Erin E. Turner

Making Connections in Practice: How Prospective Elementary Teachers Connect to Children’s Mathematical Thinking and Community Funds of Knowledge in Mathematics Instruction

This study examines the ways prospective elementary teachers (PSTs) made connections to children’s mathematical thinking and children’s community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that asks PSTs to visit community settings and develop problem solving mathematics lessons that connect to mathematical practices in these settings (Community Mathematics Exploration Module). Using analytic induction, we identified three distinct levels of connections to children’s mathematical thinking and their community funds of knowledge evidenced in PSTs’ work (emergent, transitional, and meaningful). Findings describe how these connections reflected different points on a learning trajectory. This study has implications for understanding how PSTs begin to connect to children’s mathematical funds of knowledge in their teaching, a practice shown to be effective for teaching diverse groups of children.

“Everything is Math in the Whole World”: Integrating Critical and Community Knowledge in Authentic Mathematical Investigations with Elementary Latina/o Students

This critical ethnographic study of an after-school mathematics club for elementary-aged Latina/o youth focuses on connecting critical, community, and mathematical knowledge in the context of authentic, community-based investigations. We present cases of two extended projects to highlight tensions and dilemmas that emerged, particularly tensions related to ensuring rich mathematics in the contexts of projects that were personally and socially meaningful to the students. Our analysis offers insights into critical mathematics education with elementary aged students, and has the potential to counter dominant deficit perspectives of Latina/o youth. Additionally, the findings of this study inform critical approaches to teaching mathematics in schools attended by marginalized students in order to reverse prevalent trends of our educational system failing these students.

A Review of Research on Prospective Teachers’ Learning About Children’s Mathematical Thinking and Cultural Funds of Knowledge

Researchers have studied the preparation of elementary teachers to teach mathematics to students from diverse racial, ethnic, and linguistic backgrounds by focusing either on teachers’ learning about children’s mathematical thinking (CMT) or, less frequently, about children’s cultural funds of knowledge (CFoK) related to mathematics. Despite this important work, elementary teachers continue to be underprepared to teach mathematics effectively in diverse communities. We suggest that one way to address this persistent challenge is to integrate these two lines of work. This review focuses on research related to how prospective teachers (PSTs) learn to connect to CMT and CFoK in mathematics instruction. We use the review to describe elements of a robust theoretical framework of PST learning about CMT and CFoK, and synthesize how the studies reviewed contribute to these different elements.

Student Participation in Collective Problem Solving in an After-School Mathematics Club: Connections to Learning and Identity

This study examined the participation of a group of middle school students in an after-school mathematics club as they worked on cryptography problems. The analysis focused on interactions characterized by collective problem-solving activity, when intellectual work was distributed and various students took on active problem-solving roles, paying particular attention to intersections between task structures and positioning moves. We found that all open-ended tasks—those tasks that afforded multiple strategies and had multiple solutions—resulted in at least some collective problem solving, though it was not always sustained (Turner, Gutiérrez, & Sutton, 2009). We also found that the task structures, in combination with interactive positioning moves by facilitators and students, served to sustain or disrupt collective problem-solving activity.RésuméCet article analyse la participation d’un groupe d’étudiants du premier cycle du secondaire aux activités d’un club de mathématiques alors qu’ils tentaient de résoudre des problèmes de cryptographie. L’analyse est centrée sur les interactions caractéristiques des activités collectives de résolution de problèmes, au cours desquelles les tâches intellectuelles sont distribuées et plusieurs étudiants assument un rôle actif de résolution des problèmes. L’analyse se concentre en particulier sur les points d’intersection entre la structure des tâches et les actions de positionnement. Nos résultats indiquent que toutes les tâches ouvertes, c’est-à-dire les tâches qui permettent l’utilisation de stratégies multiples et conduisent à de multiples solutions, ont mené au moins en partie à la résolution collective de problèmes, même si la solution envisagée n’était pas toujours durable (Turner, Gutiérrez et Sutton, 2009). Nous avons également constaté que la structure des tâches, alliée à certaines actions de positionnement interactives de la part des facilitateurs et des étudiants, est en mesure de soutenir ou de perturber les activités collectives de résolution de problèmes.

Prospective and Mentor Teacher Perspectives on Co-learning Events

One response to the disconnect between principle-based university methods courses and practice-oriented elementary school classrooms has been to create co-learning spaces by bringing prospective teachers (PSTs), practicing mentor teachers (MTs), and teacher educators together to explore key ideas related to teaching and learning. The purpose of this study was to examine MTs’ and PSTs’ perspectives on their experiences in co-learning events designed to maximize co-construction of knowledge that might lessen the gap between theory and practice. Findings from the analysis of interviews with 16 PSTs and 22 MTs included numerous benefits of co-learning events, including opportunities for (a) MTs to learn about PSTs’ world and build relationships; (b) PSTs to learn from MTs’ practical knowledge; and (c) to foster diverse perspectives and mutually beneficial collaboration. Participants also described tensions related to positioning MTs and PSTs in collaborative roles. Implications for the design of co-learning events in teacher education are discussed.

Curriculum spaces for connecting to children’s multiple mathematical knowledge bases

Abstract Elementary mathematics curriculum materials can serve as a lever for instructional change. In this paper, we promote a particular kind of instructional change: supporting teachers in learning to integrate children’s multiple mathematical knowledge bases (MMKB), including children’s mathematical thinking and children’s home and community-based mathematical funds of knowledge, in instruction. A powerful means of supporting pre-service teachers in integrating children’s MMKB in instruction may be to scaffold teachers’ noticing of potential spaces in elementary mathematics curriculum materials for connecting to children’s MMKB and then developing practices for leveraging these spaces during instruction. We focus on existing and potential spaces in written curriculum materials, or curriculum spaces, so as to better support teachers in enacting curriculum that opens spaces for connecting to children’s MMKB.