If someone struggles in math, there are often three misconceptions to which people will point as an explanation.
The first misconception is that people divide into categories that classify them as inherently “either good or bad at math.” People mistakenly believe that math fluency and understanding is a fixed ”talent” or ability that can only marginally be improved upon with study or perseverance. Either one “has it or one doesn’t” goes the story. Those who believe that they “were never good at math” and that the situation is unchangeable are the ones that often hold this misconception. Time and again what we observe in practice is that because mathematics is a subject that builds upon itself, those that believe that they “aren’t good” at math actually have a couple of discoverable foundation areas whose understanding needs shoring up. Once those areas are strengthened, the “house” of mathematics gets stronger.
Next, some instructors and parents mistakenly believe that mathematical thinking and abilities are inherited and so if a parent struggled with math, then one is most likely to do the same. Clearly, if parents and teachers hold these beliefs, they do not foresee students improving in mathematics because the success or non-achievement is fixed; there is little chance of making great changes. This belief is simply untrue. One way we know this is that the author of this blog post has degrees in aerospace engineering and applied mathematics and had a mother who struggled with math. While there is definitely some advantage to growing up in a household where mathematical fluency is present because having parents that can explain points of struggle is an asset, success in math has far less to do with inherited abilities than is commonly believed.
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The third misconception, encapsulated by the classic question, “When I am going to use this?” is that math is difficult and not useful in everyday life. People don’t often see a use for mathematics beyond arithmetic and thus, students are not encouraged to stretch their understanding and skill level beyond fundamental skills. Instructors can be guilty of this too and often do not try to solve or teach problems that seem difficult. With virtually every opportunity we have, we stress the “here’s how this is used” aspect of mathematics and almost every time we do, the student response is “Oh, I didn’t know that. That’s kinda cool.”
