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Contextual images in mathematics problem solving.

Article Excerpt
Abstract

Solving word-problems is a difficult task for many students. Understanding, the first step to solving a problem (Polya, 1945; Kintsch & Greeno, 1983), requires the activation of three schemata; the language, the contextual, and the mathematical. Students who are unable to construct a contextual understanding of a problem situation are limited in their understanding of the problem (Brown & Wheatley, 1997). This study investigated the effects of providing a dual system of contextual information, the words of the problem coupled with an image to activate the contextual schema, on the mathematical problem solving of 5th and 6th grade students. MANOVA indicated that the presentation of the contextual images had no effect on problem solving performance. An analysis of student work indicated that many students chose a correct strategy to solve a given problem. However, their application of the strategy (for example an algorithm) was incorrect or incomplete.

Background

Even though problem solving has long been a major focus of mathematics education (NCTM; 1989, 2000), students continue to score relatively low on tests of problem solving ability. An example of this is scores on the Stanford Nine (a test administered annually to students in my state) subscale "computation in context" (i.e. word problems) which are typically among the lowest of all the subtests administered. This study examined the effect of supplying a context setting image on students' ability to correctly solve word problems. The use of imagery to evoke a contextual setting for the problems presented was derived from Paivio's dual-coding theory of memory.

Solving word-problems, even the most routine ones typically found in Elementary grades textbooks, is a difficult task for many students. One of the first steps to solving any mathematics problem is "understanding the problem" (Polya, 1945; Kintsch & Greeno, 1983). Understanding requires the activation of three schemata: first, the contextual schema that relates to the situation of the problem, second, the language schema to understand what the problem is asking, and third, the mathematical schema that corresponds to the implied action of the problem. For example, a division word problem requires a student to read the words (their language schema), access their contextual schema for sharing, and then their schema (i.e., a mathematical division strategy) for resolving a "sharing" situation. The contextual image is crucial for doing mathematics and a student who fails to construct an adequate image in a problem solving situation is limited when asked to give meaning to the situation (Brown & Wheatley, 1997). In other words, schema activation for context setting allows a child better to understand and solve a presented problem.

Problem solving is a complex cognitive activity requiring students to see relationships in order to gain meaning. Thinking involves the manipulation of what is represented mentally. It involves forming and manipulating relationships between items of information and forming a representation of the problem in the mind (Marschark & Hunt, 1989)....