# An Algebra Teacher's Instructional Decision-Making Process with GeoGebra: Thinking with a TPACK Mindset

Jacob Felger (Mississinewa Community Schools, USA) and Kathryn G. Shafer (Ball State University, USA)
DOI: 10.4018/978-1-5225-0120-6.ch019
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## Abstract

This chapter shares results of a classroom-based action research study on instructional decision-making when teaching a unit on linear functions with GeoGebra, a dynamic algebra environment. The TPACK / Student Knowledge Matrix developed by provided a structure for unit planning and lesson development. The matrix combines the three categories of teacher knowledge – technological, pedagogical, and content – with four levels of student knowledge – declarative, procedural, schematic, and strategic. While implementing the four-week unit, the algebra teacher used multiple data sources to document day-to-day decision-making. Data analysis revealed decisions were guided by the need to improve clarity, to increase interactivity, to highlight connections between representations, and to use GeoGebra as a tool to increase understanding. Throughout the unit, GeoGebra became a tool for computation, transformation, data collection and analysis, and error checking.
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## Background

Principles and Standards for School Mathematics (NCTM, 2000) suggests important standards regarding the teaching and learning of linear functions in middle grades. First, students should be able to compare the properties of linear versus nonlinear functions and describe the nature of change between quantities in a linear relationship. Linear patterns should be expressed in tables, graphs, rules, words, and symbols (NCTM, 2000, p. 223). These multiple representations become important as students learn to model and solve contextualized problems in various ways. As Bayazit and Aksoy (2010) noted, “... students’ ability to see interrelations between representations and between ideas is seen as a crucial stage in developing conceptual understanding of mathematics” (p. 94).

## Key Terms in this Chapter

GeoGebra: Free dynamic geometry and algebra software package used for teaching and learning mathematics.

Interactivity: Students manipulating parameters within a piece of technology and receiving immediate feedback.

Action Research: A systematic investigation of one’s own practice.

Analytic Memo: A reflective summary of a specific finding from data analysis, typically completed during study implementation.

Applet: An interactive computer based application that provides feedback based on input or action taken by the user.

Template: A blank computer file created to help guide students along a preselected path of inquiry, by simplifying, formatting, and labeling, and by pre-creating tedious or confusing parts of a task.

Technological Pedagogical Content Knowledge (TPACK): The construct that describes the transformed teacher knowledge that emerges from the interaction of technological knowledge, pedagogical knowledge and content knowledge.

Video Postmortem: A detailed summary of a classroom teaching observation based on observed behavior that was video recorded. The postmortem typically has a specific focus (e.g. discourse patterns).

Data Audit Trail: A list or table created to track information regarding data collection, analysis, and usage.

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