Abstract
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.
TopIntroduction
Mathematics teachers need to be able to integrate technology into their instruction in ways that support communication and sense making (e.g., Association of Mathematics Teacher Educators (AMTE), 2009; National Council of Teachers of Mathematics (NCTM), 2000, 2014; National Governor’s Association Center for Best Practices and Council of Chief State School Officers (NGA & CCSSO, 2010)). Throughout, the technology to be used is less important than the learning opportunities that it provides (NCTM, 2014). In mathematics, technology is more powerful when it is used beyond drill and practice activities (Polly, 2008; Wenglinsky, 1998). For example, technology should foster creativity and communication, promote reflection, and encourage the development of mathematical understanding (AMTE, 2009; NCTM, 2014; Orrill & Polly, 2013).
This chapter focuses on how to best support teachers’ learning of skills and knowledge related to using technology. Many teachers have not had opportunities to learn about or with technology in the ways suggested. Further, many teachers have not had the opportunity to learn mathematics in an exploratory way, influencing their beliefs about teaching (NCTM, 2014; Polly, McGee, Wang, Lambert, Pugalee, & Johnson, 2013). Yet, teachers are expected to create rich learning environments for their students (NGA & CCSSO, 2010; NCTM, 2000). In other words, creating innovative professional development that can support teachers in developing Technological Pedagogical Content Knowledge (TPACK; AMTE, 2009; Mishra & Koehler, 2006; Niess, 2005; Polly & Orrill, 2012) for mathematics is an important goal.
In this chapter, we examine what TPACK development looks like in one professional development program aimed at supporting teachers’ use of technology and exploration-based mathematics in their mathematics classroom. The program, InterMath, allows teachers to work alone or in groups on mathematics tasks using digital technologies, such as graphing calculators, spreadsheets, and dynamic geometry software. In this way, the technology serves as a tool for teachers to test conjectures, explore patterns, and engage in other inquiry-oriented practices important for mathematics learning (NGA & CCSSO, 2010; NCTM, 2000). These uses of technology align to best practice recommendations in the fields of mathematics education (NCTM, 2000, 2014; Zbiek, Heid, Blume, & Dick, 2007) and educational technology (New Media Consortium, 2014; Niess, 2005). Further, these uses of technology are also the ones teachers are least likely to have experienced in their educational preparation.
What does professional development that promotes the development of TPACK look like and what features seem important for supporting teacher learning? This question is examined through this chapter. To situate the reader, we provide the background and design framework from InterMath. Then, we present a description of the program and the data that support the claims of its effectiveness, including pre/posttest studies from some implementations of InterMath (Bleich, Ledford, Orrill, & Polly, 2006; Izsák, Jacobson, de Araujo, & Orrill, 2012; Orrill & Brown, 2012; Orrill & Kittleson, 2015; Orrill & the InterMath Team, 2006; Polly 2006; Polly & Orrill, 2012). Vignettes of an InterMath experience highlight the ways in which it supports the development of different aspects of TPACK. The chapter concludes with a discussion of the TPACK framework in which we critically examine ways in which the InterMath program develops TPACK as well as the ways in which it falls short in meeting the needs for aligning to all of the knowledge elements in TPACK. Finally, we propose implications and future directions for professional development programs like InterMath to more robustly develop teachers’ TPACK for mathematics.
Key Terms in this Chapter
Technological Content Knowledge (TCK): Knowledge of how to use technology within a specific content area. Knowing how to use a spreadsheet provides an example of how to analyze a set of data for patterns or knowing how to use Fraction Bars to show a proportional relationship.
Technological Knowledge (TK): Knowledge of how to use technology such as, how to create a spreadsheet.
Technological Pedagogical Knowledge (TPK): Knowledge of how to teach students to use technology in learning situations.
InterMath: A learner-centered professional development program that engaged middle school teachers in learning about the mathematics they teach through technology-enhanced investigations.
Mathematical Knowledge for Teaching (MKT): The specialized knowledge mathematics teachers need to support their students learning that goes beyond the mathematics that any educated adult might need. Examples include knowledge of representations to teach particular concepts, knowledge of a variety of approaches to solve a problem, and understandings of why algorithms work.
Pedagogical Knowledge (PK): Knowledge of teaching strategies. For example, a teacher should know when and how to teach with double number lines.
Content Knowledge (CK): Knowledge of the content of interest. For example, in mathematics, knowing how to calculate a proportion or knowing how to divide a fraction is content knowledge.
Technological Pedagogical Content Knowledge (TPACK): Knowledge of how to use technology to teach particular topics related to a content area. For example, knowing how to support students in learning to use spreadsheets to identify patterns that lead to an algebraic expression.
Learner-Centered Professional Development (LCPD): Professional development designed around the principles that teachers need sustained opportunities to focus on student learning; to take ownership of their learning; to be actively engaged in their learning; to collaborate with each other; and to reflect on their learning.