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.

Active Learning

Active learning was a major topic for us again this year. Henrich, Blanco, and Klee shared ideas for supporting productive collaboration and conversation. LaRose argued that effective teaching is essentially inefficient, and that active learning is a prime example of this. Ellis Hagman interviewed several colleagues to find out how their use of active learning impacts students from marginalized populations. Bremser reflected on a broadly-used form of active learning many of us overlook: tutoring.

• Allison Henrich: “I Am So Glad You Made That Mistake!”
• Saúl A. Blanco: Teaching in a Collaborative Classroom
• Steven Klee: If You Don’t Talk to Your Students About Math, Who Will?
• Gavin LaRose: The Inefficiency of Teaching
• Jess Ellis Hagman: To Active Learning and Beyond: Attending to Student Thinking AND Student Experience in Active-Learning Math Classes
• Priscilla Bremser: Help Wanted: Mathematics Tutor

K-12 Education

It is impossible to discuss postsecondary mathematics education without considering K-12 education as well. Lai, Howell, and Lahme discussed effective pre-service teacher education. Wilson, Adamson, Cox, and O’Bryan made the case that our standard method for teaching inverse functions is counterproductive. Schanzer outlined the challenges that exist for mathematics due to the growing movement to teach computer science at the K-12 level. Beck and Wiegers shared their experiences directing an NSF-funded program connecting graduate students with K-12 students.

• Yvonne Lai, Heather Howell: Conventional Courses Are Not Enough For Future High School Teachers
• Frank Wilson, Scott Adamson, Trey Cox, Alan O’Bryan: Inverse Functions: We’re Teaching It All Wrong!
• Emmanuel Schanzer: Integrating Computer Science in Math: The Potential Is Great, But So Are The Risks
• Brigitte Lahme: Our Responsibility – Our Opportunity: Mathematical Habits of Mind
• Matthias Beck, Brandy Wiegers: Creating Momentum Through Communicating Mathematics

Summer Experiences

Both K-12 and undergraduate education take place beyond the constraints of classrooms; summer programs are frequently a source of inspiration for students. Through an interview with REU students, members of the editorial board explored their impact on five current undergraduates. García Puente provided a faculty perspective on leading undergraduate research projects. Duval reflected on his own profound experience as a high school student in a summer program that inspired a lifetime of mathematics.

• 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: Students’ Views of REUs: a “Magical Place of Thinking”
• Luis David García Puente: Undergraduate Research: Viewpoints from the Faculty Side
• Art Duval: The Mathematical Encounter That Changed My Life

Assessment

Along with the responsibility of creating meaningful classroom experiences, mathematics faculty have the responsibility of assessing students in a meaningful way. Bagley, Gleason, Rice, Thomas, and White investigated the efficacy of the Calculus Concept Inventory as a means to assess student conceptual understanding. Patterson discussed the influence of growth mindset research on his classroom assessment techniques. Dewar turned the focus around with a thorough consideration of what instructors should know about student ratings of teaching.

• Spencer Bagley, Jim Gleason, Lisa Rice, Matt Thomas, Diana White: Does the Calculus Concept Inventory Really Measure Conceptual Understanding of Calculus?
• Cody L. Patterson: Theory Into Practice: Growth Mindset and Assessment
• Jacqueline Dewar: Student Evaluations Ratings of Teaching: What Every Instructor Should Know

Diversity and Inclusion

A deep and important challenge for the mathematics community is to find ways to increase our diversity and meaningfully include every mathematics student. Pons discussed her experience at ECCO 2016, a research conference that excelled in this mission. Hobson provided six ideas for instructors seeking ways to support diversity and inclusion. Katz reflected on the impact of implicit messages in our teaching, providing frameworks through which instructors can evaluate their impact on students.

• Viviane Pons: An Inclusive Maths Conference: ECCO 2016
• Natalie LF Hobson: Six Ways Mathematics Instructors Can Support Diversity and Inclusion
• Brian Katz: On What Authority? — Considering Implicit Messages in Our Teaching

Curricular Issues

Curricular issues are a perennial concern for mathematicians and mathematics departments. Armstrong made the case for an expanded presence of linear algebra in standard undergraduate coursework. Pudwell described her experience teaching courses on experimental mathematics and the role this course offers within the standard undergraduate curriculum.

• Drew Armstrong: More Linear Algebra, Please
• Lara Pudwell: What is an Experimental Math Course and Why Should We Care?

Mathematical Culture

Our final three articles this year dealt in different ways with mathematical culture. Braun wrote about the challenge of balancing our ideals and our reality in the realm of teaching. Ellis Hagman wrote about the cultural differences between mathematics research and mathematics education research, and the questions she often gets from colleagues about her work as an educational researcher. Buckmire, Murphy, Haddock, Richardson, and Driscoll described several of the mathematics education projects funded by the National Science Foundation, and invited readers to contact them with ideas for proposals and projects.

• Benjamin Braun: Aspirations and Ideals, Struggles and Reality
• Jess Ellis Hagman: What is Math-Ed Research All About? As Explained by a Muggle in a Math Department
• Ron Buckmire, TJ Murphy, John Haddock, Sandra Richardson, Brent Driscoll: The National Science Foundation Has Resources to Help You Improve the Teaching and Learning of Undergraduate Mathematics