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Results from the Fourth Mathematics Assessment

of the National Assessment of Educational Progress

National Council of Teachers of Mathematics, 1989. Edited by Mary Montgomery Lindquist.

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This assessment included approximately 20 items assessing fraction concepts and operations. Three of these items were administered to 3rd-grade students. Most of the remaining items were administered to both 7th-grade and 11th-grade students. The three items administered to 3rd-grade students tested simple fraction concepts. The items administered to 7th-grade and 11-grade students included computation and simple concepts. The computation items were limited to subtraction and multiplication; no problems measuring students’ understanding of fraction operations, and three simple word problems involving operations with fractions. (The preceding paragraph and the following tables and comments were condensed from Chapter 8, "Number and Operations", by Vicki L. Kouba, Thomas P. Carpenter, and Jane O. Swafford.)

About two-thirds of the 7th-grade students could identify the larger of two fractions, but their performance was much lower when they had to identify the largest and smallest of four fractions in a sample situation (table 8.16). About 80 percent of the 7th-grade students could change a mixed fraction to an improper fraction, but fewer than half of the 7th-grade or 11th-grade students recognized that 5 1/4 was the same as 5 + 1/4. This is one of several items suggesting that significant gaps exist in many students’ basic knowledge of fractions. It appears that many students who are successful at routine, frequently encountered calculations have difficulty when they are asked questions about fractions that do not have standard calculations, even when the questions involve basic fraction concepts.

Although none of the calculations in the above table involved large numbers, both of the subtraction items required finding the common denominators, and the three multiplication items involved both fractions and whole numbers. Consequently, the items tapped most of the different skills involved in subtracting and multiplying fractions.

The subtraction item requiring regrouping was significantly more difficult than the other four items. Performance was relatively consistent over the other four items. About half of the 7th-grade students and 70 percent of the 11th-grade students could perform simple comparisons of fractions and computation involving subtraction and multiplication with mixed numbers.