Secondary Preservice Teachers’ Opportunities to Learn About Modelling in Algebra

The U. S. Department of Education (2009) noted that teaching is becoming increasingly challenging as teachers seek to meet changing needs and requirements: Diversity of student populations is growing and state graduation requirements, especially with respect to algebra, are evolving. Algebra is a foundation for advanced mathematics and a gatekeeper for high school students to enter a college or university (e.g., Kilpatrick & Izsák, 2008). Given this context, teacher education programs play a vital role in supporting pre-service teachers (PSTs) to overcome these challenges and prepare their students to learn about algebra.  

Modeling is an area that has been emphasized since Common Core State Standards for Mathematics (CCSSM) included modeling as a mathematical practice for all K-12 students (NGA & CCSSO, 2010). The processes of modeling described in CCSSM (e.g., identifying and selecting variables) is related to algebra learning because students choose variables and develop algebraic representations (e.g., graphs, equations) to solve realistic problems. The new expectations from CCSSM related to modeling raise questions about whether teachers are being prepared to teach algebraic modeling in secondary school mathematics classrooms.

As part of a larger project, Preparing to Teach Algebra, we gathered data at five universities to investigate PSTs’ opportunities to learn about algebra. We interviewed instructors of required mathematics and mathematics education courses for PSTs and collected corresponding instructional materials. We also interviewed two groups of PSTs from each institution. With these data sets, we aim to answer the question, “What opportunities do secondary mathematics teacher preparation programs provide to learn about algebra related to the modeling standards described in CCSSM? For data analysis, we coded our data according to each modeling process described in CCSSM and compared different types of opportunities.  

We will present concentrations of opportunities provided to PSTs to learn about and learn to teach algebra related to each modeling process within and across mathematics and mathematics education courses in five institutions. For example, at Gamma University, both instructors and PSTs describe diverse opportunities to learn about creating algebraic representations and few opportunities to reason behind their solutions to modeling problems. Teacher educators can look across opportunities provided from these exemplar teacher education programs to find gaps in their programs and refine their instructions about algebraic modeling.