tag:blogger.com,1999:blog-58166494865768815402014-10-20T10:07:20.197-07:00Math Ed MattersMathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.comBlogger22125tag: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.com8tag:blogger.com,1999:blog-5816649486576881540.post-79663016364029954412013-07-09T08:29:00.000-07:002013-07-21T13:26:27.146-07:00Grade School Utopia?<span style="display: none;">claimtoken-51ec2a9fa2ade</span><br /><i>By Dana Ernst</i><br /><b><br /></b><b>A Montessori Observation </b><br /><div class="MsoNormal"><br />Towards the end of April, my wife and I spent an hour observing our boys' classrooms at <a href="http://havenmontessori.org/">Haven Montessori</a>in Flagstaff, Arizona. Wow. We sat in the corner and just watched for 30 minutes in each classroom. My younger son (age five) is in a Primary Classroom, which is for children three years to six years (including kindergarten). My older son (age seven) is in Lower Elementary, which is for first through third grades. Both of our boys started Montessori in January of this year, and we have been thrilled with the outcome. We were hesitant to transfer them in the middle of the school year, especially after having moved to Arizona from New Hampshire less than a year ago, but we have no regrets about our decision.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">This wasn't my first observation of a Montessori classroom, but each time I do it, I am blown away. Here are a few quick observations:<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoListParagraphCxSpFirst" style="margin-left: 41.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><!--[endif]-->All of the students were working quietly and respectfully.<o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 41.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><!--[endif]-->Students were working either independently or collaboratively with another student or two.<o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 41.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><!--[endif]-->There were a variety of different things going on at the same time.<o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 41.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><!--[endif]-->Students moved freely about the room, but were always focused on their respective tasks.<o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 41.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><!--[endif]-->Students were smiling and enjoying themselves but not goofing off.<o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 41.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><!--[endif]-->Students appeared to be working on stuff because they were genuinely interested.<o:p></o:p></div><div class="MsoListParagraphCxSpLast" style="margin-left: 41.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><!--[endif]-->There were no incentives and no grades!<o:p></o:p></div><div class="MsoNormal"> <o:p></o:p></div><div class="MsoNormal">It seems like a utopia. If you've never seen a Montessori classroom in action, I encourage you to go check it out. I'm sure the success of each classroom has a lot to do with the teacher, so we are tremendously grateful that our boys ended up with great teachers. <o:p></o:p><br /><br /><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/-HGpuRm9rudU/UdwA7isBzgI/AAAAAAAAHqE/XfReWTgKrEw/s1600/timthumb.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-HGpuRm9rudU/UdwA7isBzgI/AAAAAAAAHqE/XfReWTgKrEw/s1600/timthumb.jpg" height="175" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">(photo courtesy of <a href="http://annalabenz.com/" target="_blank">Anna LaBenz</a>)</td></tr></tbody></table></div><div class="MsoNormal"><br /></div><b>What is the Montessori Method? </b><br /><div class="MsoNormal"><br />So, what is <a href="http://www.amshq.org/Montessori-Education.aspx">Montessori</a>? <a href="http://www.amshq.org/Montessori-Education/History-of-Montessori-Education/Biography-of-Maria-Montessori.aspx">Dr. Maria Montessori</a> (1870-1952) was an Italian physician (the first female to earn a medical degree in Italy) who formulated the Montessori Method of education. Dr. Montessori opened her first school in Rome in 1907. The hallmarks of the Montessori method include multi-age groupings that foster peer learning, uninterrupted blocks of work time, and guided choice of work activity that often involves the use of specially designed <a href="http://en.wikipedia.org/wiki/Manipulative_(mathematics)">manipulatives</a>. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">The mixed-aged classrooms feature three-year age ranges. The intent is for older students to act as leaders and mentors for younger students while the younger students gain experience working with older students. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Unlike a conventional classroom, a Montessori teacher does not stand at the front delivering the same information to 30 students while trying to keep everyone on the same page. Instead, teachers move around the room, working with students one-on-one or in small groups. Also, in a traditional Montessori approach, there are no grades, no exams, and no homework.<o:p></o:p></div><br /><b>Connections to Inquiry-Based Learning </b><br /><div class="MsoNormal"><br />In my view, there are a lot of similarities between Montessori and <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html">inquiry-based learning</a> (IBL), which is the approach that I take when teaching mathematics classes. All of the wonderful things I witnessed during my observation are exactly the kinds of things I strive for in my own classrooms: creativity, collaboration, and critique of ideas. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">IBL is a learner-centered mode of instruction that engages students in sense-making activities. Students are given tasks requiring them to solve problems, conjecture, experiment, explore, create, and communicate. All of this is exactly what Montessori strives to do! If you want to know more about IBL, check out our blog post titled "<a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html">What the Heck is IBL?