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.

Thursday, February 20, 2014

Engaging in Inquiry-Based Learning

by Dana Ernst, Angie Hodge, and TJ Hitchman

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?

It was all smiles at the 14th Legacy of R. L. Moore
Conference in 2011.
Well, wonder no more. This year’s Legacy of R. L. Moore and Inquiry-Based Learning Conference 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 R. L. Moore, for whom the Moore Method is named. The Educational Advancement Foundation, the Mathematical Association of America, and the Academy of Inquiry-Based Learning generously subsidize the conference. If you are unfamiliar with IBL, check out our previous post, "What the Heck is IBL?" 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.

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!

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 Discovering the Art of Mathematics project will kick off the conference with an engaging demonstration of IBL that will be educational to all IBL’ers.

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!

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.

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:

  • My Favorite IBL Activity: Share your favorite IBL activity or group of activities with the participants.
  • IBL Outreach: Share how you use IBL in outreach activities such as Math Teachers’ Circles, Math Student Circles, math clubs, and math camps. 
  • IBL Professional Development: Share how you educate others in the preK-16 educational community about IBL. 
  • Nuts & Bolts: Share your most successful (or not so successful) approaches to engaging students, grading, assessment, and marketing in an IBL classroom. 
  • General IBL: Share other engaging IBL topics that do not fit into any of the above sessions.

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).

To submit a proposal for a talk or workshop session, send the following information to Angie Hodge (amhodge@unomaha.edu), TJ Hitchman (theron.hitchman@uni.edu), and Norma Flores (nflores@edu-adv-foundation.org) with the subject line “Legacy 2014 Abstract Submission.”

Name:
Affiliation:
Title of talk or presentation:
Abstract (200 words or less):
Email:
Preferred Session:

Description of how the proposed session will be active or engaging for the participants (50 words or less):

Registration is also open and is very affordable! When else can you get registration, most meals, AND hotel for under $200? What a steal!!!

The 17th 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!

Friday, January 10, 2014

Math Ed Mania at the JMM

by Dana Ernst and Angie Hodge

2013 JMM Exhibit Hall OpeningIn our previous post, we highlighted numerous talks and events with an inquiry-based learning theme that will be taking place at the upcoming Joint Mathematics Meetings in Baltimore.

However, there are lots of mathematics education-focused sessions that we didn’t mention. Of course, you can browse the JMM Program, 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.

Nearly all of the MAA Contributed Paper Sessions 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.

Flipping the Classroom
  • Part I: Friday January 17, 2014, 8:00 a.m.-10:55 a.m.
  • Part II: Friday January 17, 2014, 1:00 p.m.-5:55 p.m.
  • Part III: Saturday January 18, 2014, 8:00 a.m.-10:55 a.m.
  • Part IV: Saturday January 18, 2014, 1:00 p.m.-2:35 p.m.

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 Math Ed Matters posts. Robert Talbert 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.

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.

Assessing Student Learning: Alternative Approaches
  • Part I: Wednesday January 15, 2014, 8:00 a.m.-10:55 a.m.
  • Part II: Wednesday January 15, 2014, 2:15 p.m.-5:50 p.m.
  • Part III: Thursday January 16, 2014, 8:00 a.m.-11:55 a.m.

Assessment of Proof Writing Throughout the Mathematics Major
  • One Session: Thursday January 16, 2014, 8:00 a.m.-9:15 a.m.

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.

Bridging the Gap: Designing an Introduction to Proofs Course
  • One Session: Thursday January 16, 2014, 7:40 a.m.-11:55 a.m.

Innovative and Effective Ways to Teach Linear Algebra
  • Part I: Friday January 17, 2014, 8:00 a.m.-10:55 a.m.
  • Part II: Friday January 17, 2014, 1:00 p.m.-2:55 p.m.

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!

AMS Session on Mathematics Education
  • One Session: Thursday January 16, 2014, 1:00 p.m.-3:55 p.m.

AMS Special Session on The Changing Education of Preservice Teachers in Light of the Common Core
  • Part I: Wednesday January 15, 2014, 8:00 a.m.-10:50 a.m.
  • Part II: Wednesday January 15, 2014, 2:15 p.m.-6:05 p.m.
  • Part III: Thursday January 16, 2014, 8:00 a.m.-11:50 a.m

AMS Special Session on Outreach for Mathematically Talented Youth
  • Part I: Friday January 17, 2014, 1:00 p.m.-5:50 p.m.
  • Part II: Saturday January 18, 2014, 8:00 a.m.-10:50 a.m.

