A Theoretical Framework for Implementing Technology for Mathematics Learning

A Theoretical Framework for Implementing Technology for Mathematics Learning

Travis K. Miller (Millersville University of Pennsylvania, USA)
DOI: 10.4018/978-1-60960-750-0.ch011
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This chapter details a theoretical framework for effective implementation and study of technology when used in mathematics education. Based on phenomenography and the variation theory of learning, the framework considers the influence of the learning context, students’ perceptions of the learning opportunity, and their approaches to using it upon measured educational outcomes. Elements of the TPACK framework and the CTFK model of teacher knowledge are also addressed. The process of meeting learning objectives is viewed as leading students to awareness of possible variation on different aspects, or dimensions, of an object of mathematical learning.
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Implementation and study of technology within the mathematics curriculum must consider an appropriate theoretical framework. Leading theories of mathematical learning tend to focus upon one particular aspect of learning: cognition, social interaction, or context. Further, technology use and educational research based upon these theories limit focus to the primary considerations of the chosen theory, with limited scrutiny or examination of alternatives. The view of learning taken by the phenomenographic research approach and its associated variation theory (Bowden & Marton, 1998; Marton & Booth, 1997; Prosser & Trigwell, 1997; Runesson, 2005) avoids these limitations. Phenomenography and variation theory share a unique relationship; the fundamental assumptions of the phenomenographic view of learning are detailed in the recently developed variation theory, which itself evolved from the findings of empirical phenomenographic research studies (Bowden & Marton, 1998; Marton & Booth, 1997; Runesson, 2005). As an approach to research, phenomenography searches for the qualitatively different ways of experiencing an educational phenomenon. As a theory of learning, the aligned variation theory focuses upon guiding learners to an awareness of the different aspects of the learning object.

This chapter considers three essential questions regarding the implementation and study of technology within the mathematics curriculum:

  • 1.

    How is the application of a learning theory influential in the implementation and study of technologically enhanced mathematical learning?

  • 2.

    What is the derivation of the variation theory of learning, and how does it apply to the teaching and learning of mathematics?

  • 3.

    How can variation theory help to establish an effective framework for implementing and researching technology use in mathematics education?

The chapter first briefly examines constructivism and the situative perspective, two predominant theories of learning in mathematics education. This is followed by a discussion of the central tenets and historical development of variation theory from phenomenography. Next, variation theory conceptualizations of learning mathematics via technology are presented as a guide for the development of effective technology-enhanced experiences that facilitate mathematics learning, a concern of the mathematics Technological Pedagogical Content Knowledge (TPACK) Framework (Association of Mathematics Teacher Educators, 2009; Mishra & Koehler, 2006; Niess et al., 2009; Ronau, Rakes, Wagener, & Dougherty, 2009). Finally, the chapter concludes with the implications of phenomenographic methods and the presented framework for research of technology-rich learning opportunities in mathematics courses. These research considerations also align with the TPACK framework (AMTE, 2009; Mishra & Koehler, 2006).



The initial search of the existing literature for this work was part of a comprehensive and broader doctoral dissertation literature review (Miller, 2007). Searches for recent publications on learning theories and technologies utilized the ERIC, Educause, and JSTOR databases to focus upon issues in education. Manuscripts were included based upon two criteria: (1) examination of either the constructivist or situative perspectives, and (2) application of technology to improve learning. Article selection considered a historical view of the theories via publications from their originators alongside more recent interpretations and applications. Identification of writings regarding phenomenography and the variation theory of learning took a similar, albeit more comprehensive, approach. A more thorough review of phenomenography and variation theory was facilitated by their more recent development and the smaller body of published work.

