Mathematical Understanding for Secondary Teaching Framework: A Tool for Research

• In Event: 70.043 - Investigating Knowledge for Teaching Secondary Mathematics

Abstract

Purpose
We will introduce participants to the Mathematical Understanding for Secondary Teaching (MUST) framework developed at two NSF-funded Centers for Learning and Teaching, encouraging them to use the framework in their research.

Theoretical Foundations
The MUST framework was influenced by previous studies, frameworks and specifically work in grades K-12 (e.g., Adler & Davis, 2006; Ball, Thames, & Phelps, 2008; Cuoco, Goldenberg, & Mark, 1996; Even, 1990; Kilpatrick, Swafford, & Findell, 2001). Our synthesis of work about mathematical knowledge for teaching suggested that there was a need to characterize mathematical understanding, which includes both mathematical knowledge and the ability to use that knowledge. We separated the mathematical understanding from the pedagogical concerns and focused on mathematics specific to students at the secondary level.

Methods and Data Collection
The MUST framework was based on data from mathematics classes in grades 6-12 and university classes for preservice secondary teachers. Researchers collected brief descriptions of notable mathematical events (e.g., student questions, teacher comments, misconceptions, insights). As a research group, we discussed each event and determined important mathematics that would be useful to the teacher. We wrote Situations that included the classroom event, the mathematical understanding that would be useful, and additional commentary. The Situations focused solely on the mathematics and did not attend to pedagogical issues or teaching strategies. The Situations were reviewed by mathematics educators, mathematicians, and teachers. The revised Situations provided the data needed to construct the framework.

MUST Framework
The MUST framework consists of three perspectives that provide a thorough look at secondary school mathematics from different viewpoints—Mathematical Proficiency, Mathematical Activity, and Mathematical Context of Teaching.

Although previous frameworks have influenced our thinking, the MUST framework is substantially different because it looks at mathematics in grades 6-12, provides lenses for viewing mathematics divorced from pedagogy, and is grounded in classroom practice. The framework explains how the mathematical understanding for secondary teaching differs from the understanding that is useful to other professionals.

Scholarly Significance
As we developed the framework, we invited experts not involved in its development to discuss and critique the framework. In addition to advice, the experts provided examples of significant influence that the framework could have on secondary and tertiary curricula, mathematics teacher education, mathematics task development, assessment, policy, and research. In this presentation we will focus on the potential of the framework to facilitate research in mathematics education. We would like to suggest possible uses in research design, research task development, and data analysis. We will encourage the participants to elaborate on uses in research.

Author

• Patricia S. Wilson, University of Georgia - Athens