The challenges in the assessment of knowledge for teaching geometry

In our research, we focused on the design of assessment instruments for measuring teachers’ mathematical knowledge for teaching geometry. Since 1987 when Lee Shulman conceptualized pedagogical content knowledge, different research groups have expanded on this construct and developed their own measurement instruments. The strengths and limitations of these instruments have been described in the literature. Compared to researchers who have designed instruments for a broad range of mathematical topics, we propose that the measures should be designed as “probes” around specific topics commonly taught by a targeted group of teachers (e.g., middle school). In this paper, we focus on methodological issues of measuring mathematical knowledge for teaching, describe our approach in designing the probe targeting knowledge for teaching the Area of a Trapezoid task and accompanied assessment tools, identify challenges in designing assessments, and discuss possible solutions. In designing the measures and rubrics of teachers’ knowledge, we used the Delphi and Grounded Theory research methods.