Exploring Mathematical Pedagogical Content Knowledge: An International Study of Future Teachers

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

Abstract

Objectives
Shulman (1986) posed the “missing paradigm” problem: how the subject matter of the teacher was transformed into the content of instruction (1986, p. 6). He also proposed three categories of knowledge necessary for effective teaching: content knowledge, pedagogical content knowledge, and curricular knowledge. This study explores the relationship between mathematical content knowledge, general pedagogical knowledge, and pedagogical content knowledge for teaching in the context of teacher preparation programs across four countries.

Theoretical Framework
Ball, Thames, and Phelps (2008) map the domains of mathematical knowledge for teaching, defining knowledge in broad terms, including skills and habits of mind, and suggesting the domains are interrelated. In particular, specialized content knowledge is unique to teaching and has been linked to student achievement (Hill, Rowan, & Ball, 2005). More studies are needed to address how teacher preparation programs design coursework and field experiences to cultivate participants’ mathematical knowledge for teaching.

Research Questions
Within four TEDS-M countries, to what extent does the relationship between mathematical content knowledge (MCK) and mathematical pedagogical content knowledge (MPCK) vary by opportunities to connect classroom learning to practice (OTL) within primary and secondary preparation programs?

Methods
The data were collected from 2008-2009 for the TEDS-M study, a cross-national study of future primary, lower-secondary, and secondary teachers. Prior to graduation, a representative sample of future primary and secondary teachers were administered the following instruments:
• Mathematical Content Knowledge and Mathematical Pedagogical Content Knowledge (MCK and MPCK, respectively; Brese & Tatto, 2012) were assessed in four domains with 24 and 10 items at the primary-level, respectively: Algebra, Geometry, Number, and Data. The same domains were assessed using 23 and 9 items at the secondary-level. The mean MCK and MPCK of participating countries was scaled to 500 (SD = 100).
• Opportunity to Learn (OTL; Brese & Tatto, 2012) in the domain “Connecting Classroom Learning to Practice” is composed of 8 items (α = .95).
For the purposes of this study, four countries were selected for in-depth analysis: Georgia, Poland, USA, and Singapore.
Results
Using regressions of MPCK on MCK, OTL, and the interaction between them, for primary and secondary future teachers by country and program, effects for MCK were all statistically significant; effects for OTL were only statistically significant in Poland and the USA; interaction effects were only significant in the USA. Thus, higher MPCK is correlated with higher MCK, and usually correlated with higher OTL. The interaction effects in the USA tell us that the higher OTL levels have a tapering off of the correlated increase in MPCK.

Scholarly Significance
Teachers with higher mathematical pedagogical knowledge have more equitable student outcomes. Better understanding individual components of specialized content knowledge can help programs equip future teachers with knowledge associated with high quality instruction. More research is needed to investigate the size and valence of these effects, to determine potential differential impact relative to length of program, math knowledge prior to the program, and emphasis on pedagogy within programs.

Authors

• Anthony D Albano, University of Nebraska

• Traci Shizu Kutaka, SRI International

• Wendy M. Smith, University of Nebraska - Lincoln

• Chansuk Kang, University of Nebraska - Lincoln