Evidence for or against the claim that some students are "algebra people" and others are "geometry people"

Question

Where I live and work, there is a widely-accepted and often-repeated claim that there are two kinds of students: "algebra people" and "geometry people". This claim sometimes gets expressed in different ways; sometimes it is articulated as a difference in ability ("The students who are good at algebra tend not to be good at geometry and vice versa") and other times as a difference in interest ("The students who like algebra tend not to like geometry and vice versa"). This belief is often conflated with claims about some students being "visual learners" (despite the fact that so-called "learning styles" do not exist).

On its surface, this belief seems to me to be almost certainly a myth -- at least when expressed in terms of ability. But it also seems like it could be empirically tested. If people who are good at algebra were bad at geometry and vice versa, that would surely show up through an analysis of the grades they get in school, or how students perform on standardized tests that include both kinds of content.

As far as interest goes, the claim has slightly more surface plausibility. I know plenty of adults who will testify that the only math class they ever enjoyed was Geometry, and others who will say with equal conviction that Geometry was the only math class they hated. But a few anecdotes is hardly compelling evidence. This, too, seems like it could be easily studied empirically with some kind of attitudinal survey.

So the question:

Have there been such studies? Is there any evidence for or against the claim that people tend to be either "geometry people" or "algebra people"?

Answer 1

This is the story of an attempt to find some evidence for something "similar". Let me start with an anecdote.

Personal anecdote. Yeeeears ago, as a math student I was good at continues mathematics (e.g., analysis) and bad at discrete mathematics (e.g., algebra, graph theory). To be honest, I wasn't even able to accept the given proofs in graph theory as "real" proofs, let alone to attempt for one.

Why this is related to your question. I don't know if there is an established difference between continuous and discrete mathematics, but I feel the distinction between geometry and algebra as you mentioned is somehow related to it. If not, you can see the rest of my answer as an attempt to address a similar concern.

Research. Yeeears after my student time, I was a mathematics educator working in a math department where I had a chance to tell the anecdote above to my mathematician colleagues. Interestingly, many of them knew someone else with the same experience. Thus I decided to find some hard evidence to show there is something called "continuous thinking" and something called "discrete thinking" where some people are good at one but not necessarily at the other. A master student of mine "chose" this as the topic of her dissertation. We focused on understanding of proof in analysis and algebra. We saw a proving activity as a problem solving activity and accordingly we use some of the variables in research on problem solving (as introduced here by Kilpatrick) to study whether there is any difference in students' thinking of proofs in analysis and algebra.

Design of the experiment. We gave students several pairs of proofs. In each pair, one proof was from algebra and the other from analysis. Both proofs had the "same structure". Students didn't know that the pairs are purposefully related. They were reading the proofs and then answering some questions designed in the light of some of the variables (given by Kilpatrick).The variables were too many, we just tried some of them. Unfortunately, I couldn't remember now which variables we used, perhaps because of the result of the research.

Result. We didn't find any difference noticeable!

Conclusion. I still believe there is some differences there that we have failed to find!!

Answer 2

I don't know if this has been studied. Here's how to do it.

I think the data required for this might very well be public in Finland. At least the final grades of pupils are public knowledge. I don't know about the situation elsewhere.

One could go to a school and ask for grades of mathematics courses.

There are two forms of the hypothesis.

The strong one is that geometry and algebra grades are negatively correlated. This is very unlikely, since practically all grades across subjects are positively correlated (e.g. history and mathematics), at least in the compulsory school levels.

The weak one is: After accounting for the average mathematics grade, the geometry and algebra grades are negatively correlated. This might even be true, but I would be surprised if the effect was large.

Answer 3

Not quite the same question, but along the same lines is On the Persuasiveness of Visual Arguments in Mathematics. It looks at how convincing different mathematicians find visual proofs compared to written ones.