Measuring mathematical knowledge for teaching: Insights from a large-scale evaluation in a Sub-Saharan African country

• In Event: Highlighted Session: Building teacher’s content and pedagogical knowledge in early mathematics

Proposal

In 1986, Lee Shulman introduced the term pedagogical content knowledge (PCK) to better understand the qualities that characterize effective teachers. PCK captured great interest because it situated teacher knowledge and practice within the teaching of a specific discipline. Researchers gravitated towards the idea of PCK even though it lacked a clear and consistent operational definition for research and measurement.
Multiple studies describe the difficulties of measuring pedagogical content knowledge. A first layer of complexity in measuring PCK is the lack of a universally accepted framework. In mathematics, one of the most accepted frameworks is from Ball et al. (2008) which conceives PCK as comprising knowledge about student thinking, instructional strategies, and curriculum. This framework, also known as Mathematical Knowledge for Teaching (MKT), expands the notion of PCK to formally include 'teachers' Content Knowledge (CK) as essential for their ability to teach (Miller, Pinerua, Margolin, & Gerdeman, 2022).
Another layer of complexity is related to the multiple approaches one can use to measure PCK and particularly, MKT. A recent review distinguishes three broad approaches: quantitative tests and surveys, qualitative interviews, lesson observations, and clinical simulations (Miller, Pinerua, Margolin, & Gerdeman, 2022). Each methodology has its own benefits and challenges. For example, quantitative tests allow researchers to measure PCK at scale but do not always provide depth. In low-income contexts, the challenges are furthered by structural barriers.
Despite its measurement challenges, PCK and particularly, MKT remains a promising construct, due to its relationship to student outcomes. Previous analysis suggests a positive association between MKT and student achievement, even when controlling for SES. For example, Marshall et al. (2009) found an association between teachers' MKT and achievement in Cambodian primary schools, as did Ngo (2012) who found a positive effect of MKT on third-grade student achievement in Cambodia. Marshall and Sorto (2012) used several aspects of MKT and found that it was associated with student achievement in Guatemala. Finally, Carnoy and Arends (2012) found a positive association between MKT and student achievement in Botswana.
The scarcity of research on how to properly measure and use MKT in certain contexts, such as Sub-Saharan Africa, may limit its potential to inform educational programs and teachers’ professional development efforts. This presentation describes the authors' experience developing and using a self-administered paper and pencil MKT tool with in-service mathematics teachers in a Sub-Saharan African country. The content of the tool mirrored Ball’s (2008) framework and included close ended and open-ended questions. The tool also asked the same content questions to teachers and students to understand the degree to which 'teachers' knowledge gaps are predictive of 'students' misconceptions.
The presentation will focus on the adequacy of the development, administration and use of the tool. The presentation will also explore the relationship between MKT scores and students’ outcomes and provide insights for research and practice.

Authors

• Lauren McAskill, School-to-School International

• Candace Debnam, School-to-School International

• Fernanda Gándara, Room to Read