Working in Mathematical Borderlands: Preservice Teachers Bridging Bilingual Children's Funds of Knowledge and Mathematics Lessons

• In Event: 42.042 - Practice in the Borderlands: Teaching and Teacher Education and the Promise of Educational Opportunities

Abstract

Objectives
This presentation describes an arts-focused teacher preparation program aimed at addressing issues of language and cultural diversity through a co-teaching approach in a bilingual school. Furthermore, this presentation also describes pre-service teachers’ (PSTs) work in a mathematics education methods course developing mathematical tasks related to their students’ funds of knowledge.

Theoretical Framework
The acknowledgement of children’s linguistic, intellectual, cultural, and social resources nurtured through their experiences in and within their homes and communities served as a platform to integrate funds of knowledge in mathematics. A careful ethnographic analysis of the transmission of these resources at home and their application into school instruction will support a convincing demonstration of children's knowledge in their academic performance (Moll, 1992). Besides considering children’s funds of knowledge, in mathematics education it is important to include open-ended problem-solving tasks since these offer students multiple ways of engaging in mathematics, as well as to make sense of these tasks by engaging in mathematical activity (Lesh et al., 2000; Common Core State Standards for Mathematics, 2010). To integrate these two perspectives, mathematization processes were applied (Gravemeijer, 1997) in the development of culturally relevant mathematical tasks that might promote the emergence of a “zone of mathematical practice” (González et al., 2001).

Methods & Data Sources
Through content analysis (Holsti, 1969), we compare and contrast two cohort of PSTs’ work, journal reflections taken during course classes and fieldwork experiences, as well as the instructors’ notes to learn how PSTs mathematized and explored their students’ funds of knowledge to develop mathematical tasks that linked mathematics with community practices. Special attention is provided to how PSTs’ funds of knowledge play out in the mathematization and teaching practices while working with bilingual and bicultural students.

Results
PSTs’ work bridging children’s funds of knowledge and mathematics during the design of mathematical tasks evolved through the process of exploring and understanding three knowledge sources: (a) students’ funds of knowledge, PSTs creatively developed various ways to learn about their students’ funds of knowledge and developed a thorough analysis and reflection of what they learned; (b) the cognitive demand and group worthy design of mathematical tasks, PSTs centered on developing mathematics tasks linked to a clear mathematical big idea that included features that supported its facilitator in a collaborative learning environment; and (c) PSTs funds of knowledge, while PSTs’ funds of knowledge served as a rich platform to make connections with what their students knew. When unfamiliar with their students’ funds of knowledge, PSTs dedicated time to learn about them, processes which turned out most helpful to link these knowledges. PSTs’ limitations and effortful work establishing such challenging links is presented through vignettes.

Scholarly Significance
The ultimate goal of educational innovations “depends on when and how teachers become part of the decision to initiate change” (Moll, 1992, p. 229). This study describes PSTs evolving learning on their commitment and practice to include their students’ knowledge in mathematical instruction.

Author

• Carlos Alfonso LopezLeiva, University of New Mexico