The impact of a constructivist framework on preservice teachers' number sense concepts and their beliefs and attitudes about the teaching and learning of mathematics

Abstract

This study was designed to investigate the conceptual understanding of number sense of preservice teachers as it relates to their self-efficacy beliefs and attitudes about the teaching and learning of mathematics within a constructivist setting. Furthermore, the relationships between selected demographics collected on the preservice teachers and number sense, beliefs and attitudes were studied.

The context for the implementation of the constructivist framework was an elementary mathematics methods course. The classroom implementation implied adoption of a problem-centered, active student learning approach, whereby the teacher played a guiding role. The sample consisted 22 preservice teachers in their last semester before student teaching.

A one-group pretest-posttest design was used. Paired t-tests for correlated means were computed to compare the preservice teachers'' scores on pre- and post-tests for self-efficacy beliefs, attitudes and number sense. Test results showed significant differences between pre- and post-test scores of preservice teachers on both the self-efficacy beliefs and the number sense instruments. There was no significant difference in the preservice teachers scores on attitudes toward mathematics. Preservice teachers characteristics of high school class size, high school class rank, high school GPA, number of high school math courses taken and the level, SAT scores, college GPA general, college GPA math and parents'' educational level were compared to the scores on each of the tests using a Pearson-Product Moment Correlation. The significant interactions noted were the negative correlations between the number of math classes taken and the preservice teachers'' change of beliefs, and also between their change of attitude and change in their conceptual understanding of number sense. The positive correlations observed were between their understanding of number sense and their attitudes at the onset of the course, also GPA general and their number sense concepts at the end of the course.

Implications of the study are that the constructivist framework did influence the preservice teachers'' understanding of mathematics and beliefs about what it means to learn and teach mathematics.