Assessing Higher Order Thinking in Mathematics

By Gerald Kulm | Go to book overview
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Calculators and Mathematics


The National Council of Teachers of Mathematics (NCTM), in its position paper, Calculators in the Mathematics Classroom, called for the use of calculators in assessment. According to NCTM,

The evaluation of student understanding of mathematical concepts and their application, including standardized tests, should be designed to allow the use of the calculator.

The paper further recommended that authors and test writers integrate the use of the calculator into their mathematics materials at all grade levels ( NCRM, 1986).

When the Chicago public schools decided to purchase calculators for all students, the anxiety of educators, parents, and society in general regarding the effect of the calculator on computational skills was apparent. Many people expressed concerns that students would no longer master basic computational skills.

Mathematics educators have warned about the danger of total abandonment of paper-and-pencil skills. On the other end of the spectrum were teachers who feared that teaching with a calculator available would be unfair if calculators were used to support instruction but students were not allowed to use them in testing situations. Realizing the importance of the support of teachers and the community, the Chicago school system was determined that a successful program must include two important components: (i) assurance of mastery and maintenance of computational skills, and (ii) calculators as an integral part of the testing program. This solution, though trivia proved to be profound. A dual testing technique appears to have satisfied most of the concerns regarding the use of calculators for mathematics instruction.

The tests are organized into two parts: Part I, the noncalculator section, evaluates mastery of the objectives for arithmetic computations. This component of the test assesses students' mastery and maintenance of estimation, mental computations, and paper-and- pencil computational skills. Students are expected to demonstrate 80 percent mastery on the 10 items included in this section of the tests, which they must do without calculator support.

Part II, the calculator-supported component of the tests, evaluates students' mastery of the objectives for mathematics concepts, strategies, processes, and applications. Mastery of mathematical skills in seven areas of learning -- arithmetic, quantitative relationships, measurement, algebraic concepts,

All figures are copyright 1987 by the Board of Education of the City of Chicago.


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Assessing Higher Order Thinking in Mathematics


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