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Table of Contents
Robert N. Ronau, Christopher R. Rakes, Margaret L. Niess
Robert N. Ronau, Christopher R. Rakes, Margaret L. Niess
Chapter 1
Margaret L. Niess
Technology, pedagogy, and content knowledge (TPACK) is a dynamic lens that describes teacher knowledge required for designing, implementing, and... Sample PDF
Teacher Knowledge for Teaching with Technology: A TPACK Lens
Chapter 2
Matthew J. Koehler, Tae Seob Shin, Punya Mishra
In this chapter we reviewed a wide range of approaches to measure Technological Pedagogical Content Knowledge (TPACK). We identified recent... Sample PDF
How Do We Measure TPACK? Let Me Count the Ways
Chapter 3
Thomas C. Hammond, R. Curby Alexander, Alec M. Bodzin
The TPACK framework provides researchers with a robust framework for conducting research on technology integration in authentic environments, i.e.... Sample PDF
Assessment in Authentic Environments: Designing Instruments and Reporting Results from Classroom-Based TPACK Research
Chapter 4
Robert N. Ronau, Christopher R. Rakes
In this study, we examine the validity of the Comprehensive Framework for Teacher Knowledge (CFTK) through a systematic review and meta-analysis.... Sample PDF
A Comprehensive Framework for Teacher Knowledge (CFTK): Complexity of Individual Aspects and Their Interactions
Chapter 5
Lynn Bell, Nicole Juersivich, Thomas C. Hammond, Randy L. Bell
Effective teachers across K-12 content areas often use visual representations to promote conceptual understanding, but these static representations... Sample PDF
The TPACK of Dynamic Representations
Chapter 6
Erica C. Boling, Jeanine Beatty
This chapter informs teacher educators and individuals involved in teacher professional development about the tensions that frequently arise when... Sample PDF
Overcoming the Tensions and Challenges of Technology Integration: How Can We Best Support our Teachers?
Chapter 7
John K. Lee, Meghan M. Manfra
To address the myriad effects that emerge from using technology in social studies, we introduce in this chapter the concept of vernaculars to... Sample PDF
TPACK Vernaculars in Social Studies Research
Chapter 8
Stephen J. Pape, Karen E. Irving, Clare V. Bell, Melissa L. Shirley, Douglas T. Owens, Sharilyn Owens, Jonathan D. Bostic, Soon Chun Lee
Classroom Connectivity Technology (CCT) can serve as a tool for creating contexts in which students engage in mathematical thinking leading to... Sample PDF
Principles of Effective Pedagogy within the Context of Connected Classroom Technology: Implications for Teacher Knowledge
Chapter 9
Christopher J. Johnston, Patricia S. Moyer-Packenham
Multiple existing frameworks address aspects of teachers’ knowledge for teaching mathematics with technology. This study proposes the integration of... Sample PDF
A Model for Examining the Criteria Used by Pre-Service Elementary Teachers in Their Evaluation of Technology for Mathematics Teaching
Chapter 10
Joseph M. Piro, Nancy Marksbury
With the continuing shift of instructional media to digital sources occurring in classrooms around the world, the role of technology instruction in... Sample PDF
Technologizing Teaching: Using the WebQuest to Enhance Pre-Service Education
Chapter 11
Travis K. Miller
This chapter details a theoretical framework for effective implementation and study of technology when used in mathematics education. Based on... Sample PDF
A Theoretical Framework for Implementing Technology for Mathematics Learning
Chapter 12
David A. Slykhuis, Rebecca McNall Krall
In this review of recent literature on the use of technology to teach science content, 143 articles from 8 science education journals were selected... Sample PDF
Successful Implementation of Technology to Teach Science: Research Implications
Chapter 13
Irina Lyublinskaya, Nelly Tournaki
A year-long PD program was provided to four NYC integrated algebra teachers. The PD comprised of teacher authoring of curriculum that incorporated... Sample PDF
The Effects of Teacher Content Authoring on TPACK and on Student Achievement in Algebra: Research on Instruction with the TI-Nspire™ Handheld
Chapter 14
Robert N. Ronau, Christopher R. Rakes
This chapter examines issues surrounding the design of research in educational technology and teacher knowledge. The National Research Council... Sample PDF
Making the Grade: Reporting Educational Technology and Teacher Knowledge Research
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