In an effort to help schools overhaul the mathematics curriculum it says has dominated instruction for 500 years, the National Research Council’s Mathematical Sciences Education Board has issued a curriculum framework for the subject.
The document, “Reshaping School Mathematics,” is aimed at providing guidelines for implementing the “vision” for the subject outlined in reports issued last year by the nrc and the National Council of Teachers of Mathematics.
Echoing the earlier reports, the new framework argues that changes in the job market, in technology, and in mathematics itself demand a “complete redesign of the content of school mathematics and how it is taught.”
In particular, the new report urges that all students study the subject every year, and that schools use calculators and computers in every grade to emphasize real-world problem-solving, rather than paper-and-pencil computation.
It also proposes that math instruction focus on developing students’ “mathematical power” by enabling them to read, write, and speak about the subject.
Renaissance-Era Curriculum
The report notes that the core mathematics course of study followed in most schools “differs in only superficial ways from the curriculum followed by tutors in the Renaissance.”
Moreover, said Kenneth M. Hoffman, the mseb’s executive director, that curriculum is based on the erroneous view that mathematics represents an immutable set of8laws, and that to learn the subject is to memorize rote procedures.
In fact, he said, “mathematics is a subject with a purpose--understanding something about the world, as other sciences do.”
The increased availability of new technologies, the report adds, has enabled schools to tap into this view of the field.
“As calculators and computers diminish the role of routine computation,” it says, “school mathematics can focus instead on the conceptual insights and analytical skills that have always been at the heart of mathematics.”
To that end, the report suggests that the elementary curriculum shift from an emphasis on manual skill in arithmetic operations to a focus on developing children’s “number sense.”
Such a change would require the use of calculators “from kindergarten on,” the report states.
“The replacement of most paper-and-pencil drills with calculator-based instruction will not itself be a panacea,” it says. “Although it is possible to assign mindless drills with calculators as with paper and pencil, young children can instead be given activities with calculators that emphasize discovery and exploration in ways not possible or practical with paper and pencil.”
The report also urges the use of “real objects and real data” in mathematics instruction. “To develop sound intuition for length, area, volume, and shape,” it says, “children studying mathematics must draw, cut, fold, construct, pour, and measure.”
Core Curriculum
In middle schools, mathematics instruction should focus on solving practical problems, the report ar4gues, to enhance student motivation and to build on the skills developed in the elementary grades.
High-school mathematics, which has traditionally introduced students to abstract symbols, should focus on developing their “symbol sense,’' according to the report. Using calculators and computers, it says, schools should shift from an emphasis on manipulating symbols to a stress on problem-solving.
The report also urges that high schools require all students to take mathematics for four years. Such a core curriculum, it says, would raise expectations for all students and help prepare them for higher education or the job market.
Copies of “Reshaping School Mathematics” are available for $7.95 each, plus $2 for shipping and handling, from the National Academy Press, 2101 Constitution Ave., N.W., Washington, D.C. 20418.
