Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses

One important goal of teacher education has been to improve pre-service teachers' understanding of the connection between real-life events and mathematics. Toward this goal, we designed two mathematics teacher education courses based on the Models-and-Modeling Perspective. This study presents a three-tier modeling investigation of (a) pre-service teachers' views about characteristics of realistic mathematics problems, and (b) teacher-level skills required to write such problems. A team of researchers analyzed 15 pre-service mathematics teachers' written artifacts and audio recordings of their discussion by employing the data analysis methods of constructivist grounded theory. In these two modeling-based courses, pre-service teachers completed several modeling cycles, during which they exhibited significant changes in their understandings about the characteristics of realistic problems and the skills that are needed to write-revise-refine such problems. The results thus indicated that modeling-based courses helped pre-service teachers think critically about stereotypical textbook problems, view realistic contexts as a medium through which mathematical ideas could be reasoned, understand the mathematical residuals of lessons involving realistic problems, and attain the skills needed to write and revise such problems. Hence, the modeling perspective provided an effective approach for pre-service mathematics teacher training, ensuring pre-service teachers' development as they express-test-revise-refine their thinking, understandings, and skills