Disciplinary Content Knowledge

In this paper, we focus on the design of assessments of mathematics teachers’ knowledge by emphasising the importance of identifying the purpose for the assessment, defining the specific construct to be measured, and considering the affordances of particular psychometric models on the development of assessments as well as how they are able to communicate learning or understanding. We add to the literature by providing illustrations of the interactions among these critical considerations in determining what inferences can be drawn from an assessment.

Graph technologies are now widely available in K-12 science and mathematics classrooms. These technologies have the potential to impact the learning of science and mathematics, especially by supporting student investigations. We use meta-analysis to analyze 42 design and comparison studies involving data from 7699 students spanning over 35 years. In these studies, graphing technologies include computer software such as simulations; online tools such as graph utilities; and sensors such as temperature probes. We characterize the assessments used to measure graphing.

We describe an experience within mathematics teacher preparation that engages pre-service teachers of mathematics (PMTs) in Making and design practices that we hypothesized would inform their conceptual, curricular, and pedagogical thinking. With a focus on the design of new tools that can generate new possibilities for mathematics teaching and learning, this Learning by Design experience has PMTs exploring at the intersection of content, pedagogy, and Making.

During the last three decades, scholars have proposed several conceptual structures to represent teacher knowledge. A common denominator in this work is the assumption that disciplinary knowledge and the knowledge needed for teaching are distinct. However, empirical findings on the distinguishability of these two knowledge components, and their relationship with student outcomes, are mixed. In this replication and extension study, we explore these issues, drawing on evidence from a multi-year study of over 200 fourth- and fifth-grade US teachers.

Smith, P. S., Plumley, C. L., Hayes, M. L., & Esch, R. K. (2018). Personal and Canonical PCK: A Synergistic Relationship? In S. Graves, M. Harford, R. Thompson, E. Shay, & S. Uzzo (Eds.), Pedagogical Content Knowledge in STEM (pp. 49-66). The Netherlands: Springer.

This chapter focuses on the design of simulation assessments to learn about pre-service teachers’ capabilities with eliciting and interpreting student thinking. We present a simulation assessment and show what a performance on that assessment can reveal about a pre-service teacher’s eliciting and interpreting skills, as well as their mathematical knowledge for teaching. We consider the specific design features that make it possible to appraise pre-service teachers’ capabilities.