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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Student Evaluations Ratings of Teaching: What Every Instructor Should Know

By Jacqueline Dewar, Loyola Marymount University

What happens to the data from your teaching evaluations? Who sees the data? Are your numbers compared with other data? What interpretations or conclusions result?  How well informed is everyone, including you, about the limitations of this data, and conditions that should be satisfied before it is used in evaluating teaching?

Despite many shortcomings of student ratings of teaching (SRT), some of which I mention below, their use is likely to continue indefinitely because the data is easy to collect, and gathering it requires little time on the part of students or faculty. I refer to them as student ratings, not evaluations, because “evaluation” indicates that a judgment of value or worth has been made (by the students), while “ratings” denote data that need interpretation (by the faculty member, colleagues, or administrators) (Benton & Cashin, 2011).

Readers may be asked to interpret the data from their SRT on their annual reviews or in their applications for tenure or promotion. They may even find themselves on committees charged with reviewing the overall teaching evaluation process or the particular form that students use at their institutions, as I did.  For these reasons, I thought it might be helpful to discuss some general issues concerning SRT and then present a few practical guidelines for using and interpreting SRT data.

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Undergraduate Research: Viewpoints from the Faculty Side

By Luis David García Puente, Contributing Editor, Sam Houston State University

Over the years I have been asked the questions: Why do you direct undergraduate research? How do you pick a research problem for your students? How do you manage a research group? In this blog post I would like to present my personal points of view regarding these questions.

I have been involved in research with undergraduates since 2001. I have worked with students as part of REU programs at large research universities, at mostly undergraduate state universities, and at programs in mathematics institutes. I have also worked with small groups of local students. In 2001, I was a graduate TA at the Summer Institute of Mathematics for Undergraduates (SIMU), an REU program hosted at the University of Puerto Rico – Humacao that received the first ever Mathematics Programs that Make a Difference award from the AMS in 2006.  This program fundamentally shaped my view regarding working on research with undergraduate students.   Continue reading

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Theory into Practice: Growth Mindset and Assessment

By Cody L. Patterson, University of Texas at San Antonio

Several years ago, I took up running. At first, I wasn’t particularly good at it, but I persisted: about two or three times each week, I would go for a jog, increasing my pace or distance in small increments. This measurable growth in my running ability and physical fitness was a great motivator for me, and I increased the frequency of my workouts. After about a year, I was able to complete a local 5K race; this remains among the proudest achievements of my life to date. This was the most authentic experience I’ve had of putting sustained effort into a domain in which I had little natural ability, observing my own growth, and working toward a specific, achievable goal. I attribute my success to two factors:

  1. I didn’t measure my own performance against others’. I knew that many people were more accomplished at running than I was when I got started. I set this thought aside and enjoyed the fresh air and the feel of the pavement under my feet.
  2. I took notice of any growth in my distance or speed, no matter how small. I took pleasure in being able to observe so many improvements in such a short time.

I have often wondered how I can create a similar experience for students in my mathematics classes, especially for those students who lack confidence in their mathematical knowledge and skills. These are the students who are in danger of developing the mindset that the sustained effort they need to master challenging topics indicates that they are not qualified for advanced study in mathematics. Therefore, one goal of every class I teach is to help students let go of concerns about how they are performing relative to their peers, and enjoy observing their own growth and learning. In his September 2015 article in this blog, Benjamin Braun described some of the mindset interventions he uses to help focus students’ attention on their mathematical growth.   In this article, I’ll describe how the recent work on growth mindset has influenced assessment practices in my own courses. Continue reading

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