To what degree does the methodology used to develop a mathematical concept predict students' mathematical success

Abstract

The purpose of this study was to investigate how children acquire mathematical concepts. Specifically, the study compared the achievement levels of the control and experimental groups following an intervention period. During the intervention, the control group received mathematical concept development by the "traditional" instructional paradigm. This paradigm uses teacher lecture and textbook resources as the dominant method for concept development. The experimental group was provided mathematical instruction by the concept attainment model. The concept attainment instructional paradigm operates from the premise of developing concepts by means of a developmental approach. The three components that define this approach are concrete, semi-concrete, and abstract. Also investigated was the academic abilities of the two gender groups. The achievement levels of each gender group was compared to the other gender group. The final area of investigation focused on the attitudinal nature of the treatment groups towards the subject of mathematics. Each treatment group's attitudinal results were compared to the others. The sample size consisted of 203 middle school students in grades six, seven, and eight. The statistical technique of analysis of covariance was used to analyze the data. The covariates were the scores on the pretests of both the Enright Diagnostic Inventory of Basic Arithmetic Skills (revised) and the Mathematics Anxiety Rating Scale (revised). Findings of the study did not disclose a significant difference in the achievement levels of the participants receiving instruction by the two instructional paradigms, the traditional model and the concept attainment model. There was also not a significant difference in academic achievement levels noted between the two gender groups. However, females displayed higher mean scores than males. On the skills component of the achievement assessment, females' scores at each grade level exceeded males' scores. Males' performance exceeded that of females on the concepts component in each grade, except grade six. Findings did not reveal significant attitudinal differences between the subjects receiving the two instructional paradigms.