The Dynamic Process of Teaching and Learning Mathematics: Preservice Teachers as Learners, Teachers, and Researchers

• In Event: Proportionality Dynabook: Because “To Know Is Not Enough” in Mathematics Teacher Professional Development

Abstract

In this paper, we discuss changes in teacher candidates’ thinking about proportional reasoning (specifically ratio) during and after they engage in a sequence of Dynabook-mediated activities structured to focus their attention on reasoning (their own, and others’) and representation. We are interested in how teachers’ comprehend their own learning, the forms of literacy required to discuss their learning and how these factors affect their approach to teaching students with Learning disabilities (LD).
There is a unique challenge in preparing special education teachers to teach middle school mathematics because they need to understand proportional reasoning and the individual difficulties that that students with learning disabilities (LD) bring to the classroom (Seyeski & Paulsen, 2010). Students with LD have deficits in attention, memory, background knowledge, vocabulary, language processes, strategy knowledge and use, visualspatial processing, and self-regulation (Baker, Simmons, & Kame’enui, 1995; Geary, 2003). The challenge for special educators is twofold. First, to determine individual student’s level of proportional reasoning and deficits presented by their disability. Second, utilize pedagogically sound ways to assist students in making shifts from no proportional reasoning to higher, more meaningful levels of proportional reasoning (Seyeski & Paulsen, 2010).
Drawing our methodology from Mason and Spence’s (1999) theoretical framework of “ knowing-to-act,” we analyzed classroom discussions, interviews, teacher created scripts, observations and other artifacts, to examine the emerging changes in our credential candidates’ understanding of their own learning of ratio and how these emerging changes may affect approaches to teaching ratio to students with LD.
Participants are graduate students seeking an Education Specialist Credential (special education certification to teach students with mild to moderate disabilities in grades K-12) who were enrolled in one of three sections of an advanced methods class. The focus of this class is on preparing teachers to perform assessments and design sound instructional strategies to teach mathematics and reading. For this study, we are only using data from the two three-hour class sessions that focused on teaching ratio. Our data collection and analysis included both qualitative and quantitative methods.
Preliminary findings suggest that teachers’ engagement with the Dynabook activity system provided the crucial opportunity to reflect on self-learning of ratio and the specific literacies involved in assessing and teaching ratio. Sharing and group discussions of these critical reflections seemed to heighten teachers’ awareness of individual differences in learning and comprehending mathematics, which led to anticipation of difficulties they may face when teaching ratio. As our candidates performed activities with Dynabook, they became more aware of the required ratio, pedagogy, and technology literacies necessary to discuss student assessment, levels of understanding, and common ratio misconceptions and procedural errors. This awareness of required literacies enriched discussions about pedagogically sound strategies and helped candidates create teaching scripts. Findings and implication will be discussed in this presentation.

Authors

• Susan Courey, San Francisco State University

• Jody Siker, University of California - Berkeley

• Pamela C. Lepage, San Francisco State University