</a>"<o:p></o:p></div><br /><b>Are There Any Cons to a Montessori Approach? </b><br /><div class="MsoNormal"><br />Montessori isn't all rainbows and unicorns. My wife and I believe that the approach is working for my boys right now. Would we be so thrilled if one or both of their teachers weren't as good? I doubt it. Will the Montessori approach continue to be successful for both of my children as they grow older? Time will tell. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I've met a few people who have reported negative experiences with Montessori schooling. Maybe a poor teacher was to blame or the Montessori approach was not a good fit for the child. This is similar to students having a negative IBL or <a href="http://legacyrlmoore.org/method.html">Moore method</a> experience in a college mathematics class. It can happen. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Some people have concerns about the lack of homework and exams in a traditional Montessori approach. I worried about this initially, but I don't anymore. When my older son wasn't enrolled in Montessori, he regularly had homework to do. He would always do it without complaint, but he definitely did not enjoy it. Now, neither of my kids has homework. But they are more fired up to show off what they have learned at school and to learn things at home than they ever were before. They are constantly concocting "research projects" to work on. One of the recent ones entailed learning about Mars. They made up a list of questions and then set about finding the answers. Will this enjoyment of learning continue? I sure hope so. <o:p></o:p><br /><br /><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/-DCKLvvEFk90/UdwCmLzQTSI/AAAAAAAAHqU/5blitPgiDvE/s1600/timthumb2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-DCKLvvEFk90/UdwCmLzQTSI/AAAAAAAAHqU/5blitPgiDvE/s1600/timthumb2.jpg" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">(photo courtesy of <a href="http://annalabenz.com/" target="_blank">Anna LaBenz</a>)</td></tr></tbody></table></div><div class="MsoNormal">How smoothly will my boys transition out of Montessori when they enter high school where homework and exams are the norm? I'm optimistic that this won't be a problem, but I won't really know until we get there.<o:p></o:p></div><br /><b>Some Final Thoughts </b><br /><div class="MsoNormal"><br />While I was observing my boys' classrooms, I kept daydreaming: "What if students were provided with this type of experience throughout their entire education?" In particular, I spent quite a bit of time pondering my last observation above about grades and incentives. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">As a teacher, I try to de-emphasize grades as much as possible, but they are so entrenched in our educational system. The <a href="http://en.wikipedia.org/wiki/Overjustification_effect">overjustification effect</a> may partially explain some of the problems that we see in conventional education. According to Wikipedia:<o:p></o:p></div><div class="MsoNormal"><br /></div><blockquote class="tr_bq">The overjustification effect occurs when an expected external incentive such as money or prizes decreases a person's intrinsic motivation to perform a task. According to self-perception theory, people pay more attention to the external reward for an activity than to the inherent enjoyment and satisfaction received from the activity itself.</blockquote><br /><div class="MsoNormal">Is it possible to eliminate the need for incentives? Is there something that happens in our development that diminishes our curiosity flame?<o:p></o:p></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com2tag:blogger.com,1999:blog-5816649486576881540.post-60505100740166352082013-06-21T05:49:00.000-07:002013-06-21T07:06:59.706-07:00Try, Fail, Understand, Win<div class="MsoNormal"><i>By Dana Ernst and Angie Hodge</i></div><div class="MsoNormal"><br /></div><div class="MsoNormal">“Try, fail, understand, win.” These were the four words written on a course evaluation at the end of <a href="http://teaching.danaernst.com/mat320s13/">Dana’s introduction to proof course</a> from the spring 2013 semester. We believe that this perfectly captures the essence of an effective <a href="http://maamathedmatters.blogspot.com/2013/05/what-heck-is-ibl.html">inquiry-based learning</a> (IBL) experience for a student. Dana couldn’t ask for a better student comment. He should retire now; it’s all downhill from here.<br /><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://2.bp.blogspot.com/-itKY4zVdARs/UcRc-wwctlI/AAAAAAAAHa8/3DTAkiagvi0/s1600/A99+MATH335.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-itKY4zVdARs/UcRc-wwctlI/AAAAAAAAHa8/3DTAkiagvi0/s1600/A99+MATH335.jpg" height="232" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Dana asks a question at the Legacy of R. L. Moore Conference.</i></td></tr></tbody></table></div><div class="MsoNormal">The “big” IBL conference is the annual <a href="http://legacyrlmoore.org/events.html">Legacy of R. L. Moore Conference</a>, which recently took place in Austin, Texas. The theme of this year’s conference was “We are IBL,” which was chosen to represent all of the different groups of people engaged in or interested in IBL. This was Dana’s fifth Legacy conference and Angie’s sixth. Dang, what a great conference! It’s amazing to be around so many people who are passionate about student-centered learning. We always leave all fired up to teach and change the world. It was great seeing all our IBL pals and meeting lots of new folks too.<o:p></o:p><br /><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/-Eqf3IiztWiw/UcRdthL-KiI/AAAAAAAAHbI/QO2FOmsl0V4/s1600/A99+MATH89.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-Eqf3IiztWiw/UcRdthL-KiI/AAAAAAAAHbI/QO2FOmsl0V4/s1600/A99+MATH89.jpg" height="230" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Angie introduces a speaker at the Legacy of R. L. Moore Conference.</i></td></tr></tbody></table></div><div class="MsoNormal">If you want more details about what went down this year, check out <a href="http://theiblblog.blogspot.com/2013/06/rlm-conference-reflections.html">this post</a> by <a href="http://www.stanyoshinobu.com/">Stan Yoshinobu</a> over on <a href="http://theiblblog.blogspot.com/">The IBL Blog</a>.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">As we reflect on this year’s conference, “try, fail, understand, win” provides a good outline of the lessons learned.