Understanding Arithmetic Story Problems.

Open-ended individually administered questions can ascertain whether students can reason about arithmetic problems. Free response test items are useful in assessing students' thought processes as they solve mathematics story problems. Since story problems do not state explicitly which arithmetic operations are required for solution, students must decide to use a particular operation. Higher order cognitive skills are used in solving such problems. Different strategies may be used to solve a problem, reflecting different understandings of the problem. Appropriate schema--a memory structure describing common elements in seemingly different situations--are necessary to solve problems. To assess use of appropriate schema knowledge, it is necessary to know which information is considered by the student to be important in solving the problem. Test items can ask students to state what is important directly; to act out the problem using objects or drawings; to group problems according to similarity; to retell the problem; or to construct similar items. The emphasis in the paper is on story problems typical of first through eighth grade arithmetic. Six story problems, especially appropriate for grades 3 and 6, are included to illustrate the measurement of understanding of strategies and problem solving knowledge. (GDC)