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.
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.