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Try:</div><ul><li><span style="background-color: white; color: #222222; font-family: inherit;">We try something new in our classrooms.</span></li><span style="font-family: inherit;"><li><span style="background-color: white; color: #222222; font-family: inherit;">We try to engage our students in mathematics and inspire them to crave more.</span></li><li><span style="background-color: white; color: #222222; font-family: inherit;">We try to provide our students with a safe environment where they are willing to take risks.</span></li><li><span style="background-color: white; color: #222222; font-family: inherit;">We try to relinquish control, sit back, and see what our students can do.</span></li></span></ul><span style="font-family: inherit;"></span><span style="font-family: inherit;">Fail:</span><br /><div><ul><li><span style="background-color: white; color: #222222; font-family: inherit;">We may fail to get “buy in” from our students.</span></li><li><span style="color: #222222; font-family: inherit;">We may not receive a teaching award, because someone observing our classroom may not think we are “teaching” since we aren’t lecturing.</span></li><li><span style="color: #222222; font-family: inherit;">We may not have the support of our colleagues.</span></li><li><span style="color: #222222; font-family: inherit;">We may have students complain to our administrators that we aren’t lecturing enough.</span></li><li><span style="color: #222222; font-family: inherit;">We may try something new and it may not go as well as we had hoped.</span></li></ul>Understand:<br /><div class="MsoNormal"></div><ul><li><span style="background-color: white; color: #222222; font-family: inherit;">We understand how to market IBL to our students and colleagues.</span></li><li><span style="color: #222222; font-family: inherit;">We understand the importance of working together as an IBL team; “We are IBL.”</span></li><li><span style="color: #222222; font-family: inherit;">We understand that teaching our students to become explorers in a detective story gives them a taste of what mathematics really is.</span></li><li><span style="color: #222222; font-family: inherit;">We understand that class time is precious and that we should avoid lecturing on things students can learn on their own.</span></li><li><span style="color: #222222; font-family: inherit;">We understand that what matters most is that our students become independent thinkers and learners.</span></li></ul>Win:<br /><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"></div><ul><li><span style="background-color: white; color: #222222; font-family: inherit;">We win when we have taught our future elementary teachers to teach themselves what they don’t know.</span></li><li><span style="color: #222222; font-family: inherit;">We win when we teach our students to conjecture and ask why without anyone asking them to do so.</span></li><li><span style="color: #222222; font-family: inherit;">We win when we realize that there’s always something we can do better in the classroom.</span></li><li><span style="color: #222222; font-family: inherit;">We win when students no longer look to us as the sole authority.</span></li><li><span style="color: #222222; font-family: inherit;">We win when our students have the ability to reach conclusions by reasoning logically and are able to justify those conclusions in clear, persuasive language.</span></li><li><span style="color: #222222; font-family: inherit;">We win when our students experience the unmistakable feeling that comes when one truly understands something.</span></li></ul>Just as our students “win” after experiencing an effective student-centered approach, the attendees of the Legacy Conference “won” if they were at least challenged to ponder how to provide students with a transformative experience.<br /><div class="MsoNormal"><o:p></o:p></div></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com1tag:blogger.com,1999:blog-5816649486576881540.post-71859124400555058252013-06-05T06:00:00.000-07:002013-06-05T06:00:01.301-07:00If You Aren't Having Fun...<div class="MsoNormal"><i>By Angie Hodge<o:p></o:p></i></div><div class="MsoNormal"><br /></div><div class="MsoNormal">As you watch the video below (made by my students!), keep in mind that my teaching motto for years has been “If you aren’t having fun, you aren’t learning.”<o:p></o:p></div><div class="MsoNormal"><br /></div><iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/57xzQBuGIQ8?rel=0" width="560"></iframe> <div class="MsoNormal"><br /></div><div class="MsoNormal">Smiling? I hope so!<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Before I describe how this video came together, let me say that not everything I’ve tried in my classes over the years has been such a success. Sometimes things flop. Sometimes things work. This one worked.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">For the last two years, I’ve offered students in my second semester calculus classes an opportunity to earn extra credit. After watching <a href="http://matheatre.com/calculus/"><i>Calculus the Musical</i></a> for the first time last spring, I thought it would be neat to motivate my students to create fun videos or skits about the mathematical concepts they had learned in Calculus II. I asked students to pick a topic that they had learned in the course and create a video that would help other students review the material for the final exam. For example, they could select “tests for series convergence” and create a video reviewing these tests and when to use each of them.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">The first time I gave this extra credit assignment I called it “Calculus the Musical Doc Hodge Style.” (My students that semester had given me the title of Doc Hodge.) I had no takers on the video, but one group did create a fun song with calculus words. This was nice, but it wasn’t something that could easily be shared with others to inspire them to learn math. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">This year, my students took it to the next level. One student wrote a song about l'Hôpital’s rule. Then she found two other students in the course who could sing well and a host of students willing to be the dancers in the video. Lastly, the editors of the video (also students) put everything together. The video was premiered to our class with theater-style lighting and programs. