The Second Year of “On Teaching and Learning Mathematics”

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

Another year has flown by, and so it is once again a good time to collect and reflect on all the articles we have been able to share with you since our last annual review.  I enjoyed the chance to re-read all the articles, and I was also surprised at the interesting variety of themes that emerged when I sorted them out.  It was not easy to put each article in a unique box, and I will point out the blurring between categories.  I hope you enjoy the chance to revisit these articles, and perhaps find new meaning from the juxtapositions here.

Active learning.  We devoted two months in the fall to our six-part series on active learning.  Taking the article on this subject by Freeman et al. that had recently appeared in the Proceedings of the National Academy of the Sciences as jumping off point, we explored different aspects of active learning.  It was exhausting and exhilarating for us to work together as an editorial board to write those articles, starting each new one before all the previous ones were done, and finding new things to say in reaction to ideas that emerged from earlier articles.

• Active Learning in Mathematics, Part I: The Challenge of Defining Active Learning
• Active Learning in Mathematics, Part II: Levels of Cognitive Demand
• Active Learning in Mathematics, Part III: Teaching Techniques and Environments
• Active Learning in Mathematics, Part IV: Personal Reflections
• Active Learning in Mathematics, Part V: The Role of “Telling” in Active Learning
• Active Learning in Mathematics, Part VI: Mathematicians’ Training as Teachers

Teaching practices.  It should be no surprise that, once again, the bulk of our articles land in this category.  Each one discusses something someone has done in their classroom and/or that you can do in yours.  But there were some interesting sub-themes that showed up.

• Conceptual, procedural, and modeling: Whether looking at a framework for integrating the procedural and conceptual, or using modeling, derivative machines, or even our own bodies, all of these articles explore how to include the concrete with the abstract.
  • Karen Keene and Nicholas Fortune, A Framework for Integrating Conceptual and Procedural Understanding in the First Two Years of Undergraduate Mathematics
  • Tevian Dray, Thick Derivatives
  • Brian Winkel, Learning Mathematics in Context with Modeling and Technology
  • Hortensia Soto-Johnson, Learning Mathematics through Embodied Activities
• High-impact practices: Maria Mercedes Franco’s article included many high-impact practices she uses, and then Priscilla Bremser focused on one of these practices, service learning.
  • Maria Mercedes Franco, Why High-Impact Educational Practices (Despite Being So Labor-Intensive) Keep Me Coming For More
  • Priscilla Bremser, A Skeptic’s Guide to Service Learning in Mathematics
• Class frameworks: These three articles focused on the class syllabus and two different ways to implement grading.
  • Priscilla Bremser, What’s in Your Syllabus?
  • Kate Owens, A Beginner’s Guide to Standards Based Grading
  • Elise Lockwood, Let Your Students Do Some Grading? Using Peer Assessment to Help Students Understand Key Concepts
• Everything else in the classroom: These are the remaining articles that addressed things we do, or could do, in the classroom. Drew Lewis’ article on social media included a mention of how this helped him learn about Standards Based Grading, listed above.
  • Drew Lewis, Social Media as a Teaching Resource
  • Elise Lockwood, Don’t Count Them Out — Helping Students Successfully Solve Combinatorial Tasks
  • Johanna Hardin and Nicholas J. Horton, Preparing the Next Generation of Students in the Mathematical Sciences to “Think with Data”
  • Elise Lockwood, Attending to Precision: A Need for Characterizing and Promoting Careful Mathematical Work
  • Art Duval, (Don’t?) Make ’em Laugh

The affective domain.  I was struck by the different articles that explored aspects of the affective domain.  Benjamin Braun (our Editor-in-Chief) wrote two articles directly about this, but Taylor Martin and Ken Smith’s article about classroom culture is also largely about what we can do as teachers to structure our classes to help students develop in this direction.  Of course, Martin and Smith’s article also goes nicely with the Class frameworks articles above.

• Benjamin Braun, The Secret Question (Are We Actually Good at Math?)
• Benjamin Braun, Believing in Mathematics
• Taylor Martin and Ken Smith, Creating a Classroom Culture

Student voices.  Once again, we featured several articles written by students giving their different perspectives.  A.K. Whitney wrote about beginning math courses, Sabrina Schmidt about her undergraduate math major overall, and Steve Balady about the program he started as a graduate student.

• A. K. Whitney, Shredding My (Calculus) Confidence
• Sabrina Schmidt, What I Wish I Had Learned More About in College Mathematics
• Steve Balady, We Started a Directed Reading Program (And So Can You!)

K-12.  Although our main focus is on undergraduate mathematics teaching and learning, it is neither possible nor wise to put a rigid barrier between K-12 and post-secondary.  All of these articles find some connection or another between these two levels, whether through curriculum, outreach, or teacher preparation.

• Erin Baldinger, Shawn Broderick, Eileen Murray, Nick Wasserman, and Diana White, Connections between Abstract Algebra and High School Algebra: A Few Connections Worth Exploring
• Matt Baker, Number Theory and Cryptography: A Distance Learning Course for High School Students
• Kathleen Fowler, Start Small, Think Big: Making a Difference Through K-12 Mathematics Outreach
• Jennifer S. McCray, What is Early Math and Why Should We Care?

Policy, etc. These are articles that are more broad than a single classroom, and report on, or advocate for, changes that can be made to curriculum and beyond.  The latter two articles include actions that ordinary mathematicians and mathematics instructors can take, mostly aimed at the K-12 level.

• Benjamin Braun, Recent Reports and Recommendations Related to Courses in the First Two Years of College Study
• Art Duval, Kristin Umland, James J. Madden, and Dick Stanley, Wanted, Mathematicians for an Important but Difficult Task
• Priscilla Bremser, Imagining Equity

And one more thing.  Not fitting into any one other category was the article collecting the varied personal reflections about this year’s Joint Math Meetings by each of the members of the editorial board.

• From the Editors: Blog Update and 2016 Joint Meetings Highlights