Exploring the impact of a standards-based Mathematics and pedagogy class on preservice teachers' beliefs and subject matter knowledge.

Abstract

This case study explored the impact of a standards-based mathematics and pedagogy class on preservice elementary teachers' beliefs and conceptual subject matter knowledge of linear functions. The framework for the standards-based mathematics and pedagogy class in this study involved the National Council of Teachers of Mathematics Standards, the Lesh Translation Model, building algebra through the elementary grades, social constructivism, and research on childrens' mathematical thinking from the Rational Number Project. The rich description of the mathematics and pedagogy class in this study provides relevant information for properly structuring mathematics content classes to prepare elementary teachers to be able to help all students learn mathematics. Overall, the preservice teachers demonstrated the most developed understanding in the realistic, language, symbolic, and concrete representations; while the pictorial representation was often not as fully developed. They also showed the ability to provide reasoning and justification for their mathematical ideas. The preservice teachers' beliefs about the teaching and learning of mathematics became more inline with standards-based learning environments. The preservice teachers were especially impacted by the Rational Number Project research on fraction division and fraction multiplication to see the benefit of having conceptual understanding of concepts in different representations. However, there were a few areas where the preservice teachers showed little evidence of beliefs: that the teacher should let children do most of the thinking in a mathematics class and that mathematics is a web of interrelated concepts and procedures.