Title: Contextual Images in Mathematics Problem Solving
Abstract: Abstract Solving word-problems is a difficult task for many students. Understanding, the first step to solving a (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 of a situation are limited in their of the (Brown & Wheatley, 1997). This study investigated the effects of providing a dual system of contextual information, the words of the coupled with an image to activate the contextual schema, on the mathematical solving of 5th and 6th grade students. MANOVA indicated that the presentation of the contextual images had no effect on 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 solving has long been a major focus of mathematics education (NCTM; 1989, 2000), students continue to score relatively low on tests of solving ability. An example of this is scores on the Stanford Nine (a test administered annually to students in my state) subscale computation in (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 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 is asking, and third, the mathematical schema that corresponds to the implied action of the problem. For example, a division word 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 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 in the mind (Marschark & Hunt, 1989). This was demonstrated by Bransford and Johnson (1972) who had subjects read a clear, simple passage that could not be understood without the benefit of an image. The illustration was necessary to provide a cognitive framework within which to understand. In other words, the illustration activated the subject's contextual schema. The pictures presented to the students in this study are also intended to activate their contextual schema. Language How children solve mathematics word problems provides an excellent domain to examine how knowledge is constructed and integrated. Unlike some other forms of discourse, many mathematics word problems contain clear-cat criteria. However, word problems, like all other texts, can share the ambiguity and fuzziness of natural language. …
Publication Year: 2004
Publication Date: 2004-06-22
Language: en
Type: article
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Cited By Count: 1
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