The effect of using as many variables as are needed to solve word problems on the problem-solving skills and attitudes of students in Algebra I

This dissertation reports on the cognitive and affective effects of an experiment in word-problem solving in Algebra I. The experimental treatment was to teach students, when they first started solving word problems with two unknowns, to translate the word problems from the prose representation to symbolic representation using two variables, one to represent each of the unknowns, and two equations. The control treatment was to teach students to solve word problems with two unknowns in the traditional way, using only one variable to translate from prose to one (more complicated) algebraic equation. Four algebra teachers who each taught at least two sections of Algebra I, and 196 of their students participated. Each teacher taught an experimental group and a control group (a factorial block-randomized design). The performances of the experimental and control groups, in solving word problems with two unknowns, were compared on tests taken from the same pool of questions. A Mann-Whitney U-test showed that, at a critical level of.0031, there was a statistically significant difference in the median scores of the experimental group and the control group on these word problem tests. The experimental group median score was 23% higher than that of the control group. A linear regression analysis indicated a 10 point higher expected score for students in the experimental group, attributable to the experiment. A Thurstone-style instrument was developed to measure attitude toward word problem solving in school mathematics. The participating students completed a pretreatment attitude questionnaire and a posttreatment attitude questionnaire to determine if the students' attitudes toward problem solving in school mathematics changed during the experiment. The attitudes of the students in the experimental group had a median decrease of 1.1105, and the control group had a median decrease of 0.8140. Mann-Whitney U-tests indicated that both decreases were statistically significant at a critical level of less than.0005. The researcher concluded that the substantial improvement in problem-solving performance resulting from the experimental treatment warrants confirmatory research and subsequent adoption in Algebra I texts and courses.