Friday, September 12, 2014

A First-timer’s Experience with IBL

a guest post by Ellie Kennedy

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 inquiry-based learning (IBL) seemed like a method that might work for me. So, last spring when I taught discrete math, I used a modified Moore method. I'd like to share my experience as a first-timer and some of what I learned.

Ted Mahavier started me off with a set of notes, and Dana Ernst 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.

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.

I used the felt tip pen idea 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 self-assess, which can be an effective learning tool. 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.

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!

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.

 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.

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.

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.

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!

Friday, August 1, 2014

Teaching Math to Non-Math Teachers

by Angie Hodge

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.

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.

photo credit Lindsay Augustyn
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.

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.

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.

Day 1: Be firm and friendly
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.

Day 2: Persevere (pep talks are a must!)
"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." 

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.

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.

Day 3: The calm before the storm
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.

Day 4: Beware of your first "hit" of hard material
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?

Day 5: Make every moment a teachable moment
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!

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.

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.

Friday, July 11, 2014

Service-Learning and Making a Difference

a guest post by Karl-Dieter Crisman


Crisman at the 17th Annual Legacy of R. L. Moore—Inquiry-Based 
Learning Conference (photo Kirk Tuck/EAF)
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?

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: Service seems useful, and we certainly want learning. But what is service-learning, and what does it have to do with math?

At its core, service-learning involves students participating in some useful service to the community, but in such a way that the service is itself 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.

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 MAA's book on this subject: "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 website. In one survey of attitudes[*], 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."

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:

  • Analyzing energy use and sustainability practices on campus (quantitative reasoning)
  • Assessing volunteer versus state-provided aid in a local fire (intro statistics)
  • Helping local American Diabetes Association focus fundraising (finite math)
  • Tutoring high school precalculus students (calculus)
  • Creating math fun fair games (upper-level math and math ed)
  • Designing a new layout for a food pantry (upper-level modeling)
  • Providing feedback on cash flow for a local non-profit (upper-level modeling)
  • Analyzing (scrubbed) freshman orientation data (upper-level math/stats)
  • Running a math camp for middle-schoolers (graduate students)

A math game event is service; what are your ideas for turning this 
into service-learning?
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 recent special issue of PRIMUS 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 very minimalist website, and other journals in statistics, math ed, and service have related articles on occasion.

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 Gordon College from the start. 

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.

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 the December 2009/January 2010 issue of MAA FOCUS was an inspiration to me).

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.



[*] See the first article in volume 9 (2002) of the Michigan Journal for Community Service Learning.

Monday, June 23, 2014

Fear is the mind-killer

by Dana Ernst

My favorite conference of the year, the Legacy of R. L. Moore — IBL Conference, kicked off last Thursday. The day began for me with an introduction to IBL mini-workshop facilitated by Michael Starbird. For our first activity, Starbird had the participants discuss in small groups the following question.

What do you want your students to keep from their education?


After a few minutes of brainstorming, groups shared their ideas. Here’s the list we generated (I’m paraphrasing):
  • Love of learning
  • Persistence/perseverance
  • Ability to teach yourself
  • Ability to communicate verbally and in writing
  • Independence
  • Self-awareness
  • Self-direction
  • Ability to collaborate
  • Curiosity
  • Confidence
  • Receptivity to different perspectives
  • Appreciation of failure
  • Lack of fear
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.

Upon hearing this, I was immediately reminded of a quote from one of my favorite sci-fi books, Dune.

Fear is the mind-killer.

This line is part of the litany against fear, 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:

I must not fear.
Fear is the mind-killer.
Fear is the little-death that brings total obliteration.
I will face my fear.
I will permit it to pass over me and through me.
And when it has gone past I will turn the inner eye to see its path.
Where the fear has gone there will be nothing.
Only I will remain.

I believe (and there is plenty of evidence to support this) that inquiry-based learning (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?

It might be time for me to add the litany against fear to my syllabi.

Thursday, May 22, 2014

Hooking the Student

a guest post by Jeff Rushall


Six years ago, I told my chair that our Department of Mathematics and Statistics here at Northern Arizona University 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 Cantor sets, magic squares, and Latin squares. 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. 

I was very wrong. 

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. 

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:

  • Hold the seminar on a Friday afternoon. 
  • Give the gathering a snappier name. 
  • Limit the talks to about 30 minutes. 
  • Expose the audience to more than just math to entice their attendance, such as…
  • Interview a faculty member each week.  
We retooled, and in January of 2009, FAMUS (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. 

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 Tower of Hanoi to Euler bricks to the St. Petersburg paradox), on mathematicians (Hilbert, Ramanujan, Erdös, 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. 

But for many students, the highlight of FAMUS is the weekly interview of a faculty member. Structured à la the interviews on the popular Inside the Actors Studio 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. 

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. 

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?). 

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. 

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 Bryn Mawr, Charlie at the University of Montana, and Natalie at the University of Colorado at Boulder). 

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. 

Monday, May 5, 2014

Love Math?

by Angie Hodge

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 math.

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)?

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.

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!

Dr. Betty Love leading a "Meet the Professor" series
talk on operations research.
At the University of Nebraska Omaha (UNO), we kicked off Mathematics Awareness Month by getting to know one of our math professors, Dr. Betty Love, through a "Meet Your Professor" talk. Students got to learn about a UNO math professor both professionally and personally.

The UNO mathematics department also hosted two speakers, Dr. Bob Klein and Dr. Randy Cone. They each gave a "Cool Math Talk" for students and a "Math Teachers' Circle" session for local math teachers. All of these sessions both actively engaged and challenged the audiences.

I also spent four days at the National Council of Teachers of Mathematics national conference. 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 "Hands-on, Minds-on Calculus." 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.

Mathematics Awareness Month for me was capped off with a five-day visit to the University of Colorado at Boulder to discuss ways to engage students in the learning of calculus.

Wow, that was a lot of extra-curricular math for one month. Instead of being exhausted from it, though, I was surprisingly re-energized!

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!

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).

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.

So, what do you do to help others discover a passion for math?

Share your favorite story or technique with us! 

Tuesday, April 1, 2014

Encouraging Students to Tinker

by Dana Ernst

A few days ago I was in my office working on a research problem related to the combinatorics of Coxeter groups. 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.

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 Moebius Noodles, titled "Make Mistakes on Purpose," that contains a wonderful quote by the author Neil Gaiman.
Make interesting mistakes, make amazing mistakes, make glorious and fantastic mistakes.
This quote comes at the very end of Gaiman’s excellent keynote address from the 2012 commencement at the University of the Arts in Philadelphia. (I’ve included the whole address below.)

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.

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.

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.

A few months ago, Stan Yoshinobu addressed this topic over on The IBL Blog in a post titled "Destigmatizing Mistakes." I encourage you to read his whole post, but here is a highlight:
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.
Here are a few related questions I have:
  • How do we encourage students to tinker with mathematics?
  •  How do we destigmatize mistakes in the mathematics classroom?
  • How do we encourage and/or reward risk taking?
  • What are the obstacles to addressing the items above and how do we remove these obstacles?

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.

Here is Gaiman’s keynote address in its entirety. Trust me, it’s worth 20 minutes of your time.


You can find the transcript for his speech here.