Eliciting Pre-Service Secondary Mathematics Teachers' Technological Pedagogical Function Knowledge

Eliciting Pre-Service Secondary Mathematics Teachers' Technological Pedagogical Function Knowledge

Jennifer N. Lovett (Middle Tennessee State University, USA), Lara K. Dick (Bucknell University, USA), Allison W. McCulloch (University of North Carolina at Charlotte, USA), Milan F. Sherman (Drake University, USA), Cyndi Edgington (North Carolina State University, USA), Cecilia Anne Wanner (Middle Tennessee State University, USA) and Samuel D. Reed (Middle Tennessee State University, USA)
Copyright: © 2019 |Pages: 25
DOI: 10.4018/978-1-5225-7001-1.ch017

Abstract

The purpose of this study was to examine the evidence of technological pedagogical function knowledge that preservice secondary mathematics teachers (PSMTs) exhibited through engaging in a module in which they examine artifacts of students' mathematical thinking with technology. Three cases are presented to describe the evidence of technological pedagogical function knowledge that was elicited through engagement with the module. Findings show that the module was successful in eliciting PSMTs' function knowledge, technological function knowledge, and technological pedagogical function knowledge. Differences in the manners in which these knowledges were elicited are discussed and implications for teachers of PSMTs are shared.
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Introduction

Digital technologies have unarguably impacted current trends in education. Many researchers and scholars challenge that an immediate concern for education is that of developing teachers’ knowledge for infusing technology as learning tools (Mishra & Koehler, 2006; Niess, 2005). National organizations focused on mathematics education, including the National Council of Teachers of Mathematics (NCTM) and the Association of Mathematics Teacher Educators (AMTE), have echoed this call for enhanced preparation of pre-service secondary mathematics teachers’ Technological Pedagogical Content Knowledge (TPACK) (Mishra & Koehler, 2006; Niess, 2005). AMTE’s (2017)Standards for Preparing Teachers of Mathematics states that:

well-prepared beginning teachers of mathematics are proficient with tools and technology designed to support mathematical reasoning and sense making, both in doing mathematics themselves and in supporting student learning of mathematics. (p. 11)

NCTM’s (2014) Principles to Action further elaborates that teachers “need to develop deep understandings of how technology and tools can be used to investigate mathematical ideas. . . they need to reflect on how their students might use these tools” (p. 28).

To better prepare future teachers to teach with technology, an Examining Students’ Technological Mathematical Practice module was developed for pre-service secondary mathematics teachers (PSMTs). The mathematical topic of focus was the concept of function because research shows technology can be effective when developing the function concept (e.g., Dick & Hollebrands, 2011) and because PSMTs often struggle with developing a deep understanding of function (Cooney, Beckmann, & Lloyd, 2010). The module consisted of activities in which PSMTs first examined their own understanding of the function concept through engaging with an online applet and then investigated students’ mathematical thinking with technology through the examination of artifacts of middle school students (henceforth referred to as students) engaging with a similar applet. The purpose of this study was to examine the ways in which the module elicited different aspects of the PSMTs’ TPACK of function and to answer the following research question: What evidence of TPACK do PSMTs exhibit as a result of engaging in a module in which they examine artifacts of students’ mathematical thinking with technology?

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Background

This section begins with a short review of previous research on PSMTs’ TPACK. Then the section provides previous research on analyzing students’ mathematical work. Finally, the section provides the study’s focus on the function concept and the theoretical framework.

Key Terms in this Chapter

Vending Machine: A machine in which you input money, make an object selection, and an object comes out of the machine.

Pre-Service Secondary Mathematics Teacher (PSMT): A student enrolled in an initial licensure program whose certification includes a portion of Grades 6-12 mathematics.

Function: A mathematical relationship in which each input maps to exactly one output.

Concept Image: The set of mental images associated with a specific mathematical object.

Professional Noticing: A construct focused on attending, interpreting, and making instructional decisions based on students’ mathematical thinking.

Analyzing Student Work: The process of investigating authentic student mathematical work with a goal of understanding student mathematical thinking.

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