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Topic: Psychologist David Geary and the CA Maths. Reform
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Jerry P. Becker

Posts: 15,675
Registered: 12/3/04
Psychologist David Geary and the CA Maths. Reform
Posted: Sep 4, 1998 7:04 PM
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Should we reflect on what we know about the pedagogical orientation of
David Geary, the psychologist who is currently working on a revision of the
draft 1998 California Mathematics Framework?

From Jerry Becker and Bill Jacob:

"After some explanation, Hirsch continues: 'I shall briefly outline the
conflicts between educational Lysenkoism and mainstream science in testing,
math, and early education ...,' and citing math education experts Anderson,
Geary, and Siegler about what research shows math students need, 'They
would tell you that only through intelligently directed and repeated
practice, leading to fast, automatic recall of math facts, and facility in
computation and algebraic manipulation can one do well at real-world
problem solving.'" (Hirsch, 1997, p. 6)
From Bridget Murray (

"Critics of constructivist math welcome this shift. One of them is
psychologist David Geary, PhD, who says constructivist math conflicts with
cognitive findings that math learning is hierarchical.

"'The constructivist approach is back to front,' says Geary, a cognitive
researcher at the University of Missouri. 'If you don't have the pieces
first, you won't understand the whole. You can't do algebra without
multiplying and dividing first, and you can't multiply and divide without
knowing addition and subtraction.'

"Math learning is not automatic like language acquisition, says Geary.
Students need directed instruction because they aren't naturally motivated
to learn, as the constructivists believe, he says. In a recent study of 372
Chinese and American sixth-graders, 12th-graders and older adults, Geary
found that Chinese children outperformed American children on computational
and reasoning measures.

"However, Chinese and American older adults performed much the same, and IQ
scores in the two countries were also similar. The study appeared last year
in the Psychonomic Bulletin & Review (Vol. 4, No. 3, p. 425-430). According
to Geary, America's math performance sags because our country lacks a
rigorous, sequenced national math curriculum like China's.

"'If you're skipping drill and practice, you're just skipping the hard
part,' he says."
From Stanislas Debaene (The Number Sense: How the Mind Creates Mathematics)

"The erroneous conception of the brain and of mathematics, in which
intuition is discouraged, leads to failure. Studies conducted in the United
States by David Geary and his colleagues..indicate that about 6% of pupils
are 'mathematically disabled.' ... It seems more likely that many of these
'mathematically disabled' children are normally abled pupils who got off to
a false start in mathematics. Their initial expedience unfortunately
convinces them that arithmetic is a purely scholastic affair with no
practical goal and no obvious meaning. They rapidly decide that they will
never be able to understand a word about it. The already considerable
difficulties posed by arithmetic to any normally constituted brain are thus
compounded by an emotional component, a growing anxiety or phobia about
An excellent review of Geary's book, "Children's Mathematical Development:
Research and Practical Applications", appears in the January 1996 issue of
the Journal for Research in Mathematics Education.

The late Bob Davis provides a balanced and insightful view of Geary's book,
which "examines the world from the point of view of one psychologist who
stands largely outside the world of mathematics education scholars." "One
hopes...that the foundation on which we build will be considerably broader
than Geary's view (valuable though that is), because Geary's view focuses
on actions far more than on thought processes and on mathematics as a
collection of facts and commonly shared (standard) algorithms."

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618)453-4244
Phone: (618)453-4241 (office)

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