Elizabeth Green, CEO of Chalkbeat New York and author of the book, Building a Better Teacher, has a lot to say about math education in the United States. In her July article in the New York Times she chronicles the attempts and failures of the US educational establishment to foment a sense of understanding in mathematics education in lieu of simple rote memorization. Over the course of the past few decades pundits have proposed various new math regimes - the most recent of which is the Common Core - in order to reach this goal. Yet, still, there are large amounts of teachers in this country that are incapable or refuse to implement research-backed methods that have better outcomes for children.
One of the major pieces of her article focused on the idea of "I, We, You" in a math classroom. According to Green, "Most American math classes follow the same pattern, a ritualistic series of steps so ingrained that one researcher termed it a cultural script." First the teacher demonstrates a method, then completes an exercise with the class, and finally the students practice on their own. This method has been used for decades and helps students memorize specific rules that they can apply in certain situations, but falters when a new problem comes up that does not fit into the pattern. The procedural knowledge that students are gaining can be useful, but only if that student can apply it in novel situations.
In an article from 2012 in Psychology Today, Dr. Nate Kornell explores a research study on how students are (or are not) assimilating this information. In his research he found that many students are still using these rules and when they are tested in new ways on topics like fractions, "some fell back on procedural knowledge, probably because that’s the only knowledge they had about fractions." Instead of a deep understanding causing a logical thought process, these students are essentially giving up on thinking, relying on memory instead. In fact, Dr. Kornell's analysis showed that "77% of the students [surveyed] seemed to believe that math was not something that could be figured out, or that made sense."
In classrooms across the country (like the one I teach in at the Brooklyn School for Collaborative Studies) teachers are using materials like College Prep Math (CPM), providing investigation-based lessons where students have to think, write, and justify their decisions individually and in a group. These kind of lessons allow for a more nuanced approach to math education where if a student sees something new he or she will often attempt it using previous ideas and molding them to the new situation. There are no step-by-step procedures in CPM, just investigations, lab activities, justifications, etc. Lessons of this type might be called "You, Y'all, We" as they demand students to work independently and in a group before justifying their thoughts to the class.
Currently, some teachers are attending workshops and learning about investigation-based math methods like problem-based learning or other interdisciplinary approaches. Some are succeeding through tremendous odds. Others are doing a disservice to the approach by inputting old worksheets or ideas into these lessons and reforming them back to the old model. According to Dr. Kornell, these teachers, "by converting conceptual struggle into procedural learning, [are] unintentionally depriving their students of crucial elements of effective learning."
It is imperative that our students struggle in their learning and to share that struggle with their peers. If math education stagnates in the "I, We, You" methodology the next generation of Americans will not be able to troubleshoot and problem-solve as we would like them to. Hopefully books and articles like Green's and Dr. Kornell's will help make the difference.