Pushing Beyond Procedures to Enhance Mathematics Learning

Abstract

While many ideas abound in the literature about what effective mathematics instruction entails, procedural instruction still dominates in United States mathematics classrooms. Many math teachers seem to have a natural tendency to default to simply teaching procedures. However, if teachers want their students to engage in meaningful mathematics, they need to realize why this type of math instruction is insufficient. They need to see that pushing beyond procedures is both a necessary and achievable goal. To properly frame these ideas, I will begin this paper by examining the evidence that supports the claim that the culture of mathematics instruction in the United States is procedural. To more deeply understand this phenomenon, it is important that teachers are aware of the factors that cause it, factors that may be occurring in their own classrooms. I will identify some of these key factors. I will then make a case for why procedural instruction is lacking by analyzing its negative effects on learners, the learning environment, and curriculum. Having established the downsides of procedural instruction, I will then turn to the issue of how math teachers can push beyond it. I will start by identifying some common characteristics found in classrooms in which meaningful mathematics is found: the emphasis of mathematical reasoning, the framing of mathematics as a discovery process, the promotion of student agency, and the practice of mathematical discussion. I will follow up these general themes by offering some more specific suggestions for steps math teachers can take to achieve these characteristics in their own classrooms. Finally, I will offer some possible challenges in achieving this more meaningful type of mathematics instruction.