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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Six Ways Mathematics Instructors Can Support Diversity and Inclusion

By Natalie LF Hobson, Graduate Student, University of Georgia

What teaching practices support a diverse student body in your mathematics classroom? In this post, I suggest six concrete teaching practices you can implement today to help make your classroom a more inclusive environment for your students:

  1. Use students’ interest in contextualized tasks
  2. Expose students to a diverse group of mathematicians
  3. Design assessments and assignments with a variety of response types
  4. Use systematic grading and participation methods
  5. Consider your course logistics
  6. Encourage students to embrace a growth mindset

I hope these strategies can spark conversation with colleagues on how we, as educators, can support a diverse and inclusive mathematics classroom. Continue reading

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Students’ Views of REUs: a “Magical Place of Thinking”

By the Editorial Board, based on an interview at the 2017 Joint Mathematics Meeting with REU students David Burton, Kelly Emmrich, Micah Henson, Andres Mejia, and Nina Pande.

Editor’s note: The editors thank David, Kelly, Micah, Andres, and Nina for taking the time to share their thoughts and insights with us.  Biographical information for each of these students is included at the end of this article.

“Something that I’ll remember the most is there were a couple epiphany moments where we just all of sudden we seemed like we just stumbled into this, you know magical place of thinking of something we never would have thought or come up with that was really important for our project and the reason I think that I’ll also remember that for a long time is that it gave me a lot of confidence that I could do research because being able to come up with a creative way forward is sometimes I think one of those important parts.”
— REU student

Why should students participate in a summer Research Experience for Undergraduates (REU)?  What do undergrads gain from such programs?  What has driven their growth and popularity over the past several decades?  In this post, we share highlights of a conversation that the editors had with five undergraduates at the 2017 Joint Mathematics Meetings about their experiences at five different REUs (described in the final section).  If you are a faculty member, we hope this inspires you to share information about REUs with your students.  If you are an undergraduate student, we hope this inspires you to apply for an REU! (Lists of REUs can be found here and here.)

In our conversation, five major themes emerged regarding the students’ REU experiences:

  1. Collaboration: the importance of collaboration, friendships, and networking
  2. The Nature of Mathematics: an appreciation or gained understanding of the nature of mathematics and mathematical research
  3. Self-Beliefs and Agency: heightened awareness and/or insight about oneself as a learner or person in general
  4. Back to the Classroom: the positive impact of REUs on subsequent coursework
  5. Graduate School: an increased or decreased interest in graduate school or insight into graduate school

While there were some additional comments off these themes, which we include below, in this article we hope to tell a story of the impact of REUs on undergraduates through the students’ own words.  Note that all student quotes in this article have been lightly edited for clarity. Continue reading

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Aspirations and Ideals, Struggles and Reality

By Benjamin Braun, Editor-in-Chief

Two of my favorite pieces of mathematical writing are recent essays: Francis Su’s January 2017 MAA Retiring Presidential Address “Mathematics for Human Flourishing”, and Federico Ardila-Mantilla’s November 2016 AMS Notices article “Todos Cuentan: Cultivating Diversity in Combinatorics”.  If you have not yet read these, stop everything you are doing and give them your undivided attention.  In response to the question “Why do mathematics?”, Su argues that mathematics helps people flourish through engagement with five human desires that should influence our teaching: play, beauty, truth, justice, and love. In a similar spirit, Ardila-Mantilla lists the following four axioms upon which his educational work is built:

Axiom 1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

Axiom 4. Every student deserves to be treated with dignity and respect.

These essays are two of my favorites because they provide visions of teaching and learning mathematics that are rich with humanity and culture, visions that welcome and invite everyone to join our community.

The ideals and aspirations offered by Su and Ardila-Mantilla are inspiring, emotional, and profound, yet also fragile — for many mathematicians, it can be difficult to balance these with the sometimes harsh reality of our classes.  An unfortunate fact is that for many of us, a significant part of teaching mathematics consists of the struggle to support students who are uninterested, frustrated, inattentive, or completely absent.  We are regularly faced with the reality that large percentages of our students fail or withdraw from our courses, despite our best efforts, and often despite genuine effort on the part of our students as well.  How does a concerned, thoughtful teacher navigate this conflict between the truth of the tremendous potential for our mathematical community and the truth of our honest struggle, our reality?

In my practice of teaching, I have found that the only way to resolve this conflict is to simultaneously accept both truths.  This has not been, and still is not, an easy resolution to manage.  In this essay, I want to share and discuss some of the mantras that I have found most helpful in my reflections on these truths. Continue reading

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Announcement: Statement by AMS Board of Trustees

By Benjamin Braun, Editor-in-Chief

Due to connections with mathematics education, some of our readers might be interested in the following statement issued by the members of the Board of Trustees of the American Mathematical Society regarding the Executive Order on Immigration issued by the President of the United States.  To read the statement, see this link: http://www.ams.org/news?news_id=3305

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Announcement: Active Learning Article in AMS Notices

By Benjamin Braun, Editor-in-Chief

Some of our readers might be interested to know that the February 2017 Notices of the American Mathematical Society contains an article on active learning that is based on the six-part series on active learning published on this blog in Fall 2015.  See the Notices article here:

What Does Active Learning Mean for Mathematicians?” Benjamin Braun, Priscilla Bremser, Art M. Duval, Elise Lockwood, Diana White. Notices of the American Mathematical Society, Vol 64, Number 2, February 2017.

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