Preparing Teachers to Implement Technology

The Classroom Connectivity for Mathematics and Science (CCMS) program was a randomized control trial to examine the efficacy of Classroom Connectivity Technology (CCT) in Algebra I. CCT is a type of technology that allows the teacher to wirelessly communicate with his or her students' handheld calculators. Students in the classes that implemented CCT outperformed their comparison counterparts with effect sizes ranging from 0.19 to 0.37 (Irving et al., 2014; Pape et al., 2013). In this chapter, the professional development program that supported participating teachers to implement the technology is described. Categories of professional development activities including pedagogical instruction, modeling pedagogy, technological pedagogical instruction, technology instruction, student role-play, practice, small-group instruction, and participant presentation are presented in relation to their potential for supporting teacher participants' knowledge growth. Recommendations for the training of teachers to implement technology will be explicated.

Dynamic Approach to Teaching Geometry

Secondary geometry teachers from several urban school districts participated in a two-year professional development focused on integrating dynamic geometry into teaching. The chapter documents the positive impact of the professional development for teachers' Technological Pedagogical Content Knowledge (TPACK) development and their students' achievement in geometry through the use of the dynamic geometry approach. Instruments used to develop and assess teachers' TPACK included a Conjecturing-Proving Test, interviews and observation protocols. Participants' TPACK levels were identified using a TPACK Development Levels Assessment Rubric. Findings show that teachers' TPACK tended to remain within the three middle TPACK levels (accepting, adapting, and exploring). Recommendations and suggestions for future research are offered to those who implement school-based, mixed methods research studies involving technology.

Transforming Preservice Mathematics Teacher Knowledge for and with the Enacted Curriculum

In a curriculum system, instructional materials and their enactment impacts students learning of school mathematics. In this chapter, the authors re-examine enacted curriculum in light of research on Digital Instructional Materials (DIMs) and the critical role of the mathematics teacher. This chapter documents research from two different studies suggesting that, while effectively leveraging digital materials may require teachers to think outside of their traditional views of how mathematics content is learned and communicated, doing so requires more than the resources themselves. In order to seize upon the potential for DIMs to support student learning in mathematics, teacher preparation must offer opportunities for teachers to develop and transform their technological pedagogical content knowledge (TPACK) knowledge for and with DIMs. To this end, the authors propose specific recommendations for teacher preparation programs in the digital age.

Transforming Mathematics Teaching through Games and Inquiry

This chapter describes the design, development, and testing of a successful mathematics game-based intervention, Math Snacks, for students in grades 3–7. This program shows the impact of an integrative approach of developing Technological Pedagogical Content Knowledge (TPACK), where interactive digital media are combined with inquiry-based activities in classrooms facilitated by teacher involvement. Teachers played a key role in development and testing of Math Snacks, both by using them in their classrooms and by teaching core mathematics concepts connected to each module during annual summer camps. Via this multi-faceted participation, teachers experienced a change in their understanding of how digital tools can connect with inquiry-based pedagogy, mathematical content and pedagogical knowledge to facilitate successful learning for students. Teachers began to approach multimedia and games as part of an inquiry-based pedagogical approach for mathematics learning, rather than seeing games as tools for student practice after learning a concept.

Mathematics Education Technology Professional Development

The effective use of digital technologies in school settings calls for appropriate professional development opportunities that will transform inservice teachers' knowledge for integrating technologies as effective mathematics learning tools. To inform such opportunities, this study examined the contents of published mathematics education technology professional development papers over several decades using Sztajn's (2011) standards for high quality reporting in mathematics professional development research studies, the Technological Pedagogical Content Knowledge framework, and the Comprehensive Framework for Teacher Knowledge. Both the Professional Development Implementation and Evaluation Model and Education Professional Development Research Framework are recommended for further guidance on reporting key features of mathematics education technology professional development.

A Reconstructed Conception of Learner Engagement in Technology Rich Online Learning Environments

Teaching and learning in a technology rich digital context challenge established thinking about student engagement in their learning. This chapter presents a reconstructed conception of learner engagement for online environments consisting of: engagement with community; engagement with technology; engagement with mathematics content; and an amalgam of all three. This descriptive, cross-case study combines current literature with the authors' past research to develop characterizations of these components of online learner engagement. This reconstructed model of learner engagement is the focus of the study, providing: 1) a vocabulary for developing a narrative describing how teachers as students think and learn with technology in an online environment and 2) a framework for mathematics teacher education professional development. Results indicate that this model supports teacher educators in both describing and evaluating how teachers as learners engage in a unit of instruction, and framing the course design and instructional strategy choices that support learner engagement.

An Algebra Teacher's Instructional Decision-Making Process with GeoGebra

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.

Developing Teachers' TPACK for Mathematics through Professional Development

In this chapter, InterMath is introduced as a learner-centered professional development environment that supports the development of Technological Pedagogical Content Knowledge (TPACK). Evidence will be presented from the research and evaluation on InterMath to highlight some of the ways in which InterMath has been successful. Vignettes provide examples of a typical conversation in a TPACK professional development environment. An analysis of findings indicates that the InterMath project contributed to teachers' TPACK development, with a focus on teachers' knowledge of technology and content (TCK). The knowledge and skills of the professional development facilitator was a key factor in the teachers' development. Implications for the design of professional development include simultaneously developing teachers' integrated knowledge of technology, pedagogy, and content.

Designing Elementary Mathematics Games using Effective Mathematics Teaching Practices

Problem-solving digital games that make sense of mathematics do not happen by accident but by careful design. This chapter looks at a popular design framework, Game Network Analysis (GaNA), and examines how teachers can use it to turn popular digital games into strong mathematical experiences grounded in effective teaching practices that use play, purposeful explorations, and focused dialogue to make mathematical concepts more meaningful. The chapter involves a careful study of the GaNA framework in comparison with the eight Mathematics Teaching Practices of Principles to Actions: Ensuring Mathematical Success for All. The findings encourage further analysis of the GaNA framework in terms of specific academic areas. Explicit clarification is needed to use the framework to effectively move mathematics education toward its future potential.