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">From a teacher’s standpoint, three things stand out to me when watching this video: (a) trust, (b) excitement, and (c) learning. The students had to trust each other to be able to work together on such a big project, especially one where they had to sing and dance. They also had to be excited about the subject matter to have this much fun creating the video. The best part was that they showed in the video that they had learned something well enough to create a video with words that made mathematical sense. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">My last comment is that at the <a href="http://www.unomaha.edu/">University of Nebraska Omaha</a>, l'Hôpital’s rule is not a topic first learned in Calculus II. Instead, it is first taught with limits and used extensively in Calculus I. Isn’t it interesting that the students cited <i>learning</i> this in Calculus II (an inquiry-based course) and not in Calculus I? Just something to ponder…</div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com1tag:blogger.com,1999:blog-5816649486576881540.post-30822744048895186312013-05-29T06:06:00.000-07:002013-07-06T17:15:45.663-07:00What the Heck Is IBL?<span style="font-family: inherit;"><i>by Dana Ernst</i></span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Perhaps it’s the company we keep, but it seems like more and more mathematics teachers are interested in inquiry-based learning (IBL). The “big” IBL conference is the annual <a href="http://legacyrlmoore.org/events.html">Legacy of R. L. Moore Conference</a>. This year’s conference takes place June 13-15 in Austin, TX. This will be my fourth Legacy conference and Angie’s fifth. I enjoy all the conferences that I attend, but the Legacy conference is easily my favorite. </span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">It’s amazing to be around so many people who are passionate about student-centered learning. Attendance at the Legacy conference has continued to grow, and each year there are more opportunities to learn about IBL.</span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">Despite the growing popularity, we often get asked, “What the heck is IBL?” Let us begin by stating that this is a really difficult question to answer! Both Angie and I have had a lot of conversations (with each other and with others) about this topic and it’s clear that not everyone agrees on what qualifies as IBL. Furthermore, IBL manifests itself differently in different contexts. </span><br /><span style="font-family: inherit;"><br /></span><span style="font-family: inherit;">In particular, an IBL practitioner often modifies his/her approach from one class to the next. Despite the difficulty in nailing down exactly what IBL actually is, we’ll take a stab at answering this question and share our perspective. We’ll speak in general terms, but in future posts we plan to discuss the nuts and bolts of what an IBL approach might look like for a proof-based course versus a calculus course. Okay, here we go.</span><br /><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">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 think like mathematicians and to acquire their own knowledge by creating/discovering mathematics. <o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">For us, the guiding principle of IBL is the following question:<o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoQuote"><span style="font-family: inherit;"><i>Where do I draw the line between content I must impart to my students versus the content they can produce independently?</i><o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">There are so many ways one could address this question in various contexts, which is the main reason that answering the “what is IBL?” question is so darn hard.<o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">According to the <a href="http://www.inquirybasedlearning.org/?page=What_is_IBL">Academy of Inquiry-Based Learning</a>, IBL is a learner-centered mode of instruction. Boiled down to its essence, IBL is a method of teaching that engages students in sense-making activities. Students are given tasks requiring them to solve problems, conjecture, experiment, explore, create, and communicate</span><span style="font-family: Cambria, serif; font-size: 12pt;">—</span><span style="font-family: inherit;">all those wonderful skills and habits of mind that mathematicians engage in regularly. 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.</span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;"><a href="http://faculty.salisbury.edu/~elmay/">E. Lee May</a>(Salisbury State University) may have said it best:<o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoQuote"><span style="font-family: inherit;"><i>Inquiry-based learning (IBL) is a method of instruction that places the student, the subject, and their interaction at the center of the learning experience. At the same time, it transforms the role of the teacher from that of dispensing knowledge to one of facilitating learning. It repositions him or her, physically, from the front and center of the classroom to someplace in the middle or back of it, as it subtly yet significantly increases his or her involvement in the thought-processes of the students.</i><o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">Perhaps this is sufficiently vague, but we believe that there are two essential elements to IBL. Students should as much as possible be responsible for:</span></div><div class="MsoNormal"></div><ul><li><span style="font-family: inherit; text-indent: -0.25in;">guiding the acquisition of knowledge and</span></li><li><span style="font-family: inherit; text-indent: -0.25in;">validating the ideas presented. (Students should not, that is, be looking to the instructor as the sole authority.)</span></li></ul><br /><div class="MsoNormal"><span style="font-family: inherit;">In a recent blog post titled <a href="http://theronhitchman.wordpress.com/2013/05/10/when-are-you-doing-ibl/">When are you doing IBL?