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.

Cordially,

Clyde

On Nov 5, 2013, at 6:29 PM, Clyde Greeno @ MALEI <greeno@malei.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.

Bob Hansen