Math Teachers Urge Focus on Problem-Solving
Students should be provided with calculators and access to computers beginning in kindergarten, and teachers should spend less time on computational skills and more on mathematical concepts and problem-solving, according to the nation's largest organization of mathematics teachers.
In "The Impact of Computing Technology on School Mathematics," the National Council of Teachers of Mathematics argues that the use of calculators and computers to solve quantitative problems has "diminished the value" of having students master mechanical computations.
Advocates Routine Use
The council's report advocates the routine use of calculators in learning mathematics and while taking tests. The report also proposes changes in the sequence and content of mathematics instruction and in the training of mathematics teachers as a result of the increased availability of computers and calculators at home and in the classroom.
The council's recommendations reflect the concern that students know how to compute but not how to apply what they have learned. In addition, many math educators argue that students are not taught the mathematical concepts that underlie computational skills.
Shift in Focus
The use of computers and calculators, the council suggests, should free teachers to focus on the meaning of arithmetic operations in the elementary grades and on the development of "number sense," or an intuitive feeling for the relative size of numbers, in the middle grades.
That sense, the council suggests, "is essential in skillful estimation, approximation, mental arithmetic, and the interpretation of results for reasonableness."
The council adds that courses for high-school students who plan to attend college should not prepare them solely for calculus. More emphasis is needed on topics from discrete mathematics and statistics and on real-life problem-solving, the council insists.
The nctm also predicts that computers and calculators will enable students to learn some mathematical concepts earlier.
"No a priori assumptions should be made about the appropriateness of any given mathematical topic for elementary students," the nctm6suggests. Decimals, negative numbers, and scientific notation "appear naturally when using computers" and should be taught as they arise.
The council also notes that computers should make it easier to introduce geometric, statistical, and algebraic concepts to students at earlier ages as well.
For these reasons, preservice and inservice training for mathematics teachers now must also incorporate the use of calculators and computers. In addition, the council suggests that middle-school mathematics teachers complete courses on how to apply computers in education and on the use of computers for problem-solving.
Secondary-school mathematics teachers, the council writes, need to gain experience in structured programming, mathematical modeling, and other mathematics that are "fundamental" to computer science.
The report arose from a 1984 conference co-sponsored by nctm and the Center for Mathematics Education of the University of Maryland. The National Science Foundation provided financial support.
To receive a copy of the report, send a stamped self-addressed envelope to nctm, pr department, 1906 Association Dr., Reston, Va. 22091.