</a>, <a href="http://www.uni.edu/theron/">TJ Hitchman</a>proposes a definition of IBL that expands on these two key elements. <o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: inherit;"><br /></span></div><h3>The Moore Method</h3><div><br /></div><h1><span style="font-family: inherit; font-size: small;"><o:p></o:p></span></h1><div class="MsoNormal"><span style="font-family: inherit;">IBL has its roots in an instructional delivery method known as the <a href="http://legacyrlmoore.org/reference/mahavier1.html">Moore Method</a>(sometimes referred to as the Texas Method), named after <a href="http://legacyrlmoore.org/method.html">R. L. Moore</a>. In the words of J. Parker:<o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoQuote"><span style="font-family: inherit;"><i>Robert Lee Moore (1882-1974) was a towering figure in twentieth century mathematics, internationally recognized as founder of his own school of topology, which produced some of the most significant mathematicians in that field. The 50 students he guided to their PhDs can today claim 1,678 doctoral descendants. Many of them are still teaching courses in the style of their mentor, known universally as the Moore Method, which he devised. Its principal edicts virtually prohibit students from using textbooks during the learning process, call for only the briefest of lectures in class and demand no collaboration or conferring between classmates. (Exceptions were Moore's calculus and analytic geometry courses in which textbooks were used for setting problems. His doctoral students were allowed to refer to the literature mainly to ensure their theses were original.) It is in essence a Socratic method that encourages students to solve problems using their own skills of critical analysis and creativity. Moore summed it up in just eleven words: 'That student is taught the best who is told the least.'</i><o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><span style="font-family: inherit;">Loosely speaking, the majority of a Moore Method course consists of students presenting proofs/solutions that they have produced independently from material provided by the instructor. In a traditional Moore Method course, students are discouraged, in fact forbidden, to collaborate. Variations of the Moore Method take many forms and are often referred to by the generic name "modified-Moore method." In particular, one modification I make is that I not only allow students to work together, I encourage it. The Moore Method or one of its modifications is typically associated with pedagogies including inquiry-based, discovery-based, student-centered, Socratic, and constructivist learning. For more detailed information, including history, of Moore and his method, check out <a href="http://legacyrlmoore.org/reference/quick_start-3.pdf"><i>A Quick-Start Guide to the Moore Method</i></a>. <o:p></o:p></span></div><div class="MsoNormal"><span style="font-family: inherit;"><br /></span></div><h3><span style="font-family: inherit;">The Big Picture</span></h3><div><span style="font-family: inherit;"><br /></span></div><h1><span style="font-family: inherit; font-size: small;"><o:p></o:p></span></h1><div class="MsoNormal"><span style="font-family: inherit;">(Partly adopted from <a href="http://www2.kenyon.edu/Depts/Math/schumacherc/public_html/Professional/Research/Zero/guide.pdf"><i>Chapter Zero Instructor Resource Manual</i></a><i> </i>by <a href="http://www2.kenyon.edu/Depts/Math/schumacherc/public_html/">Carol Schumacher</a>) While it is generally agreed that a modified-Moore Method approach qualifies as IBL, we believe that IBL encompasses so much more (no pun intended). In general, one of the major goals of IBL is to make the students independent of the instructor. Nothing else that we teach them will be half so valuable or powerful as the ability to reach conclusions by reasoning logically and being able to justify those conclusions in clear, persuasive language. We want our students to experience the unmistakable feeling that comes when one truly understands something. For many students, the only way they know whether they are “getting it” comes from the grade they make on an exam. The goal is for our students to become less reliant on such externals. Running an effective IBL classroom can seem a little chaotic at times, but when it is working well, it’s amazing. <a href="http://www.stanyoshinobu.com/">Stan Yoshinobu</a> once said:<o:p></o:p></span></div><div class="MsoNormal"><br /></div><div class="MsoQuote"><span style="font-family: inherit;"><i>It's jazz. We have the chord changes as a basic plan but we go with the flow and adjust in real time.</i><o:p></o:p></span></div><div class="MsoQuote"><span style="font-family: inherit;"><i><br /></i></span></div><h3>IBL Resources</h3><div><br /></div><h1><span style="font-family: inherit; font-size: small;"><o:p></o:p></span></h1><div class="MsoNormal"><span style="font-family: inherit;">Want to know more? Below is a list of IBL-related resources.</span></div><div class="MsoNormal"></div><ul><li><span style="font-family: inherit; text-indent: -0.25in;">The </span><a href="http://www.inquirybasedlearning.org/" style="font-family: inherit; text-indent: -0.25in;">Academy of Inquiry-Based Learning</a><span style="font-family: inherit; text-indent: -0.25in;">is a hub for IBL in mathematics.</span></li><li><a href="http://www.youtube.com/user/AcademyIBL" style="font-family: inherit; text-indent: -0.25in;">AIBL’s YouTube Channel</a><span style="font-family: inherit; text-indent: -0.25in;"> has a list of IBL-related videos. </span><a href="http://theiblblog.blogspot.com/" style="font-family: inherit; text-indent: -0.25in;">The IBL Blog</a><span style="font-family: inherit; text-indent: -0.25in;"> focuses on promoting the use of IBL methods in the classroom at the college, secondary, and elementary school levels. Sponsored by AIBL.</span></li><li><span style="font-family: inherit; text-indent: -0.25in;">You can find Dana’s blog posts related to IBL </span><a href="http://danaernst.com/tag/inquiry-based-learning/" style="font-family: inherit; text-indent: -0.25in;">here</a><span style="font-family: inherit; text-indent: -0.25in;">.</span></li><li><span style="font-family: inherit; text-indent: -0.25in;">The </span><a href="https://plus.google.com/communities/107762594334871181831" style="font-family: inherit; text-indent: -0.25in;">Inquiry-Based Learning in Mathematics Community on Google+</a><span style="font-family: inherit; text-indent: -0.25in;"> provides a forum for discussing IBL. This is a great place to ask questions.