RH's first words, below, are correct. I did misstate the truth. I should have said, "... we have found that MANY students do flounder in school mathematics because they are too mathematical for the curricula that they encounter." The majority of diligent flounders struggle because they cannot digest key curricular presentations into personal common sense. But some students are so dependent on personally digesting such presentations into mathematical common sense that they become math-impaired for continuation up the curricular ladder. Many are even "diagnosed" as being "math impaired."
Unfortunately, RH seems to have absurdly interpreted my remark as claiming that "ALL students who flounder in algebra do so BECAUSE they are very good at mathematics." [The differences between "none", "some", and "all" are essential for logical analysis. It often is "left to the reader" to discern which of those meanings is being used by an author.]
As for the clinical evidence for which he calls, we do have a wealth of corroborating video tapes. But I have not the time, money, or inclination to merge those into a scientific documentary about that particular phenomenon. Any research clinician can get the same findings. If RH wants "proof", all he needs to do is to conduct extensive, *eductive* clinical instruction of 20 mature, severe victims of "math anxiety." He will find that very often, students "don't get it" because the "it" cannot be rationally derived from only whatever they already knew.
His attempt to discredit the Clinic's "program" is equally absurd. The MALEI Clinic is not a curricular program. Its concern is with sustaining/enhancing personal mathematical health of persons of all ages, rather than with producing high achieving students. As an instructional service, the Clinic is an academic therapy program for the prevention or treatment of Mathematics-Learning Distress (MLD: dismay, frustration, alienation, aversion, anxiety, depression, fear, phobia, etc.) Yes, some of the Clinic's patients have gone on to become math majors or math teachers. But the Clinic's role is merely to ensure their potentials for doing so.
As a research function, the Clinic empirically conducts clinical case-studies to advance mankind's state of professional knowledge about human learning of curriculum-targeted mathematics ... scientifically backed by theoretical mathematical and operations-analytic research in the instructional guidance of mathematical learning. "Civilization" has "got it wrong" to the extent that humans depend on traditional, myth-based, pre-judicial, sloppy thinking ... rather than on careful, analytic, rational inquiry. For example:
Re his: " ... that most students flounder at what we call algebra and thus what we call algebra isn't really algebra." If "thus" means "therefore", no mathematics professor would thoughtfully make such a claim. What can be said in that direction is that much of the mathematics curriculum that is mathematically common-sensible to persons who already are well versed in algebra is not at all mathematically common-sensible to most students. [Square roots of -1? ... "complex" roots of parabolas? ... binary-operation inverses of binary operations? ... "multiplications" that reverse directions? ... number-line points as "ratios"? ... et al.] So, the students must "learn" such stuff not rationally, but through non-sense acceptance of seemingly non-sensible dictates by authorities ... contrary to the rational nature of mathematics. Some mathematically-minded students are so resistant to the irrational learning of school mathematics that they cannot effectively cope with non-common-sensible curricula.
A basic principle of clinical psychotherapy is that all functional humans internally develop and rely on "schema" that function essentially as personal "theories" about whatever they encounter. [RH's responses to my earlier comments manifest his own theorizing about what he thought I said.]
The human mind is "mathematical" to the degree that its notions and processes favor precision, sensibility, and rational learning. That is how humans mathematically comprehend things. All functional humans are "mathematical" in that sense. Some are so mathematical that they they are confounded by non-mathematical curricular presentations of "mathematics." Their minds demand that they internalize the presentation into mathematically common-sensible, rational, personal theories. Of course, scores on SATs or other tests ... and grades and credits ... can badly mis-measure their mathematical potentials. Such students typically are creative, analytic and self-directive, and have strong language skills. Because they often fare poorly with mathematics curricula of the "performance-training" kind, they commonly achieve only very low mastery of school mathematics.
From: Robert Hansen Sent: Wednesday, November 06, 2013 4:32 AM To: Math-teach Teach Subject: The Myth of 'I'm Bad at Math'
On Nov 5, 2013, at 6:29 PM, Clyde Greeno @ MALEI <firstname.lastname@example.org> wrote:
In the research-oriented, MALEI Mathematical Learning Clinic we have found that a major cause for students being "no good at math" is that they are TOO good at math.
That isn't true Clyde, or at least you are hiding the evidence. As far as I can tell, in the 20 or 30 years you have had this notion, you have not produced even one mathematically strong student using your "program". And I have requested this proof a dozen times. You offer as proof the fact (not myth) that most students flounder at what we call algebra and thus what we call algebra isn't really algebra. Most students also flounder at what we call music. Are you suggesting that civilization got that wrong as well? Do these students that are too good at math ace the SAT math section, or are they also too good for that? Who works with a theory for 30 years and leaves this gaping hole in the middle of it? Unless of course this isn't scientific at all, despite all of its faux trappings.
What you are finding is that many (most) students are bad at algebra, and this makes them anxious, but they are ok with reading. Congratulations, you are now at square one.