Pedagogical 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.

Drawing on a situated perspective on learning, we analyzed written, open-ended journals of 52 pre-service teachers (PSTs) concurrently enrolled in mathematics and pedagogy with field experience courses for elementary education majors. Our study provides insights into PSTs’ conceptualizations of mathematical argumentation in terms of its meanings. The data reveals how PSTs perceive teacher actions, teaching strategies, classroom expectations, mathematics content, and tasks that facilitate student engagement in mathematical argumentation.

Teachers' use of formative assessment (FA) has been shown to improve student outcomes; however, teachers enact FA in many ways. We examined classroom videos of nine experienced teachers of elementary, middle, and high school science, aiming to create a model of FA enactment that is useful to teachers.

We report on the use of bilingual constructed response science assessments in the context of a research and development partnership with secondary school science teachers. Given the power that assessments have in today’s education systems, our project provided a series of workshops for teachers where they explored students’ emergent reform-oriented science meaning-making in our project-designed assessments.

In this chapter we discuss some of the affordances and constraints of using online teaching simulations to support reflection on specific pedagogical actions. We share data from a research project in which we implemented multiple iterations of a set of simulated teaching experiences in an elementary mathematics methods course. In each experience, preservice teachers contrasted the consequences of different pedagogical choices in response to a particular example of student thinking.

The Next Generation Science Standards call for changes in not only what is taught in elementary science but also how students engage in the learning experience to develop understanding of core disciplinary ideas. In this study we examined 5th-grade teachers’ pedagogical content knowledge (PCK) for 1 particular core idea: the small particle model (SPM) of matter. We assessed teachers’ initial PCK through a lesson plan task, the Content Representation tool, and interviews and then adapted and tested a scoring rubric to facilitate comparison of teachers’ PCK.