CAREER: Examining the Mutual Construction of Learning and Teaching in University Mathematics Classrooms

Principal Investigator: 
Project Overview
Background & Purpose: 

How do an instructor and students intending to become pre-service mathematics teachers create mathematical learning opportunities in a university mathematics classroom? What types of thinking does the instructor need to do mathematically to help build mathematical practices with future mathematics teachers?

Setting: 

University mathematics courses

Research Design: 

The project uses a cross-sectional research design and will generate evidence that is descriptive [case study, design research, and observational]. Original data is being collected from undergraduate/graduate pre-service mathematics teachers in a math course for pre-service teachers using diaries, school records, assessments of learning [achievement tests], observation [personal observation and videography], and survey research [structured, interviewer-administered, face-to-face questionnaire].

The analysis plan for this project includes:

  • Constant comparative analysis of the mathematical opportunities in the course for the first data collection (naturalistic case study with no intervention)
  • Thematic analysis of assessments
  • Pre-post analysis of task sort in the second data collection
  • Cycles of design analysis in the design research study
Findings: 

Undergraduate mathematics majors intending to be teachers have difficulty in engaging in mathematical practices, even with familiar mathematical content. They are not able to engage in mathematical practices that are key to fostering these same practices in their students. They report insufficient opportunities to engage in and learn these practices in their undergraduate mathematics courses. Similarly graduate students with undergraduate mathematics majors or their equivalent intending to be teachers have difficulties in engaging in and articulating mathematical practices. Design experiments to engage them in these practices overestimated their prior experiences with mathematical practices, and thus had to spend a great deal of time in allowing students to engage in practices before they had sufficient experience to abstract from and across these practices to generate larger ideas about the practices.