Learning to Design High-Cognitive-Demand Mathematics Lessons That Connect to Community-Based Resources

• In Event: Developing Ambitious Mathematics Teaching With an Equity Stance: Rethinking Routine Practice

Abstract

This presentation reports on a six-university collaboration – Teachers Empowered to Advance Change in Mathematics (TEACH MATH) - formed to design and research ways to help teachers develop knowledge, dispositions and practices needed to effectively teach mathematics to diverse groups of students.

A core component of TEACH MATH is the development, implementation, and refinement of instructional modules for mathematics methods courses. The modules provide opportunities for PSTs to develop ambitious practices that promote equity, including: a) eliciting and building upon children’s mathematical thinking; b) recognizing children’s home and community-based knowledge and experiences relevant to mathematics (González, Moll, & Amanti, 2005); and c) planning and implementing mathematics lessons that connect to children’s multiple mathematical knowledge bases (i.e., children’s mathematical thinking, and their cultural, linguistic, home or community-based knowledge and experiences). We understand these practices as developing dynamically, along a trajectory (Turner, Drake et al., in press), as teachers participate in multiple communities of practice (Wenger 1998).

This presentation focuses on the Community Mathematics Exploration (CME) module, wherein PSTs visit locations in the community surrounding their field-placement school, and then draw on what they learned to design a problem solving-based mathematics lesson. We focus on the various ways that PSTs made connections to children’s multiple mathematical knowledge bases in the lessons they designed, with attention to differences between emergent, superficial connections and more meaningful connections.

We analyzed 93 CME projects from across multiple sites. Each project included a) a lesson plan, and b) a presentation that described the community visit and how it might inform mathematics instruction. Initial analysis focused on a subset of projects with particular attention to how PSTs a) drew upon children’s mathematical thinking, b) described connections to community mathematical practices, and c) created a lesson task with high cognitive demand. Members of the research team analyzed each project and discussed differences in interpretation. A refined set of codes (Corbin & Strauss, 2008) was applied to the larger data set.

We found that slightly fewer than half of the projects evidenced meaningful connections (i.e, mathematically deeper, more authentic connections) to children’s multiple mathematical knowledge bases; the remaining evidenced superficial connections. Meaningful connections were made in various ways, including by mirroring the mathematical practices of adults in the community (e.g., a lesson on categorizing sweet breads that drew upon categorization schemes used in a neighborhood panadería); by building on the mathematical practices of children/families in out-of-school settings (e.g., a lesson that asked students to determine the price of various items on abuela’s (grandma’s) shopping list); and by inviting students to imagine a scenario, that while realistic, did not relate to actual experiences (i.e., a lesson on area, inspired by a neighborhood flooring center, that involved a hypothetical remodel of the classroom floor). In our presentation we elaborate these differences, and draw on multiple examples to outline a trajectory from making emergent/superficial connections to more meaningful connections to children’s multiple mathematical knowledge bases. In this way, we contribute much needed understandings about how PSTs begin to develop this equity-oriented teaching practice.

Authors

• Julia Maria Aguirre, University of Washington - Tacoma

• Erin Turner, The University of Arizona