CPM and Cognitive Psychology

Over the past few weeks I have gained ground in my understanding of College Prep Math, the curriculum being used at the Brooklyn School for Collaborative Studies where I work. I feel more comfortable using the online resources; I understand how the textbook works; and I've learned to trust that when things go wrong in an individual lesson, the textbook will circle back to those concepts later. I am by now means an expert and have been relying heavily on my co-teachers, but I see how the structure fits what I've been building to over the last few years of teaching: instead of chunking information together, it spreads it out and "spirals" so that students see the same content over the course of the year.

A friend sent me this article two months ago which discusses how "blocking" of information (teaching one concept intensely and then moving on) may provide short-term beneficial feedback but long-term detriment. When students are presented with material they are familiar with they will likely persevere and come up with a close-to correct answer. But what about when they are presented with a novel situation - will they know what formula, procedure, or algorithm to use?

One thing we are attempting to do is change the mindset of our students using CPM. What I mean by that is best summarized by a resource from Carol Dweck's mindset website:

In a fixed mindset, people believe their basic qualities, like their intelligence or talent, are simply fixed traits. They spend their time documenting their intelligence or talent instead of developing them. They also believe that talent alone creates success—without effort. They’re wrong.

In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. Virtually all great people have had these qualities.

What she is getting at with this quote is that too often people think of themselves as "bad at math" (or are told as much) and then internalize that for the rest of their lives. If we recognize this fixed mindset and move past it, we will be able to persevere against all odds. A recent article in the Atlantic continues the argument by saying, "For almost everyone, believing that you were born dumb—and are doomed to stay that way—is believing a lie. IQ itself can improve with hard work." 

While teaching with this spiraling technique I am beginning to understand how we can change student perception by offering multiple entry points for a given piece of content. Moreover, by focusing on how they approach the content instead of the outcome of the content itself, we might be offering a way out for all those who say they are "bad at math."

I hope that over the course of this year I have many more conversations with people about how to ensure this happens with my students.