Bad at math/Follow-up: College material

A topic with some overlap with my recent text on “college material” is math ability and its interpretation: The world is apparently filled with people who are (a) highly intelligent, (b) have a weak spot specifically for math, even to the point of struggling with the principles of fractions.

The sad truth is that these people are almost* certainly not intelligent—they merely believe that they are, because the material they encounter in other fields requires too little thinking to learn, or to get a good school grade, for an intelligence deficit to become obvious. If someone is taxed by understanding** something as basic as fractions, elementary trigonometry, or high-school algebra, this points to serious limitations—even in the face of e.g. a later bachelor*** in a soft field.

*Exceptions might exists, possibly relating to some neurological condition; however, if they do, they are likely rare and I am not aware of any example in my personal experiences. There have been some cases of someone using the “I am intelligent, just weak at math” claim—all of which have been fairly stupid.

**As opposed to memorizing some rules about how to use fractions—those with an understanding can derive the rules when they need to. Further, as opposed to just finding math boring and not bothering to put in the effort. (Here a part of the problem with other fields might be found: Understanding can be quite important in these fields too, but is often entirely unnecessary to pass the grade or to create the self-impression of having mastered the topic, implying that a lack of understanding is not punished and that the student might not be aware of his lack of understanding.)

***Indeed, a disturbingly large proportion of the population seems to jump to the conclusion that anyone with a bachelor is intelligent—irrespective of field, grades, effort needed, and how much was actually understood (cf. the previous footnote).

I once heard the claim (and I would tend to agree) that we all have a point where math becomes “too hard”—the difference lying in the when and where. Comparing fractions with some of the math I encountered as a graduate student is like comparing splashing about on a flotation device with elite swimming—to fail at the former is a disaster. (And note that there are further levels yet above what I encountered even at the graduate level—just like not all elite swimmers are Olympians, not all Olympians win a gold, and not all Olympic winners are Michael Phelps.)

Generally, the impression of math created in school does not have much to do with true math: Math is not about knowing or being able to calculate that 13 + 25 = 38. It is about things like being able to reason, spot a flaw in an argument, find an overlooked special case, solve problems, come up with creative solutions, think abstractly, abstract the specific and find the specific in the abstract, see similarities and differences, … While there might be some room for having more or less math-specific talent (and definitely interest) for two people who are equally good at these skills, the skills are quite generic and translate into any number of other areas, including everyday life. Indeed, I would not trust anyone unable to understand fractions with any decision of importance or in an even semi-important role—not because understanding fractions is vital, but because the inability points to more general deficits.

Using math as a proxy for being “college material” is a plausible sounding idea—and it has the advantage over “[be] able to consistently learn through a mixture of reading and own thinking” (my suggestion in the original post) that it is easier to test in advance. However, on an abstract level, it has similar disadvantages to those of an I.Q.* cut-off, while my suggestion automatically takes care of aspects like differing difficulties of various fields. Of course, more practically, the “test in advance” aspect is quite important—which explains why e.g. the vanilla SATs have a math section and not a chemistry, history, or whatnot section.

*Not only are math ability and I.Q. fairly strongly correlated, but they are both arguably proxies for the same thing(s) in the context of being college material.

Excursion on the benefit of being pushed to struggle and revealed to be wrong:
An incidental benefit of studying math is that the student has a greater opportunity to learn both humility and his own limits. Math requires thinking, can push us to the border of what our brains can understand, and the only way to escape being provably wrong, again and again, is to be superhumanly good. In the social sciences, it is possible to go through a college education and an ensuing academic career without the same exposure to “I do not understand” (cf. above) and “I was provably wrong”* (either because the actual tests are missing or because there are loopholes when the tests go the other way).

*Note that I speak of opinions based on faulty thought, not e.g. faulty memory: There are many things (e.g. the year of Napoleon’s death) that are recorded as (more or less) fix truths, which might be misremembered and the memory verified as incompatible with the accepted record. A simple memory error says relatively little about someone, however, and being exposed to a memory error is unlikely to bring humility. In contrast, an elaborate hypothesis involving Napoleon and the Illuminati might be impossible to actually disprove, even when others consider it patently absurd.

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