Reply To: Learning the why in mathematics

[Kyle Pearce]

Hi @janpeery

I think this question is going to resonate with a lot of Math Moment Makers out there as many of us (@jon and I included) *believed* we were “good at math” for years because we were able to copy steps and procedures.

When I began on this 10 year learning journey I’ve been on, I slowly but surely realized that all of the struggles I (and my students) were having in math class were very strongly connected to our collective lack of conceptual understanding. This is even more difficult in the middle and high school grades because there is so much complexity from earlier on that was simply memorized vs. understood.
I think you’re in the right place if you’re interested in learning the “why” behind math, but I would strongly encourage beginning before the actual high school concepts you might be teaching. I know this sounds counter intuitive, but if you do not have a strong foundation conceptually in things like fractional thinking and proportional reasoning (i.e.: why do I flip the second fraction and multiply when dividing? etc.) it will be extremely difficult to build the conceptual understanding on later concepts.

First and foremost, I would start with the Academy course: The Concept Holding Your Students Back. It is all about understanding Proportional Reasoning and how Proportional Relationships develop. There is some serious complexity that starts happening once you hit division that most of us never knew about but NEED to know about in order to be able to teach conceptually.

We have a new unit coming out within the week called “Shot Put” that is a 6 day unit focusing on algebraic thinking and in particular subsitution. That will really help you understand why solving systems of equations can be done through substitution algebraically, but we do it using number lines as a visual model. Keep an eye for it.

As for great reads, I’d check out any of Cathy Fosnot’s work and the John Van De Walle book Elementary and Middle School Mathematics: Teaching Developmentally. Again, not specific for high school, but so important to start there (in my opinion) before heading into more complex ideas that we really only understand procedurally.

Another resource that you might check out is Math Is Visual. It’s a side project I’ve been working on for a couple years now and is all about visualizing mathematics to build conceptual understanding. I’ll be building out a course inside the Academy as a deep dive into the Math Is Visual work in the coming months.

Hope this is a decent starting point for you… any others out there with ideas and/or perspectives to share?