Do We Get to Work at the Board Today?

By Steven Klee, Contributing Editor, Seattle University

When I first started incorporating active learning in the classroom, I struggled with getting my students to buy into being active.  I made worksheets, put the students in groups, and excitedly set them off to discover and play with mathematical ideas.  Despite this, many students were inclined to sit silently in a group of four and work on the problems on their own.

But really, who can blame them? First, this propensity towards solitude can be explained by basic human nature: specifically, the fear of being wrong.  We don’t want to be wrong. At least, we don’t want to be wrong in front of other people.  From that perspective, working alone is safe and comfortable.  We should view our job as teachers as one of helping our students overcome this basic human inclination, as opposed to viewing it as a failure or shortcoming on their part.

Beyond this, the desire to work alone can be attributed to culture and expectations.  Many students’ formative educational years have been spent sitting silently in desks passively absorbing lectures.  If they feel this is what is expected of a math class, then it is natural for them to continue to sit silently, even if the environment is meant to be collaborative.  Of course, it is not my intention to imply that this is an issue that is entirely the students’ fault – maybe my questions weren’t sufficiently open-ended, maybe I wasn’t doing a good enough job at “selling it,” maybe the students just like working alone, maybe, maybe, maybe… The list goes on.

I tried some of my standard tricks to foster communication among the students.  I would prepare impassioned pep talks about the benefits of working with your peers. This technique flopped for obvious reasons – no one wants to listen to what they are told is good for them.  Otherwise, cigarette companies and fast food restaurants would go bankrupt and I would be much more diligent about flossing.  I’d try to lighten the mood, saying “this isn’t a library, you’re welcome to talk to one another.” I’d give a difficult problem and leave the room to get a drink of water, forcing the students to rely on one another. These strategies helped, but never served to create the classroom of my dreams – one where students discuss math problems at such a frenzied pace that time ceases to exist; one that causes passersby to wonder whether we are having a math class or developing some bizarre scientific improv comedy troupe.

Over time, I continued to reflect on my own teaching and sought advice from more experienced practitioners of active learning.  As a result, I have developed a few strategies that have been effective in my classrooms. One of the most effective strategies for me has come from eliminating those pesky desks that keep getting in the way of my students’ learning.

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The Third Year of “On Teaching and Learning Mathematics”

By Benjamin Braun, Editor-in-Chief, University of Kentucky

Summer 2017 brought the third anniversary of On Teaching and Learning Mathematics and with it our annual review of the articles we have published since our previous year in review article. Over the past year, our articles have covered a range of topics and ideas, and I have loosely collated them by the following topics: active learning, K-12 education, summer experiences, assessment, diversity and inclusion, curricular issues, and mathematical culture. As we begin a new academic year, we hope you will take some time to read them (or read them again!) and be inspired. Continue reading

Posted in Assessment Practices, Classroom Practices, Communication, Curriculum, Education Policy, Faculty Experiences, Graduate Education, K-12 Education, Mathematics Education Research, Multidisciplinary Education, Outreach, Research, Student Experiences, Summer Programs | Tagged | Leave a comment

Call for Nominations: Editor-in-Chief

Applications and nominations are invited for the position of Editor-in-Chief of the American Mathematical Society blog On Teaching and Learning Mathematics. The Society seeks a college or university mathematician or mathematics educator with at least five years of experience. Applicants should be familiar with issues in mathematics education at both the postsecondary and K-12 level, and have ideas for contributors who can write knowledgeably about those issues from a variety of pedagogical and institutional perspectives.

The Editor-in-Chief is assisted by a board of Contributing Editors, selected by the Editor-in-Chief, who help to create the contents of the blog and solicit material for publication. The goal for this blog is to stimulate reflection and dialogue by providing mathematicians with high-quality commentary and resources regarding teaching and learning. This blog serves as a big tent, giving voice to multiple contributors representing a wide range of ideas. The AMS provides support to this mission through social media promotion.

The responsibilities of the Editor-in-Chief are: to create and maintain an annual publication schedule (typically 24 articles per year), edit/review/approve articles prior to publication (in collaboration with editorial board members), solicit or write between 4 and 6 articles per year, lead editorial board conference calls, and recruit new editorial board members when needed. The average time commitment is 2-4 hours per week.

Nominations and applications should be sent to by September 15, 2017, and should include the following information regarding the nominee/applicant: name, contact information, curriculum vitae, and past editorial and/or blog experience. Applicants are encouraged to submit a statement discussing the direction they would like to take the blog in the future.

Note from Ben Braun, current Editor-in-Chief:

Since we began On Teaching and Learning Mathematics in June 2014, I have had an amazing experience working with fantastic editorial board members and contributing authors. I believe that the commitment to excellence by our board members and contributors is the reason our blog attracts over 5,000 unique page views every month. For anyone who is interested in deepening their knowledge regarding the teaching and learning of mathematics, and in contributing to the improvement of postsecondary mathematics education, I encourage you to apply for this position.

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To Active Learning and Beyond: Attending to Student Thinking AND Student Experience in Active-Learning Math Classes

By Jess Ellis Hagman, Contributing Editor, Colorado State University

On a recent trip to Santa Fe, New Mexico, I met a really cool woman named Anna Sale who runs a podcast called Death, Sex, and Money (check it out). In this podcast she interviews people about things she is curious about. We talked about how her work is similar to research (come up with something you want to know more about, then go learn about it), except much less rigorous and you get answers much more quickly.

