An investigation of the relationship of reading comprehension, vocabulary, mathematical concepts, and computation on problem solving among Anglo, Black, and Chicano male and female middle school adolescents

Purpose. The purpose of this study was to determine the contribution of specific variables related to problem solving achievement in mathematics. These variables were identified through a review of literature as being reading ability, vocabulary, mathematical concepts, computation, sex, and race. Procedures. The subjects consisted of a total of 1,440 sixth, seventh, and eighth grade Anglo, Black, and Chicano male and female adolescents of average ability from a large urban school district in Southeast Texas. The 1978 edition (Forms 7 and 8) of the Iowa Tests of Basic Skills (ITBS) was utilized in order to obtain data on the designated variables. Research Questions. The specific research question for this study was: To what extent is problem solving achievement in mathematics significantly related to the six independent variables of reading, vocabulary, mathematical concepts, computation, sex, and race among students in grades 6, 7, and 8. Five research questions and corresponding hypotheses were formulated for investigation following analysis procedures suggested by Kerlinger and Pedhazur (1973): Question 1. Is the proportion of variance in problem solving achievement accounted for by the full model statistically significant and/or meaningful? Question 2. Is there statistically significant interaction between the predictor variables and the categorical variables? Question 3. Do the continuous predictor variables account for a statistically significant amount of variance in problem solving achievement beyond that accounted for by the categorical variables? Question 4. Are the categorical variables different from one another in problem solving achievement? Question 5. What are the regions in the continuum of the predictor variables over which one or more of the categorical variables are superior? This question would only be asked in the event that the interactions in Question 2 were statistically significant. [...]