# Mathematical Argumentation in K-8

The REU Fellow in mathematics education will be guided and mentored throughout the internship by the mathematics education researchers at Marquette University. Together with the mentors, the Fellow will participate in research on the effectiveness of activities designed to support middle school pre-service teachers' knowledge of mathematical argumentation in K-8 mathematics. The goal of this research is to develop better understanding of the extent to which teacher preparation activities conducted in mathematics courses for pre-service teachers impact pre-service teachers' ability to design and implement K-8 mathematics instruction with a strong focus on mathematical reasoning and proof. This inquiry is grounded in the idea that in addition to having strong reasoning skills, teachers must have knowledge that allows them to make sense of the mathematical arguments expressed by their students and recognize classroom situations that could engage students in creating and critiquing mathematical arguments.

The specific goals of the study in which the REU Fellow will contribute are to examine middle school pre-service teachers' knowledge about mathematical argumentation and proving along three dimensions: (a) pre-service teachers' own ability to formulate mathematical arguments, (b) their ability to analyze mathematical arguments, and (c) their ability to analyze situations that engage students in mathematical argumentation. A multidimensional analysis of the data collected in forms of: (a) pre and post assessment of pre-service teachers' content knowledge for teaching mathematical argumentation and proof, (b) artifacts from MATH courses for pre-service teachers, (c) video-recordings of class sessions and interviews conducted with pre-service teachers concerning their conceptions of mathematical argumentation in the K-8 mathematics classroom.

The REU Fellow will gain experience in qualitative and quantitative research methods using a framework of knowing mathematics for teaching. The fellow will receive first-hand experience using specialized data analysis software to analyze and interpret data of pre-service teachers engaged in the teaching and learning processes.