A Case Against the "Math Gene"

I'm currently teaching a mathematics course for elementary educators (think of it as math methods, but with less focus on methods and more focus on content). In a student's essay, I encountered the phrase "one is either a 'math person' or not". That is, one's ability to do mathematics is determined at birth. Either your brain is such that you can understand math, or it is not.

This is certainly not a new sentiment, but I find it deeply troubling coming from the mouth of a future elementary educator. How can this person possibly be an effective mathematics teacher if s/he splits every math class into those that can learn math and those that can't?

Are you aware of any articles, studies, etc. that dismiss the notion of the "math gene"?

Preferably, the reference will be short enough to assign as class reading. I think it is too late in the semester to assign an entire book on the subject, though it could be a possibility if I teach this course again.

The primary goal of this reading would be to convince the future teacher that an average student is able to learn math, and so is worthy of being taught seriously. I am not particularly interested in articles that show how this can be accomplished (that is the purpose of their math methods course), just that it is possible to accomplish in the average case.

Solution 1:

Lockhart's Lament might be the best reading... Unfortunately, much of the contemporary PR effort to make "great mathematicians" into "heroic figures" has played upon the weirdness of personalities, and identified common-sense mathematics with esoterica, as though it were just one remove away.

(Another hazard of L's L is that it addresses the "fine art" aspect of mathematics, rather than the common sense aspect. The criticism of the pointlessness of the usual school curriculum is accurate, though.)

First, what I view as the context... Ironically, the extreme tediousness and palpable pointlessness of (usual) school mathematics is (I suspect) what people object to, not mathematics itself. It is presented as infinitely fragile and fussy, with whimsical "rules", necessarily requiring nearly-endless drill to achieve the level of quasi-perfection necessary to "get the right answer". Blech, indeed. Why would anyone want to spend their time that way?

The genuine survival-skill mathematics that probably everyone needs to know (e.g., how to estimate things) is hard to formalize, hard to fit into "school curriculum", hard to "program" (in the sense of getting people to learn it on a regular schedule), and probably as hard to grade as essays in English composition. Thus, the drift away from this in the curriculum, into semi-pointless, rigid, and literally unpleasant activities is understandable, while extremely unfortunate.

Also, claiming that something requires special abilities is a seemingly-excellent excuse for not putting in the work to learn how to do it, and a ready-made excuse for incompetence, even gross incompetence. Worse, this is an excuse for future educators to not engage with the issues of mathematics curriculum in K-12.

As noted in other answers, genuine dyscalculia is apparently rare. Many people will grab onto such a claim just to excuse themselves... It is socially acceptable, even a sign of artiness or "humanity" to claim inability to do math. This is a bit perverse.

What to do? Well, one can "correct" the slogan "Some can do math, others can't", to "Some find math interesting, others don't... but everyone needs to be able to do the basics, to survive".

As to official studies denying the existence of a "math gene", it would surprise me if there were such things, apart from the dyscalculia notion, because the claim is diffuse and ambiguous anyway. Test whether some people "can't do common-sense math" "no matter how hard they try"? But of course nearly everyone can tell that 1375 > 892, or that 132 times 755 is bigger than 10,000, unless the very questions induce a panic-attack, which is the sort of thing that happens with some people. But all my experience with (college) students' panic/anxiety is that it is a result of many years' unfortunate experiences, not something innate. The innate aspect might be the anxiety itself...

The worst experience I've had teaching was trying to explain to future grade-school teachers the epsilon-delta version of calculus. This was the syllabus for a one-semester course required of them. No amount of cajolery, sympathy, or lenient grading could jostle them out of their apparent commitment to their belief system, their very identities, that they were unable to do math. It was "already too late" to talk to them sanely about it. A sad conclusion.

Not exactly answering your question...

Solution 2:

This is a question the Canadian mathematician John Mighton addresses in his book "The Myth of Ability". He believes nearly everyone can learn elementary (pre-calculus) mathematics, and has created a teaching program called JUMP for elementary school students. While the program is not a proper double-blind test, it has been used successfully for many years in Canadian schools, including for the learning-disabled.

Another example would be Jaime Escalante's work in teaching AP Calculus to inner-city school students.

In both cases, hundreds of students who showed no aptitude or even interest in mathematics became interested top achievers.

Solution 3:

I think the general scientific community frowns on the idea that there is a gene which nullifies ones aptitude for learning mathematics (or any discipline). This is especially true for K-12 mathematics, which is essentially mechanical and methodical.

AFAIK there aren't any formal studies debunking this on the level of genetics, but there are plenty of authors who assert convincing arguments that mathematical reasoning is part of human nature in much the same way that language is. In this view, a gene stopping one from learning mathematics is as silly as a gene stopping one from learning to read or speak. Any legitimate case of this would constitute such a tiny minority to be dismissed as a general concern for a teacher.

For an example of such an author, see Keith Devlin (an experienced writer of so-called 'popular math' books) and his book The Math Gene

However, if you're teaching people to teach K-12 mathematics, there is certainly no better text than A Mathematician's Lament. This one is a mere 25 pages, so it is certainly assignable as a short homework assignment. It's an honest and unyielding criticism of the current state of K-12 education from the perspective of real mathematicians. It's certainly a bit dramatic, but I doubt your students will ever forget reading it, and it will definitely be a great source of a discussion.

Solution 4:

Perhaps Dispelling the Math Myths would be useful. On the other hand, here's an article which claims 420,000 students in England and Wales have dyscalculia.

Solution 5:

I would also emphasise the importance of finding patterns: one great school teacher I knew wrote that if you can't see patterns, then are you really alive? Do a web search on "mathematics and patterns" to find more on this.

See also our web exhibition Mathematics and Knots and the associated article Making a Mathematical Exhibition.

The aim was to show the methodology of mathematics as part of the normal methodology in which we explore and make sense of the world. This also justifies our article The methodology of mathematics. Other issues are discussed on articles available from my page Popularisation and Teaching, for example the issue of Famous problems. But the issues there are not discussed with mathematics students, to their detriment, I feel.

I am afraid many aspects of mathematics publicity, including the "Million dollar problems", do great damage to the image of mathematics.

April 23, 2017 I would like to add a translation of a part of Grothendieck's Esquisse d'un Programme, with my emphasis:

"The demands of university teaching, addressed to students (including those said to be “advanced”) with a modest (and frequently less than modest) mathematical baggage, led me to a Draconian renewal of the themes of reflection I proposed to my students, and gradually to myself as well. It seemed important to me to start from an intuitive baggage common to everyone, independent of any technical language used to express it, and anterior to any such language – it turned out that the geometric and topological intuition of shapes, particularly two-dimensional shapes, formed such a common ground."