Contemplation and reflective writing can be powerful tools for teaching and learning. Students benefit from considering the way that they learn and do mathematics (in addition to thinking directly about the subject matter). This intellectual activity is often called metacognition. Written reflections can also help professors get to know their students, both personally and mathematically.
Three ways I engage my students in reflective writing:
- Have students write periodically in a physical journal. Assignments could be very general, such as “How’s it going in this class?” to more structured prompts, such as “Describe your process for solving one of the homework problems you found challenging” or “Name three strategies you employ when you get stuck on a problem.” When the journal is a physical book, I collect and return the posts with a smiley face, sticker or small comment so students know I looked. I used to use the old fashioned bluebooks created to administer exams because they only cost $0.10. You could use an online submission process. Paper is nice, because students seem more likely to doodle fun pictures.
- Ask students to answer a question or two (for credit) at the end of a quiz or exam. I like this approach because it communicates that I value the writing and I will already be in “grading” mode when I look at the result. On the downside, students might be more stressed and less attentive to the task during a quiz. Francis Su has outlined his approach to reflective exam questions in a previous Teaching Tidbits post.
- Direct students to complete an “exit ticket” or “minute paper” at the end of class. A prompt might ask what the student found most interesting or confusing that day. Sometimes I encourage students to pose a “what if” question. You could use slips of paper or a web form for these end of class questions. Web forms can make it easier to skim and manage comments from a large class.
Connectedness Often Translates to Engagement
The more you know about your students, the easier it can be to choose a combination of strategies that promote teaching, learning, transfer and affective gains.
In their reflective writing, my students have shared their hobbies, preferences/likes/dislikes, hopes and dreams, difficulties and triumphs in the course, questions about the subject matter, personal challenges, undiagnosed or unreported learning disabilities and general feedback on their experience in the course. I often indirectly learn about my students’ preparation for the course, attitude, culture, maturity, life pressures and personal goals.
A big caveat: some faculty do not want to know these kinds of things about their students. It is a personal choice, of course, and faculty should be aware that they are opening the door to some potentially heavy topics. Some students will want to share very personal information. Others will not. With this in mind, I try to ask relatively unobtrusive questions (such as the ones above) that students can answer many ways. Even the question, “How’s it going in this class?” has started conversations leading to decades-long connections with former students.
I recommend searching on the terms “math” and “metacognition” for related reading opportunities. Start with the reference linked at the end of this post.
These questions are from my Spring 2016 differential equations course in-class quizzes.
- What is something that you do that gives you joy and rejuvenates you? Try to think of something that you don’t judge yourself about - something that makes you happy whether or not you do it “well.”
- When I encounter mathematics that challenges me, I use these strategies to get unstuck (circle the letters of everything you try): (a) go to office hours (b) sleep on it (c) go to peer tutoring (d) look online (e) read a textbook (f) take a break (g) go over my notes (h) eat/drink a snack (i) watch a DE video (j) ask a friend (k) other:
- If you had a magic wand and could change one thing about our college, what would you change?
- What’s something you are looking forward to this summer? (Write something or draw something.)
Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp. 189-215). Hillsdale, NJ: Lawrence Erlbaum Associates.