We hope to see y’all at the JMM!!! If you see us, please stop and chat.

What sessions are you looking forward to attending?

Monday, January 6, 2014

What's So Good about IBL Anyway?

a guest post by Susan Ruff


I recently came across a striking article: “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching.” 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.

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 IBL and similar pedagogies may be too challenging for the weakest 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.

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.

One of the challenges with past research is articulated well by both Norman & Schmidt (2000) and Prince (2004): 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 personality of the instructor. 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.

Fortunately, the exciting recent study by Laursen et al. 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.

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?

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.

So, what’s so good about IBL, anyway? And what variables do you hypothesize are most important to that success?


Laursen, S., Hassi, M., Kogan, M., Hunter, A., & Weston, T., (2011). 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. Assessment & Evaluation Center for Inquiry-Based Learning in Mathematics.
Norman, G.R., & Schmidt, H. G., (2000). “Effectiveness of problem-based learningcurricula: theory, practice and paper darts,” Medical Education, 34(9):721-728.
Prince, M., (2004). “Does Active Learning Work? A Review of the Research,” Journal of Engineering Education, 93(3): 223-231.

Monday, December 16, 2013

The JMM: What's Mathematics Education Got to Do with It?

by Dana Ernst and Angie Hodge

In just a few weeks, thousands of mathematicians and mathematics educators will descend on Baltimore for the 2014 Joint Mathematics Meetings. The JMM is a joint venture between the American Mathematical Society and the Mathematical Association of America. 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.

Around 2013 JMMIf 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 conference program makes it clear that there is something for everyone. In fact, the number of opportunities is a bit overwhelming.

The handy JMM Personal Scheduler 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.

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 inquiry-based learning. The Legacy of R. L. Moore has compiled a similar list.

Wednesday January 15, 2014 

8:40am A Modified-Moore Method in Precalculus
Brad Bailey, University of North Georgia
Room 339, Baltimore Convention Center

9:40am The Sound of Mathematics: Pythagorean Music and Beyond
Randall E. Cone, Virginia Military Institute
Room 338, Baltimore Convention Center

10:00am Collaborative Assessments 
Brian Katz, Augustana College
Room 340, Baltimore Convention Center

3:00pm Using Inquiry-Based Learning in Courses for Prospective Elementary Teachers 
Stan Yoshinobu, Cal Poly San Luis Obispo
Room 347, Baltimore Convention Center

3:20pm Effective Thinking and Mathematics
Michael Starbird, University of Texas at Austin
Ballrooms I & II 4th Floor, Baltimore Convention Center

4:15pm Two sets of Moore-Method Analysis notes and two websites that support them
William T. Mahavier, Lamar University
Room 349, Baltimore Convention Center
4:55pm Gently Introducing IBL in Advanced Calculus 
Robert W. Vallin, Slippery Rock University
Room 349, Baltimore Convention Center

Thursday January 16, 2014 

9:00 – 11:50am MAA Invited Paper Session on Mathematics and Effective Thinking, I 
Edward Burger, Southwestern University;
J. Michael Pearson, MAA;
Stan Yoshinobu, Cal Poly San Luis Obispo;
Jodi Cotten, Westchester Community College, Valhalla, NY;
Sandra Laursen, University of Colorado Boulder;
David Bressoud, Macalester College
Room 307, Baltimore Convention Center

9:20am Developing Reinvention Materials in Ring Theory: Analysis of Student's Mathematical Activity 
John Paul Cook, University of Science and Arts of Oklahoma
Brian Katz, Augustana College
Milos Savic, University of Oklahoma
Room 341, Baltimore Convention Center

10:30am An IBL Approach to Advanced Calculus that Incorporates Proficiency 
Scott Beaver, Western Oregon University
Room 348, Baltimore Convention Center

10:40am Successes and Failures of Inquiry-Based Learning in an Introduction to Proofs Course 
Rachel Esselstein, California State Univ. Monterey Bay
Room 339, Baltimore Convention Center

