgTBMV0I/AAAAAAAAIzE/ecmxgR_6iRQ/s1600/group+work.JPG" width="575" /></a></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">April Halcomb asked a great question, however, in response to <a href="http://maamathedmatters.blogspot.com/2013/09/its-time-to-blow-whistle.html">my last blog entry</a>: “How do you make sure they [students] are on the right path when they are working together, and how do you make sure everyone is working together?” <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">This is, as I said, a great question. If I had the answer, I'd be rich. So I don't have it <i>all </i>figured out, but I can offer advice from experience. I’ve been using IBL group work since 2007, and I learn something new about it every year. Heck, I just learned something about it today. <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;"><b>Listen carefully.</b>Thankfully, I have ears like an elephant and can hear a pin drop on the other side of the room. That’s one key to my success with group work. Even if you don’t have great hearing, make the students think you do. Keep your ears open at all times and randomly answer questions from across the room. Once you do this a couple of times, they will know you are listening. <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;"><b>Do the random walk.</b>Move around the room in a pattern that is so random that the students won’t ever guess when you will be coming their way. I do go where there is a hand, if there is a question, but I also literally hop around from place to place. I eavesdrop, help out where needed, and walk away if I'm about to disclose too much. <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;"><b>Stop them if need be.</b>I <a href="http://maamathedmatters.blogspot.com/2013/09/its-time-to-blow-whistle.html">use my whistle</a> to stop the class if it seems like most students are stuck or if we all need to come together for some reason. This is also done at random intervals. <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;"><b>Allow some chatter.</b>I find that if you allow students some time off task, they will bond with one another and work together better. I don’t allow a lot of this and bring them back on task by asking them questions, but it’s okay if sometimes they tell a joke or two. After all, learning math should be fun. <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;"><b>Challenge them.</b> Make the work easy enough that all students can start it, but hard enough that they need one another to finish it. Challenges and goals work wonders if your students are at all competitive. K</span>nowing that they will need help from others to finish the work also encourages students to<span style="font-family: inherit;"> keep the random chatter to a minimum. Better make some headway while the necessary human resources are available!</span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;"><b>Let some work alone.</b>I often have one student per class who initially likes to work alone. I “sort of” let this slide (or at least I pretend to). I let him/her work alone, but I ask him/her to help another student if he/she gets the concept we are working on. I also have other students help the “loner” student if he/she looks stuck. I do, however, respect that some differentiated instruction is needed. I just nudge the group work and usually it pans out. <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">But…what if some groups just don’t click? What if students aren’t talking to each other? What if your random grouping leaves you with the blind leading the blind? What if? Discuss. I will offer my two cents in my next blog entry. </span><o:p></o:p></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com3tag:blogger.com,1999:blog-5816649486576881540.post-28092625742896656892013-09-19T06:51:00.000-07:002013-09-19T06:51:14.445-07:00“It’s Time to Blow the Whistle”<div class="MsoNormal"><span style="font-family: inherit;"><i>By Angie Hodge</i></span></div><div class="MsoNormal"><span style="font-family: inherit;"><br /></span></div><div class="MsoNormal"><span style="font-family: inherit;">I’m three weeks into my Calculus I course, and it’s finally time to blow the whistle! Yay!!! <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">Why am I so excited about this? Am I serious? Well…<o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">As you may know from our previous posts, Dana and I try a lot of different things in our classrooms to achieve the inquiry and engagement we're after. My “thing”</span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 107%;">—</span><span style="font-family: inherit;">for lack of a better term</span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 107%;">—</span><span style="font-family: inherit;">is collaborative learning or group work, which I currently use in a class of 40 calculus students.</span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">I've even gotten money from our dean to transform one of the traditional classrooms here a University of Nebraska Omaha into one that </span>promotes group work with <span style="font-family: inherit;">whiteboards on all the walls and tables with movable chairs. I’ll talk about why this is important and give tips on how to get this sort of funding in a future blog post. For now, though, let’s go back to the whistle.