# The relationship between performance using individualized instruction in mathematics and teacher attitude and dogmatism

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The major problem of this study was: Do prospective teachers who are open-minded and/or who exhibit positive attitudes toward individualized instruction in mathematics demonstrate a greater propensity for using individualized instructional strategies in mathematics than those prospective teachers who are closed-minded and/or who exhibit negative attitudes toward individualized instruction in mathematics? More specifically, questions basic to this study are as delineated below. 1. To what extent do prospective teachers demonstrate positive attitudes toward individualized instruction in mathematics? 2. To what extent do prospective teachers exhibit open-minded behavior in individualizing instruction in mathematics? 3. To what extent do prospective teachers perceive they are individualizing instruction in mathematics when they employ pacing, record-keeping, decision-making, flexible-sequencing, objectives, and evaluation? 4. To what extent do prospective teachers employ an individualized instruction approach in mathematics through: (a) pupil's use of materials and media, (b) teachers' use of materials and media, (c) use of varied organizational methods of instruction, and (d) use of varied instructional strategies? 5. Can prospective teachers' degree of individualization of the mathematics curriculum be predicted based upon measures of their attitudes toward individualized instruction in mathematics, their perception of the extent to which they individualized the mathematics curriculum, and the extent to which they were open-minded? Subjects for the study were thirty-five prospective elementary teachers who: (a) had experienced an individualized, competency-based, mathematics education program at the University of Houston, (b) were assigned to student teach grades 4,5, or 6 in the Houston Teacher Center during the Spring of 1976, and (c) had completed thirty-six credit hours of professional education courses. These persons participated on a voluntary basis. Research instruments were the Attitude toward Individualized Instruction in Mathematics, the Performance Test for Individualized Instruction in Mathematics, and the Rokeach Dogmatism Scale. The Attitude toward Individualized Instruction in Mathematics elicited information about prospective teachers' attitude toward individualized instruction in mathematics. The Performance Test for Individualized Instruction in Mathematics consisted of two parts. Part I: Perception yielded information about how prospective teachers perceived they individualized the mathematics curriculum, while Part II: Observations and Demonstrated Practices was used to assess prospective teachers' performance in utilizing individualized instrucitonal principles in teaching mathematics. Dependent variables were pupil's use of materials and media, teachers' use of materials and media, use of varied organizational methods of instruction, and use of varied instructional strategies. The combination of these variables formed a single dependent variable called 'Performance in an individualized model'. Independent variables were attitude toward individualized instruction in mathematics, perception of individualizing practices, and degrees of openmindedness. Data collected related to these variables were tested through the formulation of six hypotheses. Analyses of variance and stepwise multiple regression analysis were used to analyze the data. Results of the analyses led to the following conclusions and findings: 1. Prospective teachers who were open-minded did not differ significantly from prospective teachers who were closed-minded in the individualization of the mathematics curriculum. 2. Prospective teachers who exhibited positive attitudes toward individualized instruction in mathematics did not differ significantly from prospective teachers who exhibited negative attitudes toward individualized instruction in mathematics in the individualization of the mathematics curriculum. 3. Prospective teachers who were open-minded and exhibited positive attitudes toward individualized instruction in mathematics did not differ significantly from prospective teachers who were closed-minded and exhibited negative attitudes toward individualized instruction in mathematics in the individualization of the mathematics curriculum. 4. No significant difference was found in the extent to which prospective teachers exhibited positive attitudes toward individualized instruction in mathematics and in the extent to which they demonstrate performance of individualized instruction principles in mathematics. 5. No significant difference was found in the extent to which prospective teachers perceived they individualized the mathematics curriculum and their performance of individualized instruction principles in mathematics. 6. An equation was not found for predicting prospec- teachers' performance in an individualized instruction approach based on their attitudes toward individualized instruction in mathematics, their perception of how they individualized instruction in mathematics, and their degree of openness. 7. Prospective teachers who are open-minded, exhibit positive attitudes toward individualized instruction in mathematics, and have experienced an individualized mathematics program do not show a greater propensity for demonstrating individualized instruction principles than prospective teachers who are closed-minded, exhibit negative attitudes toward individualized instruction in mathemtics, and have experienced an individualized mathematics education preparation program. 8. The relationship between performance using individualized instruction in mathematics and teacher attitude and dogmatism is not influential in the teachers utilization of individualized instruction principles. The teachers' demonstrated performance in an individualized setting is not contingent on the openness of of the teachers belief system nor how they feel about the instructional strategy. 9. Open-mindedness of prospective teachers influenced their organizational methods of instruction in an individualized instructional setting.