The Self-reinforcing Myth of Hard-wired Math Inability

There is a commonly held belief that some people have brains that are pre-wired for mathematical excellence, while everyone else is doomed to struggle with the subject. This toxic myth needs to be put deep in the ground and buried in molten lead. It is as destructive as it is self-fulfilling.

The myth equally encourages people who are good at math to falsely believe (Murayama et al., 2012) they are more intelligent than those who are not, and leaves everyone else inclined to believe they can never improve. This is despite the fact that math ability has very little to do with intelligence (Blair et al., 2007).

The reason this myth exists is well understood. School students who were well prepared by their parents in math prior to starting school find themselves separated in ability from their classmates who were not. The latter group consider the seemingly unachievable abilities of their peers and quickly lose confidence in their own abilities. Once that self-confidence is lost, any attempt at completing a math problem leads to math anxiety (Ashcraft et al., 2002; Devine et al., 2012), where thoughts of self-doubt cloud the mind and make it difficult to concentrate on the task at hand.

Mathematics, like computer programming, is a discipline that requires concentration. The student needs to be able to follow a train of thought where A leads to B leads to C etc. A student who lacks self-confidence struggles to maintain the necessary train of thought due to being repeatedly interrupted by negative thoughts about their abilities.  This results in poor performance and reinforces the idea that they are incapable of learning the subject.

It is interesting to see this belief so prevalent among software developers who are perfectly capable of writing an algorithm in a programming language, but suddenly feel that it is impossible to grasp the same algorithm represented by a set of mathematical symbols. There is simply no reason that this should be the case. I’ve yet to meet an experienced programmer who would tell me they find it near-impossible to learn the syntax of a new programming language and yet that is precisely what is entailed in learning how to express an algorithm using linear algebra.

A common point of confusion for many who haven’t done a lot of math since secondary school is in the use of mathematics as a language rather than a set of equations to be solved. In academic computer science, linear algebra, as it is used to express algorithms, is not something to be solved, but rather a language used to describe an algorithm.

Understanding the language of academic computer science is becoming increasingly important as the traditional staples of academia, such as machine learning, increasingly find use in industry.  After all, even if a software developer manages to avoid the math in their work, how can they expect to keep up with the latest developments in this fast-moving field without an ability to understand the academic literature?  Yet this is precisely what some software developers are attempting to do.

Math inability is not hard wired and software developers are already well practiced in the mental skills required.  We use the skill of stepping through a problem and visualising the state changes that occur at each step, every time we read or write a piece of code.  Anyone who can do that is capable of becoming proficient enough in mathematics to understand the mathematical components of the computer science literature.

References

Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current directions in psychological science, 11(5), 181-185.

Blair, C., & Razza, R. P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child development, 78(2), 647-663.

Devine, A., Fawcett, K., Szűcs, D., & Dowker, A. (2012). Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety. Behavioral and brain functions, 8(1), 1.

Murayama, K., Pekrun, R., Lichtenfeld, S., & Vom Hofe, R. (2012). Predicting long‐term growth in students’ mathematics achievement: The unique contributions of motivation and cognitive strategies. Child development, 84(4), 1475-1490.

See Also

Andreescu, T., Gallian, J. A., Kane, J. M., & Mertz, J. E. (2008). Cross-cultural analysis of students with exceptional talent in mathematical problem solving. Notices of the AMS, 55(10), 1248-1260.

Berger, A., Tzur, G., & Posner, M. I. (2006). Infant brains detect arithmetic errors. Proceedings of the National Academy of Sciences, 103(33), 12649-12653.

Post Edits

13/07/2016 – Added references and see also sections.  Updated inline references to show primary sources rather than just linking to secondary sources.

14/07/2016 – Corrected typo in final paragraph “Math ability is not hard wired…” changed to “Math inability is not hard wired”.


Published by

James Burkill

Veteran software engineer and student of all things AI. LinkedIn: https://ie.linkedin.com/in/james-burkill-459a1513

5 thoughts on “The Self-reinforcing Myth of Hard-wired Math Inability”

  1. Our country is lagging behind in STEM because of this myth. Like all subjects one has to work at them and not give up or lack concentration. If you think of math, as a mental game, you do better. Though I think some people with real disabilities find it tougher to learn.

    1. Exactly. Of course I agree that people with certain types of disabilities are an exception to the rule. The problem seems to go beyond mathematics too. I’m currently taking a class on the R programming language in which I am surrounded by people who come from mathematical/statistical backgrounds. As far as I can tell I’m the only one there with a software development background. They’re all much better than me when it comes to the math and yet are struggling with the programming. That shouldn’t really be the case, but the feedback people are giving has anxiety written all over it. They’re getting overwhelmed.

      Big math problems need to be broken down into small components and addressed one step at a time. Big programming tasks need to be broken down into small components and addressed one step at a time. Both require a train of thought to be followed and maintained without distraction to complete the task. Anxiety is a distraction.

  2. Hi James,

    I wanted to thank you.

    I have always been great at ‘doing words’, but have similarly struggled with math. In the last few years, I picked up Python, and even had a short-lived job as a web developer before playing to my strengths as an editor.

    That is, until the coding bug got me again. I’m fascinated with AI and machine learning, to the extent I am enrolled in Udacity’s Deep Learning foundation nanodegree program. At first, everything was reasonably intuitive, then came the formulas. I found myself unable to look at them for long, and when I tried to read through them step by step, I found myself so terrified of making a mistake and ‘getting it wrong’ that I found it better not to try at all.

    When I watched the accompanying video that explained the formula (I believe it was the sigmoid function) I saw how easy it was to read, and that I was not required to ‘solve’ the function just as someone is not required to ‘solve’ a sentence.

    I’m currently working my way through the World of Math on Khan Academy, and it is stunning to me how quickly what I considered to be impenetrable and unreachable subjects became easier, and then second nature. I cannot believe my school days were filled with the fear of simply performing mechanical operations one after the other.

    Just wanted to let you know that you’ve inspired me to continue on my AI, machine learning, and math journey because of your article! A much needed boost.

    1. Really good to hear that the article had an impact. Given the science dispelling it, this myth should not be so prevalent. It might be the cynic in me, but I suspect a lot of the people on whom we bestow the responsibility to teach math to generations of children, are the ones who grew up believing they were special because they could do it. I suspect they’re invested in this myth on some level and don’t want to lose it. It also makes it nice and easy to write students off at a young age and not bother giving them the extra help and support they need to get them started. Hopefully things have improved since I was in school.

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