Leveraging Multiple Mathematical Knowledge Bases in the First and Second Years of Full-Time Teaching

• In Event: 16.039 - Supports, Challenges, and Practices of Early-Career K–8 Mathematics Teachers to Enact Equitable Mathematics Teaching

Abstract

Purpose. We investigated the [Project’s] ECTs’ practices related to children’s MMKB with the following research questions:
1. How do ECTs notice and draw on children’s MMKB in planning, enacting, and reflecting on mathematics lessons?
2. What supports and challenges do ECTs experience as they draw on MMKB in mathematics instruction?

Theoretical Perspectives. Building on the perspectives presented above, we hold that equitable instructional practice involves noticing and drawing on children’s MMKB. Noticing includes attending to classroom actions and interactions, as well as reflecting, reasoning, and responding (Hand, 2012; Mason, 2011; van Es, 2011).

Methods. We conducted a qualitative case study (Stake, 1995) of six ECTs from two universities who had participated in [Project] since their elementary mathematics methods courses and through their first or second year of teaching. Data sources included: teacher interviews; field notes for 12 mathematics lesson observations per year per teacher, pre- and post-observation interviews, lesson artifacts, students’ work, and recordings from teacher meetings and summer institutes. After first cycle coding to identify themes relative to our research questions, we used qualitative analysis software for second cycle coding to refine themes and investigate patterns regarding ECTs use of MMKB in practice (Miles, Huberman, & Saldaña, 2014).

Results. ECTs used several approaches to notice and draw on MMKB in instruction. First, they designed or adapted word problems based on their knowledge of students’ interests and experiences (e.g., problems about the school garden). Second, ECTs often began lessons by eliciting students’ experiences related to the mathematics (e.g., Where have you seen patterns?) and incorporated language supports. Third, ECTs structured opportunities for students to explain their mathematical thinking and explicitly emphasized sense-making. ECTs explained that these connections to students’ MMKB were intended to increase student engagement and persistence, and build deeper understandings of the mathematics.

We found that ECTs from both sites indicated that extended experiences in similar schools and communities (e.g., schools serving primarily Latino/a, working class communities) helped them to learn about students and families, which supported connections to MMKB. In addition, ECTs’ involvement in the research project supported drawing on MMKB in instruction by providing prompts and strategies for incorporating MMKB in instruction.

The ECTs also experienced challenges in drawing on MMKB. They reported a lack of time to work with students individually, a need to deepen their own knowledge of children’s thinking and approaches to problems, and difficulties in making connections with families.

Conclusion and Significance. Patterns in ECTs’ practices indicate that beginning teachers can engage in complex work of noticing and drawing on MMKB. We also identified key supports and challenges that have implications for teacher education. Extended experiences in communities unfamiliar to teachers might support learning about diverse students and families. Similarly, on-going prompts to consider ways to draw on MMKB in instruction might sharpen teachers’ noticing of students’ resources. These findings deepen our understanding of how to support equitable instructional practices that meet the learning needs of a culturally and linguistically diverse student population.

Authors

• Amy M. Roth McDuffie, Washington State University - Tri-Cities

• Erin Turner, The University of Arizona