Developing an Interactive Instrument for Evaluating Teachers’ Professionally Situated Knowledge in Geometry and Measurement

Abstract

In this study, we propose a content specific, short, interactive, on-line, scenario-based instrument that incorporates virtual manipulatives developed in GeoGebra, as one of the many ways for evaluating and describing teachers' professionally situated knowledge (PSK) in the domains of geometry and measurement. To define PSK of mathematics teachers, we use a combination of Shulman's Pedagogical Content Knowledge (PCK) and its corresponding mathematical knowledge. We describe the methodology used to develop the instrument as well as the corresponding rubrics. The study design followed a concurrent mixed-methods approach, in which the quantitative and qualitative phases of data collection were intermingled to explore the research questions related to identifying components of the PSK. As a case study, we used PSK of the area of a trapezoid, since (a) this topic is familiar to most middle school and secondary mathematics teachers; and (b) a narrow focus was most advantageous when using Delphi methodology to draft an instrument, which was then fully developed using methods of grounded theory. This comprehensive approach led to a deep investigation of multiple and diverse data sources collected from practicing teachers, which we used to create their PSK profiles in the area of trapezoid.