I am moved to respond to Sol Garfunkel’s “Opinion” article.1 I am a long-time high school mathematics teacher in a public school. I started teaching around the time of SMSG and have been in the trenches throughout several of the math wars. I know Dr. Garfunkel’s fine work in creating interesting modeling projects and his outspoken opinion that using technology to solve problems that apply the mathematics we are teaching will better concretize students’ understanding of the underlying mathematics. It sounds like a fine idea, but the reality is often very different.
Our problems in teaching mathematics begin in elementary school. Sadly, many teachers working with our children at the start of their mathematical journeys are not themselves comfortable with the mathematics they are trying to teach. They often only know one way to teach an idea and they may not fully understand how that method works and why it gives the right answers. Such a teacher confronted with an alternate creative method (perhaps suggested by a clever child or a seasoned colleague) may reject the alternative rather than trying to see how and why two methods produce the same result. Beyond stifling the creativity of students and discouraging them from trying to see how the mathematics works, such an approach is not fertile ground for applications and modeling projects in which creative exploration and possibly unorthodox methods are encouraged as a means of truly understanding what is happening. Teachers who lack confidence in their own understanding of the ideas may not want to include these sorts of activities in their classrooms.
Related: Math Forum audio & video.