Mathematical understanding and multiple representations

The thing that convinced me the most in the authors argument was the study comparing students who learned analytically, visually and representationally. The students who learned representationally, or as a mix of both analytic and visual, did by far the best. It makes me think back to my high school days and how I always appreciated it when teachers showed an alternative way to solve problems if the class wasn't working well with the one we had been taught. One of the things that I love about math is that although there is only one answer, there are a million different paths to get there and they are all valid. I think the more methods students are exposed to, the more flexible they will be in their thinking. Math can often involve a lot of shifting ideas. If you've chosen one way to answer a question and get partway through and find that it won't work, you have to be able to switch to another method. This method of teaching will help students develop that mental flexibility.

The main types of mathematical representations in the article compare analytical learning to visual learning or learning with objects such as blocks. One thing my high school math teacher did really well was relate things to humans. When we learned about exponential growth, he showed us in human population and explained why it was so important to understand it. He used diagrams, but his explanation and the way he related it to people made it feel so important to learn, and also so clear. I think this is a strategy that is underutilized in math. Most people don't use exponential growth every day, but I think most people in my class still understand what it is and why it is so important to understand just from a 5 minute discussion in class. Relating things to human beings can really help with understanding, and explaining why it is so crucial to understand really helps with motivation.