Two Classroom Portraits Demonstrating the Interplay of Secondary Mathematics Teachers’ TPACK on their Integration of the Mathematical Practices

Two Classroom Portraits Demonstrating the Interplay of Secondary Mathematics Teachers’ TPACK on their Integration of the Mathematical Practices

Jessica Taylor Ivy (Mississippi State University, USA) and Dana Pomykal Franz (Mississippi State University, USA)
DOI: 10.4018/978-1-4666-4086-3.ch014
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Abstract

This chapter examines the practices and beliefs of two secondary mathematics teachers with similar demographic backgrounds. The influence of their practices and beliefs on teaching and student learning is considered through the lens of the TPACK Development Model and through evidence of student engagement in the Mathematical Practices. Even though they face common barriers to instructional technology integration, both teachers speak to their successes and positive impacts on student learning. Rich descriptions of conversations, classroom observations, and self-report survey data highlight critical contrasts between the practices of the two teachers. These differences represent the unique challenges faced by instructional technology researchers and other educational stakeholders. The purpose of this chapter is to highlight these subtle, yet far-reaching, areas of distinction in which the teachers unknowingly provide different levels of opportunity for teaching and learning in the mathematics classroom.
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Background

TPACK and the Standards for Mathematical Practice

Data obtained through this study was examined through the lens of an established development model, described briefly in this paragraph. The knowledge needed to teach mathematics with technology is known as Technology, Pedagogy, And Content Knowledge (TPACK; Niess et al., 2009). This construct grew out of an identification of the types of knowledge necessary for teaching. This unique type of knowledge, known as TPACK, encompasses the intersection of content knowledge, pedagogical knowledge, and technological knowledge. This chapter assumes a familiarity with the themes and levels described in the TPACK Development Model (e.g., Niess et al., 2009).

The ability to foster students’ engagement in the Standards for Mathematical Practice (SMP) is connected to a teachers’ own understanding of each of the standards. Further, the teacher must have a developed understanding of TPACK with a given technology to be able to apply it to the SMPs. Clearly if students in a classroom are going to use technology to “make sense of problems”, “model with mathematics”, or “use appropriate tools strategically”, the teacher must understand the interplay of the relevant technology, pedagogy, and content. Moreover, teachers must reconcile the challenges they face when using technology with their beliefs and practices. Many teachers integrate technology in their classrooms in ways which do not engage students in the aforementioned Mathematical Practices – and the authors propose that these practices correspond to low levels of the teaching and learning themes of the TPACK Development Model.

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