</span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">I’m teaching calculus as a night course this semester. It meets twice a week for two hours and 15 minutes per session. Such lengthy classes allow me to not only try longer conceptual activities, but also pair them with skills practice. Twice weekly classes aren't as conducive as daily ones are to building a community of learners, however. The students only interact with one another twice per week instead of four to five times. That’s a big difference! <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">Because of the less frequent contact, I was worried that it would take a while to build a meaningful and trusting community in my class. I was wrong. Today, I entered the class 65 minutes before it began. The room was buzzing with math talk!! About 15 out of 40 students were already in class clustered at the front table discussing the homework and take-home quiz. Not only are my students allowed to talk to one another about these assignments, their fellow students are the <i>only</i> humans with whom they may discuss them. That's probably why they were in the room early jabbering about math!<o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: inherit;"><br /></span></div><div class="MsoNormal"><span style="font-family: inherit;">But I still haven’t told you about the whistle.</span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">This “math talk” went on right up until class began. I helped answer questions when I was “needed,” but for the most part students were helping one another. It was clear from their conversation that they were catching on to some important mathematical skills: justifying, questioning, discussing, etc. They did this to such an extent that I had occasion to “blow the whistle.” <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">About a year ago, w</span>hen a inquiry-based calculus class of more than 40 students got rather noisy, I jokingly said that <span style="font-family: inherit;">I needed a whistle. Over winter break last year, I found an old-school whistle in a drug store near my parents’ small town. I bought it, still not knowing if I would actually use it.</span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">Spring semester started and some of the students who had me for first semester calculus knew I had joked about buying and blowing a whistle. So when the class got working and was talking loudly, I blew the whistle. At first, it’s awkward to blow a whistle in a college class. It works, though!!! <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">We are like a sports team in my math classes. I may help by showing my students a new skill or leading them to discover it, but they need to practice the skill. They often need to work as a team to discover new strategies or figure out why those strategies work. The students need to be able to talk out loud to do this, so I let them. The only rule is that when the whistle blows, they stop the discussion. I promise not to take up too much time when I blow the whistle to bring the class together as a group, and the time I do take isn't just filled with me talking. I also let students share their ideas. Blowing the whistle is a fast, easy way to transition from gym-like loudness to focused, quiet attention.</span></div><br /><div class="MsoNormal"><span style="font-family: inherit;">I know it’s silly, but try it sometime if you have a large class. Dare to let your students explore their thinking, share their thoughts, and be mathematicians,</span><span style="font-family: inherit;"> knowing that one quick blow of the whistle is all it takes for the class to regroup!</span></div><div class="MsoNormal"><o:p></o:p></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com4tag:blogger.com,1999:blog-5816649486576881540.post-69979166743811636962013-08-27T08:40:00.000-07:002013-08-27T08:42:49.923-07:00Give the Students the Colored Pen<span style="font-family: inherit;"><i>By Dana Ernst</i></span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">When I first started using <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html">inquiry-based learning</a> (IBL), grading/assessing students caused me the most anxiety.<span style="font-size: x-small;"> </span></span><span style="font-family: inherit;">When it comes to grading, I always feel like I am trying to solve an optimization problem. I want to maximize useful feedback to students and data to justify grades while minimizing the amount of time it takes for me to do the grading. After some trial and error, I’ve settled on a method that I feel is both effective and efficient.