Abstract
This paper addresses two critical issues in mathematics education, the need: (a) to understand the nature of educator’s subject matter knowledge and pedagogical content knowledge; and (b) to find ways to measure them. It stems from a mixed-methods study designed to inspect the secondary mathematics teachers’ pedagogical content knowledge (PCK) related to the area of a trapezoid, a common topic in intermediate/secondary school classes. Based on the provided exemplars of student work, in-service teachers were invited to propose possible ways for addressing perceived difficulties of students and provide extensions. Using a Grounded Theory approach, we identified themes in our data and incorporated them with existing conceptualizations of knowledge for teaching secondary level mathematics, and developed rubrics that allow discriminating different levels of teachers’ PCK. In this paper, we describe the process of developing the rubrics, and propose ways to: (a) extend the existing frameworks for PCK in/for teaching mathematics at the secondary level; and (b) measure multiple facets of PCK in order to design technology-based professional development for mathematics teachers.
Highlights
Researchers agree that teachers can significantly and positively influence student learning outcomes, especially if they use particular teaching methods, and if they expect much of their students and have good relationship with them; in other words, “what teachers DO matters” [1] (p. 22, emphasis in original)
Is more direct when asserting that, “A mathematics teacher needs to know mathematics” (p. 86), and Alex Lawson [7] calls for action stating that, “Teachers’ lack of mathematical content knowledge and mathematical pedagogical knowledge is one of the most central issues we face in effective mathematics instruction” (p. 12). This is the first critical issue that we address in this paper, especially from the point of developing tools to measure teachers’ subject matter knowledge and pedagogical content knowledge, and potentially using this information to guide and plan professional learning
“theoryless” or because we were skeptical “of the usefulness of the theories that have been generated in the field” [29] (p. 333); on the contrary, the previously developed theories of pedagogical content knowledge (PCK) were part of our theoretical and conceptual framework, and we could see their main aspects emerging from our data
Summary
Researchers agree that teachers can significantly and positively influence student learning outcomes, especially if they use particular teaching methods (e.g., based on problem solving or peer collaboration), and if they expect much of their students and have good relationship with them; in other words, “what teachers DO matters” [1] (p. 22, emphasis in original). (3) Teachers need to be aware of what each and every student is thinking and knowing, to construct meaning and meaningful experiences in light of this knowledge, and have proficient knowledge and understanding of their content to provide meaningful and appropriate feedback . That government agencies and teacher organizations pay particular attention to success of mathematics students [2,3,4], there are increased expectations for mathematics teachers to be more observant and reactive to their students’ current mathematical thinking and understanding (e.g., [5]), so that they can be proactive and use it for instructional decision-making during and when planning lessons. While the researchers and practitioners seem to agree that what teachers do in the classroom matters, there is no consensus if what teachers know matters and in which way it may matter
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