</span></li><li><span style="font-family: inherit; text-indent: -0.25in;">The </span><a href="http://www.jiblm.org/" style="font-family: inherit; text-indent: -0.25in;">Journal of Inquiry-Based Learning in Mathematics</a><span style="font-family: inherit; text-indent: -0.25in;"> publishes university-level IBL course notes that are free, refereed, and classroom-tested.</span></li><li><span style="font-family: inherit; text-indent: -0.25in;">The </span><a href="http://eduadvance.org/" style="font-family: inherit; text-indent: -0.25in;">Educational Advancement Foundation</a><span style="font-family: inherit; text-indent: -0.25in;"> is a philanthropic organization that supports the development and implementation of IBL and the preservation and dissemination of the Moore method.</span></li></ul><br /><div class="MsoNormal"><o:p><span style="font-family: inherit;"> </span></o:p><span style="font-family: inherit;">What is IBL to you?</span></div><div class="MsoNormal"><o:p></o:p></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com1tag:blogger.com,1999:blog-5816649486576881540.post-3801826263219277032013-04-25T09:38:00.001-07:002013-05-30T09:53:00.842-07:00Two Worlds Collide: Mathematics and Mathematics Education<i>by Angie Hodge</i><br /><br /><a href="http://archives.math.utk.edu/projnext/">Project NExT</a> (New Experiences for Teachers) is a professional development program for new or recent Ph.D.s in the mathematical sciences. It addresses all aspects of an academic career including teaching, research, and service. It also provides the project fellows with a network of peers and mentors.<br /><br />New fellows and the previous year’s fellows come together at an ice cream social every year at <a href="http://www.maa.org/mathfest/">MAA MathFest</a>. At this point, the new fellows have spent a week in sessions learning about ways to teach math and ways to conquer the obstacles they may face as new mathematics/mathematics education professors. The ice cream social is the end of the initial training and the beginning of their connecting into a social network of NExTers, or Dots, as some people call them. (We’ll explain what the heck a Dot is in a later post.)<br /><br />At the social in August 2008, I was there as an “experienced new fellow” to greet the new fellows who had just finished this intense week of training. I met Dana at this ice cream social.<br /><br />It wasn’t math that originally brought us together as colleagues. Instead, it was mutual friends, a love of exercise, and our chatty nature. Dana and I spent several hours bonding through food, working out, and attending a session or two.<br /><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://2.bp.blogspot.com/-M170IVxjp-g/UXkmB3C6pwI/AAAAAAAAHB4/_vkCxEhvSUM/s1600/photo+(1).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-M170IVxjp-g/UXkmB3C6pwI/AAAAAAAAHB4/_vkCxEhvSUM/s1600/photo+(1).JPG" height="320" width="226" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; color: #222222; text-align: start;"><span style="font-family: Times, Times New Roman, serif; font-size: small;"><i>Dana and Angie at the start of a 50K trail ultra marathon in Flagstaff, AZ</i></span></span></td></tr></tbody></table>Once again, Project NExT succeeded in its “secret plot” to bring people together to do lots of cool things. One result was an invitation to the <a href="http://legacyrlmoore.org/events.html">Legacy of R. L. Moore Conference</a> each year, and it was there that we began to talk about math education. (We highly recommend going!!!) We will keep the details to a minimum until later posts, but the short version is that this conference inspired transformation in our teaching. This is where math and math education collided. Our common interest in <a href="http://www.inquirybasedlearning.org/?page=What_is_IBL">inquiry-based learning</a> (IBL), together with our diverse perspectives, inspired several collaborative projects centered on the <a href="http://en.wikipedia.org/wiki/Scholarship_of_Teaching_and_Learning">scholarship of teaching and learning</a> (SoTL).<br /><br />In addition to a handful of small research projects, we have also given several joint talks and organized workshops and contributed paper sessions. Because of our active involvement in the IBL community, we were recently designated as Special Projects Coordinators for the <a href="http://www.inquirybasedlearning.org/">Academy of Inquiry-Based Learning</a>. Our duties include spreading the word about IBL and continuing to organize workshops and conferences. We are both extremely passionate about IBL and we’re looking forward to playing an active role in inspiring others to take a more student-centered approach to teaching.<br /><br /><h3>Coming Up Next</h3><div><br /></div>What is inquiry-based learning (IBL)? Why use IBL? How can you incorporate more IBL into the classes that you teach? In the next few posts, we will address all of these questions, as well as discuss a few different examples of what an IBL classroom might look like in practice.Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com0tag:blogger.com,1999:blog-5816649486576881540.post-66688518161582274632013-04-10T06:46:00.000-07:002013-06-06T15:26:17.031-07:00Welcome to Math Ed Matters<i>by Dana Ernst and Angie Hodge</i><br /><div class="MsoNormal"><br />Greetings! Thanks for stopping by to read our first blog post on <a href="http://maamathedmatters.blogspot.com/"><i>Math Ed Matters</i></a>. <o:p></o:p></div><div class="MsoNormal"><br /></div><h3>What’s this blog all about?</h3><div><br /></div><i>Math Ed Matters</i> is a (roughly) monthly column sponsored by the <a href="http://www.maa.org/">Mathematical Association of America</a> authored by <a href="http://danaernst.com/">Dana Ernst</a> and <a href="http://www.unomaha.edu/math/people/hodge/">Angie Hodge</a>. Dana is a mathematician with interests in mathematics education and Angie is a mathematics education specialist. The column will explore topics and current events related to undergraduate mathematics education. Posts will aim to inspire, provoke deep thought, and provide ideas for the mathematics—and mathematics education—classroom. The coauthors' interest in and engagement with <a href="http://www.inquirybasedlearning.org/?page=What_is_IBL">inquiry-based learning</a> (IBL) will color the column's content.