Conceptual vs. Procedural

October 30^th, 2008

Many studies, such as the Amber Hill and Phoenix Park study conducted by Jo Boaler, examines different teaching approaches and their affect on student learning. Boaler (2002) suggests that students who are taught in a problem based context “do not have a greater knowledge of mathematical facts, rules and procedures than students taught in a more traditional classroom. This concerns me, due to the fact I am teaching Grade Six and as we all know, Grade Six = CRT’s, but I believe done in the right way, students will learn the necessary procedure and rules through their investigations and problems throughout the year. That being said, I would like to share an observation I made while students were working on two different types of pattern problems, one being an open type and the other, a more closed type of problem. It was through these two different questions that I wanted to investigate for myself if my students were lacking in their procedural knowledge.

I gave a closed question that involved them looking at a number pattern; find the rule and extend it. The other question, the open questions, involved them showing me to find as many ways as possible to show how the number 25 could go through an input-output machine and come out as 77. To my surprise, 80% of my students were able to show me at least three different ways to get 77 from 25, whereas only 30% of the class was able to extend the pattern correctly and give the appropriate rule. So, my class was able to answer the conceptual question with a higher accuracy than the procedural problem. I thought this was very interesting. This leaves me with questioning my own beliefs about what I think is most important – kids being able to remember facts, procedure and rules or to be able to understand they why’s of math and be able to apply it to other situations. Ultimately, in the end, if students understand the material, they will be able to use it with or without knowing the exact procedures and rules, won’t they?