</span><br /><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;">One key component of my approach to IBL is to get students to the board to present their proposed solutions/proofs as much as possible. In my upper-level proof-based courses, the student presentations form the backbone of what we do each day in class. In my calculus courses, the student presentations play less of a role, but they are still an important part of the structure of the course. </span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;">In most cases, students are presenting material that was assigned as homework. In the past, I allowed students to freely annotate and/or modify their work during the presentations. One problem with this, however, was that it was usually impossible to tell what work a student had done prior to class. Certainly, in some cases, I was giving credit to students for work they did not do. For a brief time I experimented with collecting student work prior to the presentations, but this also bothered me since I felt the advantages of giving students an opportunity to learn something by comparing what they had done to what the presenter was doing outweighed the disadvantages. </span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div style="margin-bottom: 0in;">Then <span style="font-family: inherit;"><span style="color: blue;"><span lang="zxx"><u><a href="http://www.msudenver.edu/searchchannel/jsp/directoryprofile/profile.jsp?uName=cdollard">Clark Dollard</a></u></span></span> (Metro State University) suggested having students use colored felt tip pens to annotate their work during class. I remember dismissing this idea as silly, but a couple months later I decided to give it a try. It's such a simple thing, but it has had a big impact! </span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div style="margin-bottom: 0in;">Here's my current approach to using the felt tip pens. If students are presenting material from homework that the class will ultimately turn in for a grade, the students in the audience are allowed to annotate their work, but only with one of the felt tip pens that I provide in class. Each day, I bring a box full of a variety of colored felt tip pens. The purple pens are the most popular and no one ever chooses the red ones. Students are encouraged to annotate their work as much as they want with the colored pens. Their grade on the assignment will not be impacted by what they write with the felt tip pen, but rather their grade is a result of what they had before they entered class.</div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-cfmastLELXc/Uhy_v_0zQII/AAAAAAAAIAU/2nYJtZJRBmQ/s1600/Pens.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-cfmastLELXc/Uhy_v_0zQII/AAAAAAAAIAU/2nYJtZJRBmQ/s1600/Pens.jpg" height="209" width="320" /></a></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;">Having students use the felt tip pens enables me to discern what students had done before class. Moreover, students are encouraged to reflect in the moment on their work, not days later when I return it. I have nothing other than anecdotal evidence to support this, but I strongly believe that adoption of the felt tip pen approach has changed how my students annotate their work. Not only are the annotations different, but I can also tell that deep reflection is occurring. At the beginning of each semester, it's clear that a few students think that the idea is silly, but feedback from students (both in person and on anonymous course evaluations) has been extremely positive.</span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;">On a selfish note, the felt tip pen approach also allows for speedy grading. Since we’ve already discussed each of the problems in class, I don’t feel compelled to grade the work for correctness. Instead, I use a ✓-, ✓, ✓+ scale, which makes the grading of the homework lightning fast. All that matters is what the student had done <i>before</i> class.</span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><a href="https://www.blogger.com/blogger.g?blogID=5816649486576881540" name="_GoBack"></a>In addition to the homework that is presented in class, I also assign an additional weekly homework assignment whose purpose is for students to reflect on the previous week’s presented homework. Each week, students are supposed to turn in two problems (from a subset of my choosing) that were presented during the previous week. These weekly assignments are supposed to be carefully written, and since this is the second time that students are working on the problems, the grading goes quickly, but I also feel comfortable grading them harshly. One significant advantage to this approach is that it forces students to revisit their annotations. In fact, I believe that having <i>both</i>the daily and weekly homework is key.</span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;"><br /></span></div><div style="margin-bottom: 0in;"><span style="font-family: inherit;">If you want to learn a little bit more about my felt tip pen approach, <span style="color: blue;"><span lang="zxx"><u><a href="https://speakerdeck.com/dcernst/effective-and-efficient-grading-for-an-ibl-course">check out the slides</a></u></span></span> from the "Effective and efficient grading for an IBL course" talk I gave at the <span style="color: blue;"><span lang="zxx"><u><a href="http://legacyrlmoore.org/events.html">2012 Legacy of R.L. Moore Conference</a></u></span></span> in Austin, TX.