<br /><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Thanks to the <a href="http://www.maa.org/">Mathematical Association of America</a> for giving us the opportunity to share our musings with you.<o:p></o:p></div><h1><o:p></o:p></h1><h2><o:p></o:p></h2><h3>About the authors</h3><div><br /></div><h4>Dana Ernst</h4><div><br /></div><div class="MsoNormal">My name is Dana Ernst, and I am an assistant professor in the <a href="http://nau.edu/cefns/natsci/math/">Department of Mathematics and Statistics</a> at <a href="http://nau.edu/">Northern Arizona University</a> (NAU) in <a href="https://maps.google.com/maps?q=Flagstaff,+AZ&hl=en&sll=37.0625,-95.677068&sspn=57.161276,109.511719&oq=fl&hnear=Flagstaff,+Coconino,+Arizona&t=m&z=12">Flagstaff, AZ</a>. I am also a 2008 Fellow of <a href="http://archives.math.utk.edu/projnext/">Project NExT</a>, which is a professional development program of the <a href="http://maa.org/">MAA</a> for new or recent Ph.D.s in the mathematical sciences.</div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I completed my B.S. in mathematics at <a href="http://math.gmu.edu/">George Mason University</a>and then went on to complete my M.S. at NAU in 2000. After spending a year as an instructor at NAU, I worked for two years as a full-time member of the math faculty at <a href="http://www.frontrange.edu/">Front Range Community College</a> in Boulder and Longmont, CO. In August 2003, I returned to graduate school and started working on my Ph.D. at <a href="http://www.colorado.edu/">University of Colorado at Boulder</a>. Under the guidance of <a href="http://math.colorado.edu/~rmg/">Richard M. Green</a>, I finished my Ph.D. in the summer of 2008.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">After completing my Ph.D., I spent four years as an assistant professor at <a href="http://plymouth.edu/">Plymouth State University</a> (PSU). While at PSU, I was twice named the Plymouth State University Distinguished Professor of Mathematics, an honor determined by the mathematics majors. Moreover, during my last semester at PSU, I was selected as the university’s sole nominee for the <a href="http://www.edies.org/">New Hampshire Excellence in Education Award</a>, which is a statewide teaching award. In August of 2012, I returned to NAU (yay, my dream job!) and started working as an assistant professor.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-rnO1mGSUB8w/UWgGWxBTmkI/AAAAAAAAG9w/mYWvFVyGBWs/s1600/Dana.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-rnO1mGSUB8w/UWgGWxBTmkI/AAAAAAAAG9w/mYWvFVyGBWs/s1600/Dana.jpg" height="320" width="157" /></a></div><br /></div><div class="MsoNormal">My primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, I study the combinatorics of <a href="http://en.wikipedia.org/wiki/Coxeter_group">Coxeter groups</a> and their associated <a href="http://en.wikipedia.org/wiki/Hecke_algebra">Hecke algebras</a>, <a href="http://en.wikipedia.org/wiki/Kazhdan%E2%80%93Lusztig_polynomial">Kazhdan-Lusztig theory</a>, (generalized) <a href="http://en.wikipedia.org/wiki/Temperley-Lieb_algebra">Temperley-Lieb algebras</a>, <a href="http://en.wikipedia.org/wiki/Planar_algebra">diagram algebras</a>, and <a href="http://www.emis.de/journals/SLC/books/heaps.ps">heaps of pieces</a>. By employing combinatorial tools such as diagram algebras and heaps of pieces, it is possible to gain insight into algebraic structures associated with Coxeter groups, and, conversely, the corresponding structure theory can often lead to surprising combinatorial results. The combinatorial nature of my research naturally lends itself to collaborations with undergraduate students, and my goal is to incorporate undergraduates into my research as much as possible. See my <a href="http://danaernst.com/scholarship/">scholarship page</a> for more information. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I am also passionate about mathematics education. In particular, I am interested in <a href="http://www.inquirybasedlearning.org/?page=What_is_IBL">inquiry-based learning</a> (IBL) and the <a href="http://www.discovery.utexas.edu/rlm/method.html">Moore method</a> for teaching mathematics. This educational paradigm has transformed my teaching. I am currently a Special Projects Coordinator for the <a href="http://www.inquirybasedlearning.org/">Academy of Inquiry-Based Learning</a> and a mentor for several new IBL practitioners. Moreover, I give <a href="http://danaernst.com/category/talks/">talks</a> and organize workshops on the benefits of IBL as well as the nuts and bolts of how to implement this approach in the mathematics classroom. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I am interested in using technology to enhance the teaching and learning of mathematics. Specifically, I choose free and <a href="http://en.wikipedia.org/wiki/Open_source">open-source</a>software and technologies when they are available. For example, I have been incorporating <a href="http://sagemath.org/">Sage</a> and <a href="http://www.geogebra.org/">GeoGebra</a> into my teaching. Sage is a free, open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface. For examples of a few of the cool things you can do with Sage, check out <a href="http://wiki.sagemath.org/interact">this page</a>. According to their webpage, GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics, and calculus in one easy-to-use package. There are tons of awesome GeoGebra examples located <a href="http://www.geogebratube.org/">here</a>.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">In addition to using free and open-source software, I am inspired by the recent <a href="http://iae-pedia.org/Open_Source_Textbooks">open-source textbook</a> movement and I strongly believe that educators should choose free, open-source, or low-cost textbooks when possible. For a selection of free and/or open-source textbooks, see my list located <a href="http://danaernst.com/resources/free-and-open-source-textbooks/">here</a>. Also, take a peek at <a href="http://buzzard.ups.edu/">Rob Beezer’s</a> selection on <a href="http://linear.ups.edu/opentexts.html">this page</a>.