Capturing Teacher’s Mathematical Knowledge for Teaching

• In Event: Beyond Student Outcomes in Early Grade Mathematics: Expanding Opportunities for Measurement

Proposal

The purpose of this session is to present initial results on two new tools that can provide insight into teacher’s mathematical knowledge for teaching and how it influences their classroom practice. There is an increasing focus within early mathematics to teach with understanding; that is, to ensure that students understand the concepts behind key mathematical ideas, such as addition and subtraction, and can use this knowledge to solve real world problems. However, in low- and middle-income countries (LMICs) much of early mathematics instruction is dominated by rote memorization. Measurement of teacher mathematical knowledge is important to target teacher professional development (TPD) in math to the right level, as well as to measure success of this TPD. In order to identify the gaps in teacher knowledge, Lowenburg Ball and colleagues (2009) and others have developed multiple-choice surveys for measuring knowledge for teachers in upper primary grades (Cole 2012, Ng, 2012). There is a dearth of tools that can be adapted across multiple contexts to measure teacher’s mathematical knowledge (comprising both content knowledge and knowledge of how to teach that content) and that point to gaps in their knowledge. In addition, there is a need for an observation tool that measures how this knowledge is manifested during instruction. Identifying these gaps is essential if we are to design teacher professional development and materials for math instruction that improve learning outcomes.
In this presentation, we present the two tools: a survey for teachers and an accompanying classroom observation instrument. We begin by briefly describing the process of creating the instrument, including reviews of literature and cognitive testing. We then describe the instruments, beginning with the survey instrument which has 25 items, all multiple choice. Items cover four core domains in early mathematics (number, operations, geometry and spatial sense, and measurement), and there are three items types (knowledge of developmental progressions, knowledge of scaffolding strategies, and content knowledge). We are in process of developing a classroom observation instrument that is compatible with the survey and provides information on the three item types across the four domains.
Piloting of the survey in in process in two countries in the next several months. Piloting of the classroom observation may occur but will be more dependent on school closures due to COVID.
Taken together, these two instruments will provide implementers, donors, and governments with tools to be able to measure the effectiveness of intervention programs beyond student learning outcomes, as well as provide needed knowledge for the design of programs meant to improve early grade mathematics knowledge.

Authors

• Wendi Ralaingita, RTI International

• Yasmin Sitabkhan, RTI International

• Binod Prasad Pant, Kathmandu University School of Education