Monday, February 13, 2017

More ideas on working with students who really, really don't like mathematical exploration

As I've blogged before, the area in which our program has perhaps received the most criticism is in the challenge that open tasks, labs, mathematical explorations, and group problem solving pose for students who crave a more structured, algorithmic, and predictable approach. I met with a student (new to me this semester) last week who told me that she was incredibly frustrated with her current Math class (I am the teacher) because in her prior Math class, homework was 1 through whatever odd and both homework and quizzes were repeat versions of what the teacher had shown students in class. She had found this prior class soothing and comfortable and was an excellent student in this environment, whereas now, she felt that every facet of class was constantly asking her to figure out problems she hadn't seen before and she never knew if she really understood or felt like she was on solid, comfortable ground. She was worried that her confidence was slipping and that she wasn't learning as well as she had in the more traditional environment.

My initial internal reaction was to try to convince her that my pedagogy was sound, that it would indeed be better for her long term to struggle and make sense of novel situations, apply and stretch herself, learn how to tinker and problem solve rather than regurgitate algorithms repeatedly, but I felt that this would be minimizing her experience and negating her sense of her learning and mathematical identity. She had clearly stated that things make sense to her after she is given a method and does a lot of similar problems - only then does she believe that she is able to generalize and form an underlying concept. This isn't how our program is designed and I absolutely believe that it is better for most students to experiment and play first, forming conjectures and identifying patterns before coming to or seeing more formal methods (if needed), but maybe it's not better for her. At the very least, if she is convinced that this is the wrong way for her to learn, then it will be very difficult for her to interpret her experience otherwise, thus creating a self-perpetuating cycle. 

So I'm trying something new, and I'm not sure how well it's going to work. Every week, I'm going to email her a list of concepts that we will be working on next week, along with resources either in the textbook or online for her to see these concepts explained and practice problems for her to work on. A preview, if you will. Class will then not be a time for her to explore and invent, like it is for other students, but a time for her to generalize and prove the patterns that have already been revealed and practiced. In exchange, she has agreed that in a few weeks, she will again try exploring a new topic and be open to coaching by me in order to also get better at this way of learning. 

I'm hoping that by engaging in good faith, I am able to bridge the divide in expectations and meet this student at her current level of need and that she is able to grow over time in the mathematical habits of mind that I believe are just as important as, if not more than, content knowledge. It is certainly possible that she will continue preferring doing math in predictable and routine ways, following a pattern shown to her by someone else, on mathematical autopilot. I really hope that I can convince her that she can be successful and that it's worthwhile to engage in math in a different way than she has in the past. But it's okay if that's not where she is right now. I have a whole semester to build a relationship of trust and forment and celebrate moments of mathematical success for her.

Have you had students who actively and eloquently resisted your view of math or ways of teaching? What are some ways that you've made progress over time in their willingness to go there with you? Are there students who never changed their minds? Any and all advice welcome, as always :)


  1. I myself was very much like this student. There are a lot of ways (especially social & emotional) in which our currently "best practices" pedagogy overlooks/ignores the many other kinds of interpersonal aggressions that can make a student this way. So I think it's fantastic that you are engaging with her on her terms by giving her the chance to find her own footing in her own way. This is the best way to cultivate receptivity toward doing math socially (our current math ed norm) because you are communicating through your actions how seriously you take her as a mathematical thinker.

    Great post!!!

    - Elizabeth

  2. How timely - I was just in a meeting today about a student who is struggling in my Algebra 1 class because he struggles with group work and resists it, and since my class is built around cooperative learning and exploration, I'm pretty much the devil in his eyes. He was more open to the class during the first semester when he was familiar with the math and it was mostly review for him. Now that we're getting into things that aren't familiar, his oppositional tendencies have surfaced. I'm trying to do something similar - as much as possible, meet him where he's comfortable (as much as possible) with some individual work and strict structure, and in return he'll work in a group of two with one of a few select students. This is a student with a history of various learning differences and mental health issues that impact his education, but in my experience, students are willing to do a lot for a teacher that's willing to do a lot for them. I'm optimistic that your student will appreciate the extra work you are putting in, and that it will pay off in the long run. Good luck!

  3. This is a great post. I'm not experiencing the resistance you are (thankfully!) but I could see it happening as I'm using CPM in my algebra 1 class and it's SO different from what the kids have done before. Thank you for writing it as I think what you're doing is an excellent compromise for your student. I hope she comes around!