Lola Thompson, February 22, 2015
(Department of Mathematics, Oberlin College)
I have always had a complicated relationship with textbooks. As an undergraduate, I read my mathematics textbooks meticulously in order to justify my class-skipping tendencies. It all started when I realized that one of my professors was copying his lectures verbatim from a different textbook. Feeling clever, I purchased the textbook that he was using and spent the rest of the semester reading it at a gelato shop during our regular class period. In subsequent semesters, I ate a lot of gelato and learned a great deal of math, but only set foot in the classroom on rare occasions.
As a graduate student instructor, I began to see things from the opposite perspective. I was determined not to have my students share my former attitude towards class attendance. I wanted my classes to be an indispensable component of my students’ learning. I would pepper each class period with a mix of worksheets, hands-on demonstrations, and highly interactive lectures, all of which built upon the basic assumption that the students had completed the assigned reading beforehand. I slowly had to resign myself to the reality that the vast majority of my students would never get into the habit of reading the text before class. Various attempts at training my students to read mathematics seemed to fail; too many of them struggled with parsing the dense symbol-filled paragraphs and came to class hoping that my lecture would cover exactly what they missed in the textbook. As textbook prices climbed, fewer of my students bothered to purchase the book in the first place. Over time, out of necessity, my lectures started to imitate the textbook sections. I began to seriously question the purpose of textbooks (and, to be honest, my role as an educator).
After some reflection, I decided to ban textbooks in some of my courses at Oberlin. I have also stopped lecturing in those courses. Instead, students are expected to discover the bulk of the course material for themselves and disseminate this newfound knowledge by presenting at the blackboard in front of their peers. During each class period, the students are given carefully-scaffolded lists of problems which encourage them to test examples, formulate conjectures based on the examples, and then try to prove their conjectures. The students work on these problems in assigned groups of 3-4. The groups are re-shuffled every two weeks, with the goal of exposing students to the benefits (and challenges) of working with different collaborators.
A typical lesson plan is divided into three components:
- Before Class: Students have two days to read a 1-2 page “Pre-Class Reading,” which consists mainly of definitions and reading comprehension questions (questions designed to test their understanding of the definitions and foreshadow the ideas that will be discussed during the following class period). The goal of the Pre-Class Reading is to introduce a new topic without giving too much away. The Pre-Class Readings are intentionally extremely short so that no one has an excuse to skip them.
- During Class: At the beginning of each class, I select a few students to present the reading comprehension problems in front of their classmates. This provides the students with an opportunity to hone their oral presentation skills. It also ensures that everyone is on the same page before we split into groups. I try to interject as little as possible during the student presentations because I want the students to look to one another for ideas (rather than seeking my approval or viewing me as the sole expert in the room). This usually takes about 15 minutes. The students spend the remainder of the class period working on In-Class Problems in their assigned groups. During this time, the course’s OWLS Leader[*] and I will walk around the room and dole out hints (once we feel that the students have struggled an appropriate amount). We also probe the students to explain their ideas to us and we try to mediate the group dynamics.
- After Class: After the class period ends, each group is expected to carefully write up a single set of solutions for all of the In-Class Problems. There are an additional 1-3 problems assigned at the end of each class period that are designated as Homework Problems. These problems tie in with the daily content but they’re less foundational. For example, a Homework Problem might take a concept from the In-Class Problems and present it in a new context. Each individual student has to write up their own solutions to the Homework Problems. The students seem to appreciate this mix of individual assessment and group assessment opportunities.
As one might imagine, my students generate large volumes of written work over the course of the semester. All of this written work is collected on a weekly basis and “rewarded” with generous amounts of extremely nit-picky comments. This provides the students with an incentive to revise their work. At the end of the semester, each student will compile all of their written work into their very own textbook. The textbooks are graded on a number of criteria, which include: clarity of exposition, organization of subject matter into chapters, and correctness of their solutions. The main purpose of the textbook is to provide an outlet for students to learn from their mistakes. I once watched in horror as a student retrieved his graded homework, glancing casually at his numerical score before depositing it in a nearby trashcan without even reading the comments that I had laboriously written on the back of the page!
Now that my students have to revise their work for the textbook project, they show up in my office, graded homework in hand, eager to decipher all of the red ink. In order to streamline the editing process, I require that all of my students type up their homework using LaTeX, a mathematical typesetting language. For collaborative assignments, they use an online LaTeX editor called ShareLaTeX, which allows the students in a given group to edit the same document simultaneously and coordinate their plans using the accompanying chat window.
I can’t claim most of these pedagogical innovations as my own original ideas. I have received a great deal of inspiration through attending conferences and workshops on Inquiry-Based Learning (IBL), a variant of active learning that is currently gaining traction in the mathematics community.[†] The idea of structuring each lesson with specific pre-class, in-class, and post-class tasks came from a talk given by David Pengelley at the Legacy of R. L. Moore Conference. The carefully-scaffolded worksheets that I have designed were initially conceived at the NSF-sponsored IBL Workshop that I attended at Kenyon College last summer. I have been fortunate to receive a great deal of mentoring from the IBL community throughout the process of developing and running these courses. I have also had amazing support from my colleagues in the Mathematics Department while I have experimented with these new teaching methods.
I still have a complicated relationship with textbooks. Now, they clutter the Desktop on my iMac and fill several drawers of filing cabinet space in my office. Some include elaborate anime-themed illustrations or cryptic dedications to family and friends. One was written entirely in 180-character tweets, complete with hashtags like #1amMathLibrary2daysstraight #MinimalRegrets. Each textbook is special to me. When I read them, I hear my students’ voices in their writing, and I remember their joy at finally figuring out the solution to a particular problem.
If you have any questions or are interested in brainstorming ways to use textbook projects in your own courses, please don’t hesitate to contact me (Lola.Thompson@Oberlin.edu).
[*] The Oberlin Workshop and Learning Sessions (OWLS) program is based on the Supplemental Instruction (SI) model for coursework support. Sessions are specific for a class, and are facilitated by a student (an OWLS Leader) who has taken the class and attends the class again along with the current students. The OWLS sessions integrate both “what to learn” and “how to learn”, that is, the content of the course as well as learning skills, in a fun, active and collaborative fashion that has been proved to work effectively for students to master coursework content.
[†] See, for example, Peggy Brickman, Cara Gormally, Norris Armstrong, and Brittan Hallar, “Effects of Inquiry-based Learning on Students’ Science Literacy Skills and Confidence,” International Journal for the Scholarship of Teaching and Learning 3:2 (July 2009), and John R. Savery, “Overview of Problem-Based Learning: Definitions and Distinctions,” in Interdisciplinary Journal of Problem Based Learning 1:1 (Spring 2006): 9-20.