How can pictures help students understand math? It seems that there are some hurdles set up in math education like math anxiety, and the push to learn material quickly.
“They perhaps had the luck to enjoy a positive math experience in school,” he said. “Or, frankly, from a cognitive neuroscience perspective, there is little doubt in my mind that they have quite a bit of a different brain than the average person who is trying to unlock the wonders of math, or just learn some math in order to get by.”
Wallisch is a brain scientist and math hasn't always been easy for him. The key to the beauty of math and understand it, is pictures. “As primates, we are mostly visual creatures. A good amount of the cortex in primates (upwards of 30%) is dedicated to visual processing in one way or the other. Put differently, things that look interesting or appealing are bound to attract curiosity,” he said. The brain learns in many different ways and looking at a movie or video (moving pictures!) can be very appealing to our brains.
According to Wallisch, mathematical imagery is what students are missing, and what causes confusion. He used the example of reading the words “Statue of Liberty,” and how it evokes an immediate image in the mind. But if a person couldn’t read, or had never heard of the Statue of Liberty, they would visualize only letters and words, not Lady Liberty holding her torch — and the same goes for math novices.
Since they have no experience, the mix of mathematical symbols on the page don’t mean much. “Mathematicians see equations by imagery built by long-term practice manipulating them,” he said. “The trick is to use software to visualize the equations so that those who don’t have the practice (or the unusual brain) can see the same.”
Wallisch began creating moving mathematical images for himself using technical computing environment Math lab, and said that, although he uses it for high-level research computations, high school students can just as easily build visual mathematical models with some guidance.
By creating images of equations and playing with the variables, Wallisch now sees what all the fuss is about. He wrote in a blog post: “Personally, I’m betting on aesthetics, with Kant: ‘Beautiful is that which is appealing without interest.’ As we can’t presume interest, aesthetics can serve as an important bridge(head).” You can see how pictures help students understand math.