One thing I am very curious about is how students from marginalized populations experience active-learning classes. I believe deeply in teaching in a more active way, and I also believe deeply in teaching so that all of my students have the best opportunity to succeed, and sometimes I wonder if all my active-learning moves are enough to support all of my students. So, taking inspiration from Anna, I decided to interview some experts. (I am also working on a grant proposal to look at this in a much more rigorous/slow way). Continue reading

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The Mathematical Encounter That Changed My Life

By Art Duval, Contributing Editor, University of Texas at El Paso

I just returned from an all-years reunion of the Hampshire College Summer Studies in Mathematics (HCSSiM) program, a six-week program I attended during the summer between my sophomore and junior years of high school.  It has been run by David C. Kelly, whom everyone refers to just as Kelly, since he started it in 1971.  There are several other summer high school math programs around the country (a good start is this list from the AMS), which likely share some characteristics with Hampshire, but since Hampshire is the one I have personal experience with, this is the one I am compelled to talk about.  And while several people and experiences were instrumental in my path to becoming a mathematician, Hampshire is the one that stands out most prominently in my mind, the one mathematical encounter that changed my life.  And from talking to other people at the reunion last weekend, I know that many other program alumni feel the same way.

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Help Wanted: Mathematics Tutor

By Priscilla Bremser, Contributing Editor, Middlebury College

“Can you recommend a good math tutor?” I hear this question from friends with children in local schools, academic support staff at my institution, and my own students.  Once or twice I’ve even heard it from a student on the first day of class.  Although tutoring has much in common with other educational settings, it presents its own opportunities and challenges.  In this post, I explore why one-on-one instruction is so appealing as a supplement to classroom instruction, and how effective tutors make the most of tutoring sessions.

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What is Math-Ed Research All About? As Explained by a Muggle in a Math Department

By Jess Ellis Hagman, Contributing Editor, Colorado State University

I’ve recently finished my third year as an assistant professor in the mathematics department at Colorado State University. Since my research area is mathematics education, I am often asked what it is like to be a math-ed researcher in a math department. Such curiosity points to a cultural difference between mathematicians and mathematics-education researchers, and alludes to a specific culture where it may be difficult to be an education researcher in a mathematics department. To me, this question sometimes feels akin to being asked what it is like to work at Hogwarts as a Muggle, surrounded by real witches and wizards. Certainly, this comparison carries with it some information about how I perceive the question: that mathematicians are the real researchers, and that as a mathematics-education researcher I am lurking in their world. While this may be how I hear the question, it is very far from my experience in my math department with my colleagues. There are about 30 faculty in my department and three of us are active mathematics-education researchers. I have had overwhelmingly positive interactions in my department and feel valued as a teacher and as a researcher. When asked how I have had such a positive experience in my department (i.e. how I have gained acceptance at Hogwarts by the wizards and witches), my answer is both that my colleagues are just great people and that we have good relationships because we have gotten to know each other and each other’s work through conversations rooted in curiosity. I think it’s been valuable that we respect each other both as people and as researchers. In this blog post, I want to share some of the substance of what I have shared with them about mathematics education research. Continue reading

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Teaching in a Collaborative Classroom

By Saúl A. Blanco, School of Informatics and Computing, Indiana University

For several years I’ve been incorporating active-learning and inquiry-based learning activities in my teaching. There is ample documented evidence of the benefits of these approaches for students, but equally as important, they make teaching and learning more fun! Shifting class time from lecturing to having students work on problems, present their solutions to the class, and explain answers to each other has a dramatic effect: students become more engaged, learn communication skills, and gain confidence. These soft skills are in high demand in the job market. In this article, I will describe my use of these approaches and my experience teaching in a classroom designed for collaborative learning. Continue reading

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Our Responsibility – Our Opportunity: Mathematical Habits of Mind

By Brigitte Lahme, Professor, Sonoma State University

Every university instructor would be thrilled if their students came to their mathematics classes with the ability to make viable arguments and to critique the reasoning of others; if their inclination were

  • to persevere through difficult problems,
  • to look for and make use of mathematical structures, and
  • to strategically use tools in their mathematical toolbox.

But how do students develop these mathematical practices? The foundation is laid during a student’s 13 years of mathematics classes in K-12 – learning from their teachers and engaging in mathematics with their peers. The eight Mathematical Practice Standards that are an integral part of the Common Core State Standards (CCSS) for Mathematics, have elevated the importance and visibility of productive mathematical habits of mind in K-12 education. It is now an expectation and not a bonus. But are teachers equipped to help their students develop the practices until they become habits? Do teachers even have productive mathematical habits of minds themselves?

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“I Am So Glad You Made That Mistake!”

By Allison Henrich, Associate Professor and Chair of the Department of Mathematics, Seattle University

“I am so glad you made that mistake,” I’ve come to realize, is one of the most important things I say to my students.

When I first started using inquiry-based learning (IBL) teaching methods, I had a tough time creating an atmosphere where students felt comfortable getting up in front of class and presenting their work. It is a natural human instinct to not want to expose your weaknesses in front of others. Making a mistake while presenting the solution to a problem at the board is a huge potential source of embarrassment and shame, and hence also anxiety. So how do we—as educators who understand the critical importance in the learning process of making and learning from mistakes—diminish the fear of public failure in our students? For me, the answer involves persistent encouragement. It also relies on setting the right tone on the first day of class. Continue reading

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