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Psychologist David Geary and the CA Maths. Reform
Posted:
Sep 4, 1998 7:04 PM


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 realworld problem solving.'" (Hirsch, 1997, p. 6)  From Bridget Murray (http://www.apa.org/monitor/math.html)
"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 sixthgraders, 12thgraders 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. 425430). 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 mathematics."  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 629014610 USA Fax: (618)4534244 Phone: (618)4534241 (office) Email: JBECKER@SIU.EDU



