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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.

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I thought about that, in particular the article terrytao.wordpress.com/career-advice/…, but I don't know if it will resonate well with this group. In their view, I'm afraid they will see Tao addressing individuals who already possess the "math gene" and want to go on to do even more math. –  Austin Mohr Oct 15 '11 at 19:14
This is similar to saying: you are either a "word" person or not. Either you can learn to read or not. But those in the "not" category are a very small minority, those with dyslexia or other similar problem. I have heard some thoughts of a dyscalculia where one is diabled to the point of not being able to learn mathematics. But again that is a very small minority. I think the REAL problem is that learning math is HARD and many students & teachers shy away from it for that reason. –  GEdgar Oct 15 '11 at 20:05
@GEdgar As for your other point, many people use their apparent difficulty with mathematics as evidence that a "math gene" must exist. "Some super-smart people understand this stuff, so they must have something I don't." The purpose of the article would be to convince them that, even in the face of difficulty, the material is comprehensible to an average student. –  Austin Mohr Oct 15 '11 at 20:16
Whether or not there is evidence for or against a math gene, there are certainly a ton of studies on "priming" and "attribution theory". Basically if you believe there is a math gene and one of your students doesn't have it then you will cause that student to do poorly (because you will have primed them to think they won't do well) whether or not that is true. So I can't see any way in which having that attitude would be beneficial for a teacher. –  Matt Oct 15 '11 at 23:04
"Are you aware of any articles, studies, etc. that dismiss the notion of the "math gene"?" you should be looking for articals that confirm or deny your hypothesis, not just confirmation, hopefully the reasons why are obvious –  jk. Oct 16 '11 at 2:19
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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...

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I would like to say that there are genuine cases of dyscalculia that are not mathematically disabling. My brother has been diagnosed with dyscalculia; he used to have an extremely hard time doing simple arithmetic (he takes relatively long today also), but he still managed to pass high school maths with high marks and had little problem grasping things such as Cantor's diagonal argument when I explained them to him. It seems to me that arithmetical talent isn't related to understanding abstract concepts and reasoning. –  josh Oct 16 '11 at 0:13
One small bone to pick: "Why would anyone want to spend their time that way?" Because some of us were drawn to math because we liked following rules, we liked precision and quasi-perfection, and we liked calculation. –  Jesse Madnick Oct 16 '11 at 0:35
@JesseMadnick I think what paul is trying to say is similar to the following : You don't need to be a virtuoso to have a guitar at home or a keyboard to enjoy practicing and even maybe performing in a local pub. Then imagine someone comes in and adjusts your volume knobs, changes the strings or makes up excuses because it doesn't sound right. You can't even start playing let alone enjoying. That's the feeling kids constantly get from their schools' system. –  user13838 Oct 16 '11 at 1:00
@JesseMadnick And after seeing the L's L, I see that i have repeated the wonderful argument in a very bad way :D –  user13838 Oct 16 '11 at 1:02
By the way, I have no objection to precision, nor to calculation, per se. Nor to "following rules" if it means that we've ascertained how things work, and can reliably reproduce desirable outcomes. However, my recollection of my own school-math experience (say K-12) was that the "rules" were not explained, and, in hindsight, were capricious or even wrong, or, at best, conventions. But/and the meta-complaint is that no one was allowed to ask "why?". Finally, in many more-sadistic cases, "math teachers" enjoyed asking questions they knew kids couldn't likely answer, or constraining time... Sad –  paul garrett Oct 31 '11 at 14:16
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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.

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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.

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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.

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I think that the one thing that always works (and is hard to do) is to make people experience stereotype threat (that is: partition the class according to some random attribute like eye color and tell them a couple of days that studies have shown that group X is better at math than group Y and then adjust your praise and expectation accordingly; change the treatment of the two groups after a couple of days).

Easier to implement: Let people take an implicit association test on a subject where they feel that they are enlightened and non-discriminating.

Everyone should know that: 1. you have to actively counteract prevailing prejudices to not act in a discriminating way 2. attitudes of teachers and students impact exam results significantly

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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" on http://www.popmath.org.uk and the associated article "Making a mathematical exhibition" at http://pages.bangor.ac.uk/~mas010/icmi89.html

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", available from my Popularisation and Teaching page. 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.

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http://giftedexchange.blogspot.com/2008/11/nature-some-people-are-naturally-good.html Basically states that there is a "math gene", "Those that have this acuity wind up doing better on standardized math tests, even controlling for IQ. "

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No one is arguing that people don't have differences in ability; clearly they do. For me the key quote from the question is "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."This isn't saying that it is easy; in fact, for the average student, I think we all know that it is hard to learn math. But that doesn't mean it is not worth doing. As others have pointed out, it is somewhat analogous to the fact that some are better readers than others, but all should learn to read well. –  Jonas Meyer Jan 19 '12 at 5:53
@Jonas But it isn't fair to have "math people" and normal people in the same class, they will ruin the curve for normal people. Math classes are taught by math people and for math people and if you aren't a math person you have to work incredibly hard and and get lucky just to do almost as well as a math person putting forth minimal effort. –  user138246 Apr 26 '12 at 15:20
@Jordan: I will oversimplify in these comments and state some opinion, but in another time and place there are issues here worthy of discussion. Students who really excel in math, perhaps with the aid of some innate ability, are best served moving to more advanced classes, not competing in "curves" with others in less advanced classes. Regardless, not everyone grades on "curves"; there are standards that students must be held to independently of the average performance of peers. Teachers doing what they can to help all students excel is important. On the student's end, worrying about.. –  Jonas Meyer May 1 '12 at 3:04
..."fairness" because of a perception that some of the other students do not find it as difficult is, in my opinion, likely to be a distraction and impediment to learning. Many teachers are willing to offer much help to any who ask. Students who find they need more help would often be well served by finding more time to ask for help from their teachers. One benefit this has over (or in addition to) getting outside help (from tutors etc.) is that the teacher can become more in tune with where the student is struggling, and can improve as a teacher. My advice: Focus on your own studies,... –  Jonas Meyer May 1 '12 at 3:05
...not on who might do better than you. It is hard work. Even "math people" do not excel without hard work. (If you have serious grievances about actually performing well due to hard work, and yet being graded badly because of a teacher using some bizarre "curve", I cannot offer policy advice specific to your school.) –  Jonas Meyer May 1 '12 at 3:07
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