</span></div><div id="sdfootnote1"><div class="sdfootnote"><br /></div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com7tag:blogger.com,1999:blog-5816649486576881540.post-82142395250280556662013-08-07T10:46:00.001-07:002013-08-07T10:46:36.860-07:00MAA MathFest 2013: Community Building<span style="font-family: inherit;"><i>By Angie Hodge</i></span><br /><span style="font-family: inherit;"><i><br /></i></span><span style="font-family: inherit;">As I tried to think of how to frame a blog post highlighting </span><a href="http://www.maa.org/meetings/mathfest" style="font-family: inherit;">MAA MathFest 2013</a><span style="font-family: inherit;">, I kept returning to one word: community. </span><span style="font-family: inherit;"><br /><br />For the second year in a row, Dana and I organized a session at MathFest called “<a href="http://www.maa.org/meetings/mathfest/program-details/2013/contributed-paper-sessions#IBL">Best Practices of Inquiry-Based Learning</a>,” and, for the second year in a row, we had a full house! <br /><br />“Why?” I asked myself. Why are people coming back? Why is the meeting room still packed on the final afternoon of the conference? <br /><br />You are all welcome to share your thoughts (and please do), but I attribute the sustained popularity of the session to more than just the presentation topics. I believe it has to do with the fact that we, as fans and practitioners of IBL, have created a community, a community welcoming enough to attract newcomers and friendly and enriching enough to keep them coming back. <br /><br />We come to IBL sessions to see our friends. We come to see colleagues whose work we value and respect. We come to meet new friends and to make new colleagues. We come to an environment where we can, as <a href="http://www.uni.edu/theron/">T. J. Hitchman</a> stated, “learn from not only our students’ failures, but from our own failures.” We stay afterwards to learn more. We go to lunch with session attendees (both old MathFest friends and new ones). </span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">I leave you with questions: </span><span style="background-color: white; color: #222222;"><span style="font-family: inherit;">Does your classroom create a learning environment that's collegial and nonthreatening? Enjoyable, even? Do you cultivate a we're-all-in-this-together atmosphere in your classroom?</span></span><span style="font-family: inherit;"><span style="font-family: inherit;"> Is</span> your classroom a place your students are excited to visit? How can we, as a mathematics/mathematics education community, become even more welcoming so that we can continue to learn from/with one another?<br /><br />Cheers to everyone who made MAA MathFest 2013 great!</span>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-42809702610116813712013-07-24T11:35:00.000-07:002013-07-24T12:37:46.750-07:00Personality Matters?<i>By Dana Ernst</i><br /><br />A few weeks ago, Angie and I were helping out with the <span style="color: blue;"><span lang="zxx"><u><a href="http://iblworkshop.org/home.html">IBL Workshop</a></u></span></span> that took place at <span style="color: blue;"><span lang="zxx"><u><a href="http://calpoly.edu/">Cal Poly</a></u></span></span>. Wow, what a great experience! I attended a similar workshop in Austin, TX, back in 2010 that took place prior to the <span style="color: blue;"><span lang="zxx"><u><a href="http://legacyrlmoore.org/events.html">Legacy of R. L. Moore Conference</a></u></span></span>. The conference that I attended as a participant had a huge impact on my development as a practitioner of inquiry-based learning (IBL) and it was great to be involved in helping others have similar transformations. (If you want to know more about IBL, check out our <span style="color: blue;"><span lang="zxx"><u><a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html">What the Heck is IBL?</a></u></span></span> post.)<br /><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">The workshop lasted for four action-packed days. We basically went straight through from 8AM to 5PM each day and there wasn't a wasted moment. All of the sessions and activities were worthwhile, but what I cherished most were the conversations and interactions that I managed to squeeze in during our short breaks and at lunch. Being at a workshop like this always inspires new ideas and causes me to reflect on teaching and the purpose of education. During one of the lunch conversations, I had a revelation about my personality and how it impacts the choices I make about my teaching.</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">During lunch on the third day, I was sitting at small table with Kayla Dwelle from <span style="color: blue;"><span lang="zxx"><u><a href="http://mathcs.obu.edu/?page_id=83">Ouachita Baptist University</a></u></span></span> and a few others. Kayla and I were chatting about her successes and struggles in her IBL classes. She was lamenting the fact that her introduction to proof course hadn't been going as well as her liberal arts math class. As we talked, I was asking questions about what she felt were the differences between the two classes. One significant difference is that, in her proof course, one student at a time presents at the board, while the norm is small group work in the other course. Kayla got the feeling that her liberal arts math students had bought into IBL, she said, but that her intro to proof students hadn't seemed to embrace the approach. She wondered if the different outcomes had something to do with her own comfort with the two different approaches.