Why do some people find ‘simple’ mathematics problems so impossible. I used common fractions for my research but it wouldn’t matter which specific concept I had chosen.
The answer I discovered and proved was that children and adults alike, who had a mental model of the concept, could solve the math problems. Those who didn’t were using rote rules that had no meaning, no models in their mind, so they made mistakes or gave up. They often could follow the rules successfully as long as the next problem looked exactly like the last one. If presented a problem that looked different, they couldn’t picture how to modify the rules, they couldn’t see where or how it matched up to the last one or something they had seen before.
Mental models are built by drawing, building with objects, and imagining.
One type of mental model that can help with thinking clearly and making strong decisions is the mind map. It helps you brainstorm lots of options and then it organizes those options for consideration.