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Preservice Teachers’ Analyses of Mathematics Lesson Quality: Focusing on Mathematical Thinking, Language, and Culture

Mon, April 16, 4:05 to 6:05pm, Vancouver Convention Centre, Floor: Second Level, West Room 221

Abstract

Calls continue for teacher education that addresses the mathematics education needs and advancement of our increasingly culturally and linguistically diverse student population (Grossman, Schoenfeld, & Lee, 2005; Sowder, 2007). A growing number of studies explicitly connects children’s cultural and linguistic funds of knowledge to leverage children’s mathematical thinking in instructional practice with English Learners and Latin@ students (Villaseñor & Kepner, 1993; Turner & Celedón-Pattichis, 2008). A limited amount of work with these foci takes place in mathematics teacher preparation (Turner et al, In press; Rodriguez & Kitchen, 2005; Sleeter, 2001). Few resources exist to support pre-service teachers in analyzing the relationships between mathematical thinking, language, and culture in instructional practice (see Turner et al, In press; Campbell, Adams & Davis, 2007 for exceptions). This paper documents and describes a multifaceted tool designed to support beginning teachers as they critically analyze the quality of their mathematics lessons with respect to these foci as part of their developing practice.
This study examines data related to a specific mathematics methods assignment requiring PST to self-evaluate their own mathematics lesson using a special tool re-purposed from a classroom observation tool (Kitchen, 2005; Aguirre & Zavala, 2011). Retaining five original categories with rubric scales of 1-5, such as “Intellectual Support” and “Mathematical Analysis,” the tool included additional categories focused on academic language support for English learners, community funds of knowledge, and critical knowledge (CEMELA, 2006; Civil, 2007; Gutstein, 2006; Moschkovich, 2007b). Data sources include written artifacts from 40 PST that included lesson ratings, lesson plans, and individual reflections. Artifacts were analyzed using a mixed method approach (Johnson & Onwuegbuzie, 2004). Self-reported ratings for all 8 categories were compiled and we noted patterns in variation. These patterns guided our qualitative analysis of written reflections, for which we used an open coding constant comparative approach to develop emerging themes and look for contrasting cases (Strauss, 1987).
Findings show that PSTs reported mathematics lesson limitations focused more on language, community knowledge and critical knowledge than categories associated with children’s mathematical thinking. The categories of community knowledge and critical knowledge had the lowest average ratings, with community knowledge showing the most mean variability. Analysis of PST reflections about areas for improvement showed PSTs were primarily focused on language (36.7%), then critical knowledge (25%), and next community/culture funds of knowledge (15%). Some teachers provided specificity towards improving their lesson planning, while others reported challenges in conceptualizing how to alter their lesson planning. For example, one PST described how she would incorporate critical knowledge by designing a mathematical analysis of tribal land values as follow up to a 7th grade lesson on gas price comparison. In contrast, two other PST questioned the appropriateness of critical knowledge for K-1 students. While PST responses varied, lesson analysis using this tool aided PST in identifying components and foci for future mathematics lesson development. Insights gained from this study can help improve teacher education strategies to support beginning teachers to meet the learning needs of their culturally and linguistically diverse students.

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