Mathematics Task Design and Intention to Make Content Relevant to Children Among Urban Preservice Teachers

• In Event: Community Mathematics Explorations 2.0: Expanding on the Work of TEACH Math

Abstract

In diverse urban settings where children do not necessarily attend neighborhood schools, how can CME projects support teachers to develop mathematics tasks that draw on students multiple mathematical knowledge bases? We studied this question in the context of a teacher preparation program in a densely populated urban center in California. Utilizing the Learning Trajectory of Integrating Students Multiple Mathematical Knowledge Bases (SMMKB) first posited by Turner et al. (2012), we researched how PT developed their awareness and ability to effectively incorporate SMMKB into mathematics tasks. We also looked closely at the connections between the motivations PT described for the task in their reflections, and the task itself, noting the PTs’ intention in the task design and the execution of the task.

Forty-six PT from two mathematics methods sections were included in the present analysis. These PT represent general education, bilingual education (Spanish and Chinese), and special education teacher programs. We believe that the diversity of contexts that PT are preparing to teach in also adds to our analysis, as teachers across these programs may see the purposes of mathematics education differently (i.e., a focus on life-skills for some special education teachers, or commitments to social justice among some urban Spanish-speaking bilingual PTs.) PT completed two project iterations of the CME (task card, lesson plan, and reflection). We focused on the second iteration for this analysis, to allow for PT familiarity with assignment requirements. The authors coded CME projects for: the task and context, evaluation of to whom or for whom the context was described as interesting, and key themes in PT assignment reflections on how they justified the relevance of the activity for their students. We also analyzed alignment and disconnection between what they wrote in their reflection and what actually appears in the task, using Van de Walle et al’s (2016) checklist for worthwhile tasks.

Findings suggest that PT have a variety of ways that they describe motivation for the tasks. PT draw on different resources: exploring school or immediately vicinity to the school, discussions with students about how they spend time, their own perceptions of what social issues are important to talk about with students, themes from social studies that are adapted for mathematics. We are struck by how some PTs’ work reveals their understanding of cultural difference, and hence their position on a trajectory towards effectively integrating SMMKBs into mathematics task design, and in some cases cultural bias. This analysis also raised questions for us about to what extent are PT productively challenging what is happening in their schools (i.e., creating and implementing tasks that are more “worthwhile” than those in the curriculum) , and in what ways are the CME tasks a reflection of what they see as “good” mathematics teaching in their school placements.

The research adds to our understanding of how PT develop as culturally responsive mathematics teachers, by looking at concurrent development of their ability to design worthwhile math tasks and maximize connections to SMMKBs.

Authors

• Maria del Rosario Zavala, San Francisco State University

• Luz A. Maldonado, Texas State University