10:40am Holistic, Diagnostic Grading Rubric for Student Presentations in an IBL Geometry Course
Nina Juliana White, University of Michigan
Room 340, Baltimore Convention Center

11:00am How Important is the Final Answer? Using Inquiry-Based Learning in an Introductory Proofs Course 
Susan Crook, Loras College
Room 339, Baltimore Convention Center

11:20am Using an Inquiry-Based Learning Approach in Introduction to Proofs and Advanced Calculus Course 
Jim Fulmer and Tom McMillan, University of Arkansas at Little Rock
Room 339, Baltimore Convention Center

1:00 – 4:00pm MAA Invited Paper Session on Mathematics and Effective Thinking, II 
Paul Zorn, St. Olaf College;
Katherine Socha, Math for America;
Deborah J. Bergstrand, Swarthmore College;
Carol Schumacher, Kenyon College;
Francis Edward Su, Harvey Mudd College
Room 307, Baltimore Convention Center

Friday, January 17, 2014

8:45am An Inquiry-Based Approach to Teaching Parameterization 
Fabiana Cardetti, University of Connecticut;
Nicole DeMatteo, Providence College;
Jonathan Dollar, Emory University;
Gabriel Feinberg, Haverford College
Room 348, Baltimore Convention Center

1:00pm Group Work & Modified Moore Method in Flipping Calculus 1 
Karen Bliss, Quinnipiac University
Room 337, Baltimore Convention Center

2:40pm Flipping Intermediate Algebra 
Jacqueline A. Jensen-Vallin, Slippery Rock University
Room 337, Baltimore Convention Center

Saturday, January 18, 2014

1:45pm - 1:55pm Creating a Duel-Credit/Dual Enrollment "OnRamps" Precalculus Course to Enhance the College Readiness of High School and Community College Students
Mark Daniels, University of Texas at Austin
Room 347, Baltimore Convention Center

2:00pm How About a Free Set of IBL Calculus Notes that Covers all of Calculus I, II and III? 
William T. Mahavier, Lamar University
Room 340, Baltimore Convention Center

2:30pm Inquiry-Based Problem Solving Strategies through Interactive Approaches for Engaging Students in Mathematics
Padmanabhan Seshaiyer and Jennifer Suh, George Mason University
Room 314, Baltimore Convention Center

3:00pm Resources to Aid the Transition into an IBL Mathematics Course 
Gabriel Feinberg, Haverford College;
Lily An, Williams College;
Victoria Lewis, California State University Sacramento;
Fabiana Cardetti, University of Connecticut
Room 347, Baltimore Convention Center

3:15pm Inquiry-Based Learning and Hybrid Inquiry-Based Learning in College Geometry 
Ali S. Shaqlaih, University of North Texas at Dallas
Room 347, Baltimore Convention Center

In addition to the sessions listed above, we also encourage you to visit the Educational Advancement Foundation'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? Listen to a short podcast 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).

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 Undergraduate Poster Session, 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!

Wednesday, October 30, 2013

Group Work: Be Predictably Unpredictable

By Angie Hodge

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.


April Halcomb asked a great question, however, in response to my last blog entry: “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?”

This is, as I said, a great question. If I had the answer, I'd be rich. So I don't have it all 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.

Listen carefully. 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.

Do the random walk. 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.

Stop them if need be. I use my whistle 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.

Allow some chatter. 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.

Challenge them. 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. Knowing that they will need help from others to finish the work also encourages students to keep the random chatter to a minimum. Better make some headway while the necessary human resources are available!

Let some work alone. 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.

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.  

Thursday, September 19, 2013

“It’s Time to Blow the Whistle”

By Angie Hodge

I’m three weeks into my Calculus I course, and it’s finally time to blow the whistle! Yay!!!

Why am I so excited about this? Am I serious? Well…

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”for lack of a better termis collaborative learning or group work, which I currently use in a class of 40 calculus students.

I've even gotten money from our dean to transform one of the traditional classrooms here a University of Nebraska Omaha into one that promotes group work with 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.

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!

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 only humans with whom they may discuss them. That's probably why they were in the room early jabbering about math!

But I still haven’t told you about the whistle.

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.”

About a year ago, when a inquiry-based calculus class of more than 40 students got rather noisy, I jokingly said that 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.

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!!!

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.

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, knowing that one quick blow of the whistle is all it takes for the class to regroup!