- Year 2019
- NSF Noyce Award # 1852846
- First Name Sandy
- Last Name Spitzer
- Discipline Math
- Co-PI(s)
Laila Richman, Towson University, lrichman@towson.edu; Kristin Frank, Towson University, kfrank@towson.edu; Diana Cheng, Towson University, dcheng@towson.edu;
Kimberly Corum, Towson University, kcorum@towson.edu - Presenters
Sandy Spitzer, Towson University, sspitzer@towson.edu
Need
Research suggests that for students to develop deep and connected mathematical understandings, they should solve real-world problems in which mathematics is used to model situations and construct solutions (e.g., Pollack, 1969; Lesh & Doerr, 2003). However, for teachers to effectively use mathematical modeling in their classroom, they must develop an understanding of the modeling process and learn to select, modify, and enact modeling tasks. To be prepared to enact modeling in their classrooms, pre-service secondary mathematics teachers (PSTs) need explicit support and education (e.g., Cai et al. 2016). Engaging PSTs in model-eliciting activities (MEAs, or tasks for which the creation and evaluation of a mathematical model is the primary goal) can help them both integrate and apply their mathematics knowledge and prepare to conduct such tasks as teachers (Daher & Shahbari, 2015). Meanwhile, attending to equity and social justice in pre-service mathematics teacher preparation is an urge
Goals
The research question guiding this work was: To what extent can pre-service teachers attend to a variety of mathematical features when creating a model for gerrymandering and compactness? This research question fits within one of the larger research questions of our Noyce Capacity-Building project: What strategies do teachers use to solve MEAs, and to what extent do our MEAs promote the application of mathematical content?
Approach
This poster describes a classroom activity in which students use a variety of mathematical practices and approaches to investigate the role and effects of gerrymandering. This model-eliciting activity aligns with calls for students to both engage in authentic mathematical practices and use mathematics to analyze issues of political and social relevance. The use of MEAs involving social justice contexts can allow students to ‘experience mathematics as an analytical tool to make sense of, critique, and positively transform our world’ (Aguirre et al., 2019, p. 8). Further, since teachers often cite a wish to avoid discussing controversial issues with their students (Simic-Muller, Fernandez, & Felton, 2015), a topic which is facially neutral (like gerrymandering) can be a useful entry point. All citizens can be concerned about whether or not their vote has an impact; this topic is particularly relevant for high school students who are preparing to vote for the first time.
Outcomes
With the goal of engaging PSTs in modeling for social justice, we created an MEA which asked participants to construct their own mathematical measure (i.e., model) of district ‘compactness’ and use their model to identify gerrymandered districts. This MEA draws on mathematical ideas appropriate for secondary mathematics classrooms, such as area and perimeter, scale, and attributes of shapes. Students are given data including perimeter and area of congressional districts, as well as printed maps, and challenged to find a model which can rank districts by compactness. In a pilot implementation, pre-service teachers struggled to conceptualize the geometric nature of compactness and downplayed its importance. They focused instead on issues of fairness in representation, including ideas of proportionality.
Broader Impacts
This MEA provides students with an opportunity to not only engage in rich mathematical practices, but also learn about relevant and pressing social justice issues. We will use the poster session as an opportunity to share our lesson activities and outcomes with other teachers and teacher educators. Implications of the findings suggest that pre-service teachers (as well as high school studnets) might need additional activities to understand the role of geometric compactness in gerrymandering; future iterations of the activity are being planned to address this issue.