</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">As soon as she said this, I got whacked in the head with an epiphany. I'll do my best to explain. I’ve been dabbling in group work for years, even before I started utilizing IBL. In fact, this past semester, I had my calculus students working in groups almost every day. My use of small groups never went poorly, but I also never left class thinking, "wow, that was the best class ever!" In contrast, I regularly have this thought after leaving my IBL classes where I take a <span style="color: blue;"><span lang="zxx"><u><a href="http://legacyrlmoore.org/method.html">modified-Moore method</a></u></span></span> approach and typically have one student at the board at a time presenting their proposed proof/solution to an assigned problem. I’m definitely not opposed to group work, but I’ve always felt like group work and I just don't jive. In some sense, I have the reverse of Kayla's issue. This made me realize how much of an impact each instructor’s personality has on the effectiveness of the approach he or she takes to teaching.</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">As a student, I <i>always</i> sat in the back of the room. I do the same thing at conferences and such. I hate people being behind me. Hate it. It makes me feel uncomfortable. When I lecture, I may turn my back to the class for a few moments here and there, but generally, I'm facing the audience. In my IBL classes, if I'm not doing group work, I'm usually sitting or standing in the back of the room. I feel comfortable there. When I wander around the room while students are working in small groups, however, I'm in the middle of all the action. I don't necessarily dislike this, but it definitely disrupts my mojo.</div><div style="margin-bottom: 0in;"><br /></div><div class="separator" style="clear: both; text-align: center;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-J3yTEFoxcRI/Ue_Dvwgk5_I/AAAAAAAAHwo/5jscC6So4o4/s1600/i-JxMpMHr-L.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="265" src="http://4.bp.blogspot.com/-J3yTEFoxcRI/Ue_Dvwgk5_I/AAAAAAAAHwo/5jscC6So4o4/s1600/i-JxMpMHr-L.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Dana can do small group work (as long as there's no one behind him).</i></td></tr></tbody></table><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">I also have the ability to hyper-focus for extended periods of time. It drives my wife nuts. I like to focus on one thing at a time and focus on it intensely. When a student is presenting, this is exactly what I am doing. I have a bird's eye view of what is going on in the whole room; I can process all the information, and then respond accordingly. I love it and for me it works really well. Yet, during small group work, there are a hundred different things going on and it's my job to bounce from one interaction to the next. My interaction may require no action at all, but I still have to be multi-processing. I can do it, but it's not as natural for me.</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">I conveyed my thoughts as I was having them during lunch and others at the table were pondering how their personalities influence their level of comfort and/or effectiveness with different approaches to teaching. As I recall, Kayla and Angie are more comfortable in the small group setting and feel that it has been very successful for them. I've since discussed this further with others and it is interesting to hear the wide range of responses.</div><div style="margin-bottom: 0in;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-20WNWOXUp8k/Ue_EmQSeKII/AAAAAAAAHww/rcm0rWF5hVk/s1600/i-CM7FnHn-L.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="266" src="http://4.bp.blogspot.com/-20WNWOXUp8k/Ue_EmQSeKII/AAAAAAAAHww/rcm0rWF5hVk/s1600/i-CM7FnHn-L.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Angie has found group work very successful in her classroom.</i></td></tr></tbody></table><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">As I've been reflecting on this for the past few weeks, I've been reminded that students also have a wide variety of personalities and preferences when it comes to learning. I've had students get impatient at the pace with which we are covering material in my modified-Moore method classes. I don't think this is common, but it happens. Perhaps these students would prefer to work in a smaller group where they could have more influence over the pace. By the way, the types of students I just mentioned are probably as equally impatient in a lecture class where they likely have zero influence over the pace.</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">As a final thought, I don't want to dismiss the importance of refining the skills necessary for effectively implementing both group work and a modified-Moore method approach. Technique matters. I also don't mean to imply that group work and modified-Moore method are our only options or that a teacher must stick with one approach all the time.</div><div style="margin-bottom: 0in;"><br /></div><div style="margin-bottom: 0in;">Does your personality influence the choices you make as a teacher? Do you think it influences how effective you are at implementing different teaching methods? If so, how?<br /><br /><i>Photos, taken at the 2013 IBL Workshop, courtesy of Stan Yoshinobu.</i></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com8