Joint Educational Project (jep)

Conceptual knowledge of a math topic differs greatly from procedural knowledge and fluency. Procedural knowledge and fluency focuses on the ability to memorize the steps to get to the right answer. On the other hand, Conceptual knowledge refers to the ability to have a deeper understanding of the topics. This means that if a problem is changed slightly from the one the student has learned, they will not have a problem being able to produce the right answer. An example of procedural knowledge would be the memorization of the times table. This is because the students have no deeper understanding of the multiplication process, and all that is focused on is memorization. An example of conceptual knowledge would the full understanding of a concept like place values. This understanding would allow students to use their knowledge of place values and implement it when they have addition, subtraction, multiplication, or division problems including decimals.

I believe I received an excellent math education while growing up. When learning a new topic, the focus at the beginning was always on conceptual knowledge. Then, after I had a deeper understanding of what the problem was asking, my teachers would start to focus on procedural knowledge and fluency. I believe this is the best way to learn because, once a student has conceptual knowledge of a problem, they should be able to solve multiple variations of the same type of problem. The only exception to this would be the multiplications table. That was just something that I had to spend hours memorizing. What might have made it easier learning the conceptual aspects of problems for me is that I had smaller class sizes in elementary school. I went to a small, private school until eighth grade, so the teacher was able to spend more time on each student and the troubles they were having with the conceptual knowledge. I believe that larger class sizes will force teachers to spend more time making sure that students have procedural knowledge and fluency. This is because teachers will not have as much time to efficiently explain the conceptual aspect behind every problem to every kid. They will then focus on procedural knowledge and fluency in order to be able to say that they taught their students that type of problem.