“Abstraction is only a sort of trickery and deflection of the mind if it doesn’t constitute the crowning stage of a series of previously concrete actions. The real cause of failure in formal education is therefore essentially the fact that one begins with language instead of beginning with real and material action.” -Jean Piaget, 1976

I had to read this quote several times to understand the meaning behind it and how it pertains to math (or learning in general). When you teach math, you build upon concepts and skills that are taught. The first sentence in this quote is basically saying if your student’s don’t have a strong foundation in math, teaching an abstract concept will fail.

My experience in Math has been one I struggle with. I never understood the reason why I had to learn higher level math skills. Piaget states in the second sentence that the cause of failure in formal education is that we just show students what to do and don’t teach them why they are doing it. If students do not have a strong foundation in math, every lesson they encounter will just build to the complexity of their learning. If a child cannot count, how do expect them to add? Students need math to relate to their real experiences in order for them to understand new concepts and to be successful.

Math instruction is very important. Students need to understand how math works, they need to look for patterns, they need to connect one step to the next in an environment that is safe. Teachers need to re-teach and use student mistakes as learning opportunities that they can grow from. When students have the foundation and confidence in math, they will be able to use prior knowledge to move forward in math.