Teaching Children to Think

I have been thinking about how I teach math. I always use manipulatives and hands on learning with a little bit of worksheet practice. In my centers I try to include hands on activities along with a journal topic and guided math groups. This year I tried hard to incorporate some expemplars. For those of you who are not familiar with exemplars they are word problems that encourage students to solve the problems any way they wish. They are applauded for explaining their thinking, drawing pictures, making charts, and doing calculations. Students are measured on a rubric, which they are familiar with. When I first introduced the exemplars to my students it blew their minds. I have found that students are not used to thinking of math in various ways and explaining their thinking. I think that if we start explaining our thinking about math and having students explaining theirs in Pre-K we will see a progression from year to year of students who are able to express why an answer is correct and why and how they found the answer. I was reading an article in the National Council for Teachers of Mathematics (NCTM) magazine recently and was encouraged by one teacher's story of having her students explain their thinking. She stated that they have a "mental math" time at her school. The students are expected to solve problems without counting on their hands or using paper and pencil. The teacher goes on to explain that she gave the students the problem 11 + 9. It was fascinating to read about how her students reasoned their answers. Her class included first and second graders. She explained that many of the first graders did not know how to solve the problem correctly because of their lack of knowledge of place value. After thinking about how much trouble my students have in explaining their mathematical thinking I am convinced that a mental math time each day is a great solution to the problem. If students get used to talking about problems and how to solve them without being able to use manipulatives or pencil and paper it will force them reason their processes. After all, we are not benefiting anyone if we teach children to simply compute problems. Teaching them to think about why things work they way they do and how they can solve problems multiple ways prepares our students for the real world. I encourage all teachers to try a mental math time next school year. I will be updating you all on how this goes in my classroom. Here is a link to site where you can download the above referenced article: http://www.nctm.org/publications/article.aspx?id=21447