I spent a lot of time this weekend thinking about how to develop the analytic thinking of my students. Two of my classes worked on writing and graphing inequalities last week, but the results of the quiz I gave on Friday revealed some misconceptions across the board. Among all the quizzes, I also noticed an interesting trend in the error analysis problems I included on the assessment. Every student got these questions correct, yet they made these mistakes elsewhere in their work. As I spent my Friday afternoon and Saturday planning my classes for this upcoming week, I came to the conclusion that students were able to pick out the errors easily because the answers were usually the first thought students would think of when looking at the problem. In contrast, the problems for writing and graphing inequalities required thinking through situations and relating this information to symbols.
It was perfect timing that Dylan Kane wrote about the Cognitive Reflection Test he gave his students last week. In his post, he described how he discussed fast thinking and slow thinking with his classes. Basically, most students want to rush through a problem (fast thinking) rather than carefully consider a problem (slow thinking). When Kane summarized thoughts about these modes of thinking in his classroom, he stated the following:
One thing I hope my students take from my class is to look at a problem and, instead of rushing to the first, easiest solution that their mind jumps to, slowing down. Our brains want to live in the first system, doing things as quickly and mindlessly as possible. But I’m looking for students to think carefully about what a question is asking, constructing an answer, and checking to see if it makes sense. That’s the type of reasoning that will make them successful in every area of their life. And problem solving in math is a great opportunity to practice this — looking at a new problem and considering it carefully rather than rushing to a conclusion, the same way I would love my students to reason about events in their news or their relationships with their peers.
I share this goal with Kane and I hope to continue this work moving forward. I’m planning on using the questions he used with my classes tomorrow, discuss fast vs. slow thinking, then provide time to revise work. I know my students understand the concepts; they just need to slow down and process the information that is given to them in a problem rather than jumping to the easiest idea they think of when they look at a problem.
I know this blog seems random. I want to share activities that worked well for me, yet I want to talk about the topics of teaching that puzzled me during my college years and continue to challenge me (developing thinking abilities, feedback, engagement, moving from concrete activities to abstract ideas, and questioning). It’s a work in progress. I’m trying to find the best angle.