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I also maintain a <a href="http://danaernst.com/">personal blog</a>, which is part of the <a href="http://boolesrings.org/">Booles' Rings</a> network of academic home pages/blogs. Moreover, I am active on <a href="http://plus.google.com/">Google+</a>and post regularly about mathematics, teaching, and technology. You can find my G+ profile <a href="https://plus.google.com/107135522210834007871/posts">here</a>. In addition, I occasionally post about my cycling, trailing running, and rock climbing adventures on my <a href="http://elevationgain.danaernst.com/">Elevation Gain blog</a>. Lastly, I am a husband and a father of two incredible sons. Oh, I enjoy drinking copious amounts of coffee, too.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-gU19DDvfbiE/UWgGQijCOwI/AAAAAAAAG9o/Oqv5vx7ccTM/s1600/Dana2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-gU19DDvfbiE/UWgGQijCOwI/AAAAAAAAG9o/Oqv5vx7ccTM/s1600/Dana2.jpg" height="227" width="320" /></a></div><br /></div><div class="MsoNormal"><o:p></o:p></div><h2><o:p></o:p></h2><h4>Angie Hodge</h4><div><br /></div><div class="MsoNormal">Hi all! I am an assistant (soon to be associate) professor of mathematics and the <a href="http://stories.nufoundation.org/node/899">Haddix Community Chair of Mathematics Education</a> at the <a href="http://www.unomaha.edu/">University of Nebraska Omaha</a>. I earned my Ph.D. from <a href="http://www.edci.purdue.edu/mathematics_education/">Purdue in mathematics education</a> in 2007 and my M.S. in <a href="http://www.math.purdue.edu/">mathematics also from Purdue University</a>in 2004. I am also a 2007 Fellow of <a href="http://archives.math.utk.edu/projnext/">Project NExT</a>. I have been fortunate to find a career path that has allowed me to combine my mathematics education research with my passion for teaching mathematics courses.</div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">In a nutshell, I teach mathematics courses with one of my main goals being to get people excited about mathematics (and of course help them learn mathematics deeply). Yes, excited about mathematics! Although I started out as a very traditional mathematics instructor, I now try all sorts of different things in my classroom from simple group work to <a href="http://www.inquirybasedlearning.org/?page=What_is_IBL">inquiry-based learning</a> with very little lecture. In this blog, I will tell you what I have learned from my adventures in teaching everything from traditional mathematics courses to summer workshops for teachers. I will even tell you how and why I use a whistle in my calculus courses.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-t0JenuI1-Uc/UWbEWpfJfLI/AAAAAAAAG8w/o5XmOpHG3_U/s1600/Angie.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-t0JenuI1-Uc/UWbEWpfJfLI/AAAAAAAAG8w/o5XmOpHG3_U/s1600/Angie.JPG" height="228" width="320" /></a></div><br /></div><div class="MsoNormal">In addition, I am involved in a variety of mathematics service work related to inquiry-based learning with a special focus on developing a love of mathematics in others. This includes serving as a Special Projects Coordinator for the Academy of Inquiry-Based Learning, Omaha Area <a href="http://www.mathteacherscircle.org/">Math Teachers’ Circle</a> co-leader, co-leader of a STEM summer camp for at-risk girls (<a href="http://www.girlsinc.org/about/programs/eureka-goldman-sachs-gives.html">EUREKA!</a>), and the co-advisor for the University of Nebraska Omaha’s Math Club. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">In this blog, I will share my journey: successes and flops. My lens is that of a mathematics educator who believes in strong content knowledge, hands-on/minds-on learning, and who strongly believes that collaboration is essential between those who specialize in mathematics and those who specialize in education. <o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">The “human side” of my life also colors the lens through which I view challenges in the classroom. Calling myself a “Mathlete,” I find great pleasure in endurance events such as running ultra marathons. On the softer side, I also enjoy watching college football and basketball, trying new foods, and traveling. <o:p></o:p><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-iAjv88YktRQ/UWbFpyBzCuI/AAAAAAAAG84/Rso4j6grTEU/s1600/Angie+2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-iAjv88YktRQ/UWbFpyBzCuI/AAAAAAAAG84/Rso4j6grTEU/s1600/Angie+2.JPG" height="320" width="245" /></a></div><br /></div><div class="MsoNormal"><h3>Coming Up NExT</h3></div><div><br /></div><div class="MsoNormal">So, how in the world did two people with such different backgrounds meet and what is their academic connection? This question and more will be answered in the next blog, “Two Worlds Collide: Mathematics and Mathematics Education.”</div><div class="MsoNormal"><br /></div><div class="MsoNormal"><o:p></o:p></div><h1><o:p></o:p></h1><h3>Other future posts</h3><div><br /></div><div class="MsoNormal">Here’s a preview of some of our potential upcoming blog posts.<br /><br /><ul><li><span style="text-indent: -0.25in;">History and impact of </span><a href="http://archives.math.utk.edu/projnext/" style="text-indent: -0.25in;">Project NExT</a></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;">Inquiry-Based Learning: What, Why, and How?</span></li><li><span style="text-indent: -0.25in;">How and why did Angie and Dana start implementing an IBL approach?</span></li><li><span style="text-indent: -0.25in;">What's the Buzz? (Calculus Bee)</span></li><li><span style="text-indent: -0.25in;">A recap of the </span><a href="http://legacyrlmoore.org/events.html" style="text-indent: -0.25in;">16th Annual Legacy of R. L. Moore Conference</a><span style="text-indent: -0.25in;">(June 13-15, 2013 in Austin, TX)</span></li><li><span style="text-indent: -0.25in;">A recap of </span><a href="http://www.maa.org/mathfest/" style="text-indent: -0.25in;">MathFest 2013</a><span style="text-indent: -0.25in;"> (July 31-August 3, 2013 in Hartford, CT)</span></li><li><span style="text-indent: -0.25in;">Pivotal Moments: How did Dana and Angie get to where they are now?</span></li></ul></div><div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><o:p></o:p></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><o:p></o:p></div><div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><o:p></o:p></div>Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.com1