Differences in Beliefs and Knowledge for Teaching Mathematics: An International Study of Future Teachers

• In Event: 65.066 - Mathematics Teacher Education: Results and Implications of an International Study

Abstract

Objectives
Mathematical content knowledge is part of the instructional triangle (Hawkins, 1974; Lampert, 2001) of teacher, content and students, and supports professional judgment in practice. Beliefs about the nature of mathematics, teaching, and learning are “…predispositions to action” (Rokeach, 1968, p. 113), channeling how mathematical content knowledge is used in practice. Indeed, deep mathematical content knowledge and productive beliefs about teaching and learning are important outcomes for teacher preparation programs. This study explores the extent to which future teachers’ mathematical content knowledge form different patterns of beliefs within- and between-preparation programs across 17 countries.

Theoretical Framework
Mathematics-related beliefs are psychologically held “personal judgments about mathematics formulated from experiences in mathematics, including beliefs about the nature of mathematics, learning mathematics, and teaching mathematics” (Raymond, 1997, p. 552) that are felt to be true (Richardson, 1996). These teacher belief systems are inherently sensible (Leatham, 2006) and are bounded by social and cultural contexts (Perry et al., 2006). Beliefs are distinct from, but related to knowledge (Leatham, 2006, p. 92), and interact in complex ways with teachers’ instructional practices.

Research Question
Within- and between- teacher preparation programs in the TEDS-M study, to what extent do teachers with varying beliefs about the nature of mathematics and mathematics ability differ in their mathematical content knowledge?

Method
Data come from TEDS-M (2008-2009), an international comparative study of primary and secondary mathematics teacher preparation. Four types of primary preparation programs were identified based on the subjects and grade levels for which a program prepares participants for certification. Teachers were administered the following instruments upon completion of their programs:
• Mathematical Content Knowledge (MCK; Brese & Tatto, 2012) was assessed for four domains with 24 items: Algebra, Geometry, Number, and Data. The mean across participating countries was a score of 500 (SD = 100).
• Teacher Beliefs (Brese & Tatto, 2012) were assessed in three domains, two of which were used in this study: Beliefs about the nature of mathematics (subscales of mathematics as “Rules and Procedures” and “Process of Inquiry”) and beliefs about mathematics achievement (“Fixed Ability”). A Rasch scale score of 10 is “neutral.”
Results
Hierarchical linear models were estimated within each primary preparation program type. Countries often contain multiple program types. For Primary Generalists (PK-6), the relationship between MCK and all beliefs did not differ by country. For the other three program types, the relationship between MCK, beliefs about mathematics as a body of Rules and Procedures, and mathematics as a Fixed Ability differed by country. MCK correlates negatively with beliefs of math as rules and procedures and a fixed ability mindset.

Scholarly Significance
Productive beliefs and MCK are necessary but not sufficient for high-quality teaching practices that lead to equitable student outcomes. Preparation programs design coursework and field experiences to influence teachers’ mathematical content knowledge and beliefs about the nature of mathematics learning. Understanding outcomes of teacher preparation programs can illuminate whether teacher-endorsed beliefs and MCK adequately reflect the intended outcomes of their programs and suggest areas for increased attention by preparation programs.

Authors

• Traci Shizu Kutaka, SRI International

• Wendy M. Smith, University of Nebraska - Lincoln

• Anthony D Albano, University of Nebraska

• Chansuk Kang, University of Nebraska - Lincoln