In January, the students in my Foundational Pre-Algebra class passed a key milestone in our growth as a learning community: Every student demonstrated a willingness to ask for help in the moment as they needed it. For a teacher, this is huge. It means I can address confusion and misunderstandings in real-time, and I do not have to spend as much time and energy chasing students down who just want to hide in the back of the room. But this change in mindset is even more huge for the students.
A common misperception is that middle schoolers generally know the right thing to do, but don’t do it due to immaturity. However, that isn’t how our brains work. When we need to make a decision, our brains will actually run through our options and predict an outcome for each path we might take. We then take the path with the best predicted outcome. According to neuroscientists, we make these unconscious predictions thousands of times a day, and it is a core function of the brain.
In order to make predictions, our brain constructs mental models of how the world works. These models, or internal theories, are based on our past experiences. Students who struggle in math stop asking for help because they have learned, over time, that asking for help is a waste of time and a source of frustration, for both them and their teacher. Unconsciously, their brains tell them that asking for help is the wrong thing to do because it leads to a poorer outcome.
For many of these students, their internal theory is that they are bad at math and math will never make sense to them. Therefore, their best option for getting through math class is to memorize rules and procedures so they can just get by and hopefully pass the test. How do we get students to update their internal theories? We are supposed to revise our theories naturally when they lead to faulty predictions. However, two things can short circuit that natural process: first, we develop blind spots that prevent us from seeing that our predictions are wrong; second, we avoid putting ourselves in situations that may disprove our theories.
In Foundational Pre-Algebra, I sequenced the curriculum so that, instead of constructing new theories to make sense of new concepts, students are constantly revising existing theories to make sense of new concepts. By revising their own internal math theories incrementally each day to account for new experiences, they develop the skills and mindset needed to revise theories in general, including their theories about themselves as math students. Now, my students have a more sophisticated theory: sometimes math doesn’t make sense to me, but sometimes it does. The key is experimenting to discover the factors that enable me to create understanding because that leads to a better outcome.