Math phobia is a fairly well-established phenomenon. Basically, it’s the fear of mathematics and, more particularly, the fear of having to do mathematical things oneself. It affects most people to some degree – fortunately for the sciences and engineering, not everyone – and some people do an extreme degree, to the point where they will have nothing to do with anything mathematical.In fact, there is evidence that the sensations provoked by the idea of math are actually equivalent to pain in many people. It seems to be a learned phenomenon; small children don’t have a whole lot of problem with numbers or counting, until they hit school. That’s when math phobia begins to kick in, due in no small measure to the extremely horrible teaching techniques generally applied to mathematics, particularly in the early grades. I don’t want to get involved in pedagogy right now; I just want to note that math phobia is not an inherent human characteristic, just one we’ve let ourselves be suckered into.
I’ll confess to having had a degree of math phobia myself at times. In high school, I really liked algebra and most of geometry, and did quite well with them; to the point where I was put in the advanced placement classes for math. My friends seemed to eat it up with pleasure; I stumbled through trigonometry, solid geometry, and introductory calculus with passing but not stellar grades and, I must admit, virtually no understanding. In college I took another introductory math class that at the time seemed to make calculus understandable, but it faded rapidly. I subsequently went through a Masters program in public administration/international affairs and five years with the federal government in increasingly responsible positions without having to seriously encounter anything mathematical other than budget numbers. Then I went back to graduate school to study organizational behavior and suddenly had to encounter statistics.
I was extremely fortunate to be able to take a course that was cross listed and co-taught between statistics and psychology, and thus concentrated as much on research methods as on the manipulation of numbers. In addition, the course made use of computer-based statistics, which was the time just being opened up interactively to students. Thus, I was able to see very quickly past the issue of calculation to the use and interpretation of numbers, and put them in the context of behavioral science research. In essence (and I know this point may annoy the real statisticians in my audience, if any), statistics isn’t really best understood as a branch of mathematics, but as a branch of psychology. Basically, it’s a tool for helping people avoid the inferential errors to which we are all too prone, as Kahnemann’s work has shown. So in my teaching of statistics and methods, I’ve always tried to avoid emphasizing the mathematical character of the work and concentrate on the interpretations, as well as on the integration of statistical material with the research methods they are intended to be part of. I don’t see any real problem with treating the processing of the numbers as an exercise in magic, as long as one understands what gets put in and what comes out when you wave your wand properly. So shoot me. Obviously, there are many dimensions to statistics beyond the magical, and even I have come to appreciate part of them. But it can work fine as magic.
Anyway, all this is a long prequel to the main point. I recently came across a very interesting paper by Kimmo Eriksson, published in Judgment and Decision-making last year, called “The Nonsense Math Effect”. Eriksson’s experiment involved asking a number of volunteers with Masters or PhD degrees in a variety of fields to read abstracts of a couple of papers (one in evolutionary anthropology and one in sociology). Half of the group got the original abstracts; half got the abstracts with this sentence added:
The reviewers were then asked to rate the quality of the research on the scale of 1 to 100.
So what happened? When the reviewers had degrees in scientific or mathematical areas, the addition of this bit of mathematical nonsense to the end of the article had no effect. But for reviewers in social sciences, education, humanities, and other non-science fields, the added math raised their ratings of the research significantly.
As Eriksson concluded (p. 749),
The experimental results suggest a bias for nonsense math in judgments of quality of research. Further, this bias was only found among people with degrees from areas outside mathematics, science and technology. Presumably lack of mathematical skills renders difﬁcult [one’s] own critical evaluation of meaningless mathematics….It may also be that people always tend to become impressed by what they do not understand, irrespective of what ﬁeld it represents—much in line with the “Guru effect” discussed by Sperber (2010). The scope of the phenomenon is a question for future research.
As a fairly well trained researcher, I find this conclusion rather depressing. Remember, these are reviewers with Masters and doctoral degrees; imagine what the effects might be among those with less training.
But let me bring this back around to where we started. What’s the relationship to math phobia? I would argue that the result that Eriksson obtained – a systematic overvaluing of the contribution of mathematics by those who clearly didn’t understand anything about it – is actually the precise “equally evil twin” of math phobia. That is, we are in awe of and often practically worship the things we don’t understand. And the less we understand something, the more we are inclined to give it credit, particularly when presented within a context where we believe it ought to be valued. So the more we tolerate and encourage the development of math phobia among our children, and let it persist in ourselves, the more we are open to charlatan games and other flim-flammery perpetrated by those inclined to do so. The only way out of the Eriksson phenomenon is better mathematical and scientific understanding. Failing that, we’re back to the situation that Gilbert and Sullivan described so precisely in Patience:
If this young man expresses himself in words too deep for me,
Why what a very singularly deep young man this deep young man must be!