When I went to school, there were two camps: people who believed that they get maths and people who don’t. I was always a sceptic of this segmentation. There were people who believed that they were good at maths, and also got good grades, but also the polar opposite. This seems to serve as weak evidence, that there is a distinction between people who get maths and people who don’t. Moreover, that people usually are good at predicting where they lie on the spectrum.
The first question that comes to mind is: do they first believe that they are good at maths and then get good grades? Or do children first get good grades and accept the premise that they are simply good at maths?
The scientific evidence seems pretty clear on whether personal beliefs about academic achievements influences grade performance: Skinner 1990 found that children who believe they can produce the responses that lead to desired outcomes perform better academically. Morrison 1979 found that students with high self-esteem predicted higher grades compared to their prior grade average in the course. But these studies don’t make statements about the causal direction. Do personal beliefs about academic achievements influence grade performance or vice versa?
Why does this matter? If good grades lead to higher self-esteem about academic achievements, then we shouldn’t work on improving academic self-esteem. On the other hand, if improving academic self-esteem improves grade performance, a student who believes that they get maths might get better grades. Changing how you perceive your performance will increase your grade performance.
Mason 1989 seems to suggest that the relation is bidirectional. If you get good grades, you will make it easy to believe you are good at school or maths. This will make it easier for you to motivate yourself to study, etc., which will help you in getting good grades. So, one point of improvement could be to increase your academic self-esteem. This won’t do the whole job, but part of it and leads to positive feedback loops.
To come back to the opening topic: this seems to give an answer to the knockout argument, that people don’t get maths. You plausibly can get maths, but perceiving yourself as somebody who isn’t good with numbers isn’t helping. You can achieve better results by better beliefs.
Now, there are edge-cases. Students who get bad grades, despite putting in the effort, but perceive themselves as people who get maths. Students who get good grades, but perceive themselves as people who don’t get maths. This might be due to an extra variable. The first group might get better grades if they weren’t perfectionists about getting maths. Getting good grades isn’t necessarily a matter of understanding, but also of gaming the system. I wouldn’t go as far as saying that you have to cheat or lie. I mean that you can literally optimize for getting a good grade as a proxy for understanding something and fail at understanding. As long as exams don’t test understanding, this is a possible and easier way. Similarly, students who get good grades, but believe they don’t get maths, do so righteously. They simply do what they are told. Calculate the determinant? Okay, done. What does it mean? Don’t know.
To conclude this section, the initially mentioned camps exist. People who don’t get maths, and people who get maths. But they are way smaller than they seem to be by what people say. Much more people could understand maths if they adapt a different mindset. Similarly, people who get good grades don’t necessarily understand maths. The segmentation has to look more like this:
In other words: if you are in high school, it’s unlikely that you won’t get good high-school maths grades if you want to. A large amount of the class could get good grades, but don’t, because of several reasons. Lack of motivation or perfectionism, for example. A large part of the people who get good grades doesn’t understand anything and is good at doing what they are told. There is a clear distinction between those and those that understand it.
I was part of the second camp in high-school. I didn’t think strategically about learning and getting good grades, and when I could have, I wasn’t motivated because I lacked a vision. I always got by with reasonable grades.
Even after graduating, I struggled with thoughts like ‘Judging by my grades, I simply am not smart enough, right?’. In other words, when looking things up on Wikipedia, I skipped over the mathematical formulation of things and looked for the interpretation. I always thought, ‘I could get maths! Just need to put more effort in.’ but didn’t seem to improve in high school. I had part of the mindset, but didn’t want to dive back into maths, out of fear that I truly get the approval that ‘I am not smart enough to understand maths.’.
Now, I find myself skipping over the interpretation to get to the mathematical formalization. I get the most out of actual formalized thoughts. In university, I now achieve top of my class in maths and similar exams.
How did I end up here?
The first thing I did was to study a ton when the next maths exam came up. Throw yourself at the opportunity to thrive. We had a terrible ‘foundational mathematics for neuroscience’ lecture. Subsequently, I didn’t go to the lecture, so I had to teach myself. I worked on maths problems for 4 hours straight every day until the exam, and loved it! I also got one of the best grades of my class, but I wanted to know whether I enjoy the process if I don’t stress myself. This was the first evidence I acquired – now I knew that I could get good grades if I put in the effort and that I have fun while doing it.
But it wasn’t ‘true mathematics’ in the sense that it was an introductory maths lecture for students who study neuroscience. So, I couldn’t trust the result. Thus, this semester, I enrolled for a ‘introduction to linear algebra’ lecture. I was anxious that I wasn’t going to make it and that I wouldn’t be able to keep up. It turned out to be the opposite. I relaxed because we started at simple axioms and worked ourselves up to complex conclusions. I became used to the confusion when the professor introduces a term at the beginning of the lecture and uses it throughout the lecture, while you haven’t wrapped your head around it yet. You know that this is how everybody feels and should feel – most do.
With this mindset, I wasn’t blaming myself for not understanding something, strengthening the shadow that waits for the next opportunity to tell you that you’re stupid. I was equipped by saying that everybody is going through the same problems and that you can see it as a challenge that you can conquer. Now I thrive in mathematics and enjoy solving puzzling problems.
- grade performance is influence by locus of control (do you attribute performance to internal factors like motivation or to external factors like luck?) and high self-esteem regarding high-school performance.
- This means two things:
- You can improve, even if you have bad grades. Start by adopting a growth mindset.
- Bad grades don’t refer to yourself being dumb.
- If you struggle with thoughts like ‘I am not smart enough for maths’ and shy away from mathematical symbols, I recommend enrolling in introductory maths lectures at your local university.
- This way you can achieve several things:
- Get used to mathematical notation and see the beauty in it. Learn it like a second language.
- Getting rid of these thoughts. You will see that you are more than capable to understand maths. This will help you adopt a growth mindset – you will serve yourself as evidence.
- See that maths is easier if somebody explains it from the ground up. Moreover, that you learn better and faster if you are intrinsically motivated (e.g. if you don’t stress yourself with necessarily writing the exam in the end).
Disclaimer: This is not meant as professional medical advice for people struggling with mental health issues. When I say fear, I don’t mean a pathological fear, but rather a fear within bounds.