The evolution of prospective elementary teachers' competencies : procedural knowledge, mathematical knowledge for teaching, attitudes, and enactment of mathematical practices

Abstract

The purpose of this research was to explore the evolution of prospective elementary teachers' competencies (in practices, knowledge, and attitudes); examine the relationships that occur between knowledge, attitudes and practices; and develop an idea of how certain prospective elementary teachers grow and progress in their enactment of two of the Common Core Standards for Mathematical Practice, persevering in problem solving and constructing viable arguments. This was conducted as a case study of the first two of three inquiry-based mathematical content courses for elementary teachers. Both qualitative and quantitative data was collected from a cohort of students moving through the curriculum over the course of a year. Results showed there was an increase in prospective elementary teachers' mathematical knowledge for teaching scores over time, but no change in their procedural knowledge or attitude scores. Positive, linear relationships existed between all of the pair-wise comparisons between mathematical knowledge for teaching, procedural knowledge, and attitudes toward mathematics. Overall, students grew in their ability to problem solve and construct viable arguments in mathematics while moving through the curriculum, with a few exceptions. Three factors contributed to students' learning in the curriculum: the amount of effort made by the student, the atmosphere and attitudes of students in the class, and the nature of the content and questions asked in the curriculum. Another important consideration which arose from the data analysis was the opportunities the curriculum allowed for the practice of written versus verbal explanations, and what was formally assessed. Designers of teacher education programs using a similar curriculum should evaluate the importance of written versus verbal explanations in the goals of the course, and appropriately assess the students.