Comprehension Instruction in Math

When my teacher in High School was teaching me about geometric sequences, I remember him first giving a brief reminder of what arithmetic sequences were…which we had learned before this time. My teacher gave us an arithmetic sequence problem on the board (something to do with simple interest) and asked us to find the first 5 terms and the recursive formula for the problem. He gave us time to work through it while he walked around the room answering individual questions and observing how well were remembering and if we were comfortable with this previously learned knowledge.

Next he brought us back into the classroom discussion and went over the problem on the board. He then gave a 5 minute (or so) lesson on geometric sequences basing this on the same problem that we had just done for arithmetic. He showed us how these two were connected and how we could go from the arithmetic sequence to the geometric sequence for this problem.

This particular teacher would often ask us to take a moment to think about what he had said, so that our minds had time to process, understand, and/or question. He would ask us to write questions down as he lectured…otherwise we would forget them. He often would use think aloud strategies with us. With this lesson I remember him talking about finding the value of r, the common ratio. For example, if a person had deposited $100 and this $100 would gain an annual interest of 6%, I remember him saying that he first thought to let r=.06 (since this is the decimal for 6%), so after the first year the person would have earned $6 in interest… But, then he mentioned that he wanted to know how much money would be in the account at each year, so he explained why we should let r=1.06 instead…this way we would know that there was $106 in the account after the first year. He was really great at explaining what he was thinking. He would often pose questions…for instance, he would say, “what should I do next” or “where did I go wrong”. He was great at letting us think instead of him just telling us the information.

Thinking back on this teacher I will use a lot of his strategies for comprehension instruction. I love that he would connect our prior knowledge to new topics that he was introducing (One of Buehl’s processes). I love the think aloud strategy, it made me feel like he had to work for the answer too and that he wasn’t just a math machine that knew all the answers. I will use his moments of silence to think about what was just taught. This teacher also drew a lot of pictures, diagrams, and tables (also a Buehl process) that I will use…to me it’s much easier to understand if you can visualize it. I like that he told us to write down questions throughout the lesson (Also in Buehl), I will do this as well. What I think I liked the most was that he didn’t just lecture; he asked lots of questions and helped us to lead the lesson through our own thinking instead of simply being told. It was okay to be wrong in his class…he always praised us for trying.

Just in case I sparked your "interest" into figuring out interest...here is a link to my very favorite math geek explaining simple and compound interest...he is my hero!