Transforming Mathematics Teacher Knowledge in the Digital Age through Iterative Design of Course-Based Projects

Transforming Mathematics Teacher Knowledge in the Digital Age through Iterative Design of Course-Based Projects

Jennifer M. Suh (George Mason University, USA), Debra R. Sprague (George Mason University, USA) and Courtney K. Baker (George Mason University, USA)
DOI: 10.4018/978-1-5225-0120-6.ch008
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This research in this chapter highlights a self-study of three university faculty members who were aimed at improving the design of an Elementary Mathematics Technology Integration Course (EMTIC). The self-study used the faculty unique research lenses and expertise in mathematics education and educational technology to redesign the performance based assignments to better prepare the teacher candidates to integrate technology into their mathematics teaching. This collaboration required faculty members to: 1) Reflect on their beliefs about technology integration; 2) Evaluate their current teaching practices; and 3) Adapt the design of their course assignments to better meet the skills required of teachers and students in the 21st century.
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The Technology Principle from the Principles and Standards for School Mathematics (NCTM, 2000) states that “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.” Digital technologies have the potential with its visual and dynamic displays to offer a broader interpretation of mathematical representations. Hoadley and Kirby (2004) noted that incorporating representations through the use of technology provide the “unprecedented ability to create, manipulate and share representations of [a] wide variety” (p. 2). The decisions teacher candidates make with regards to implementing technology in their mathematics classroom, whether an enhancement or a hindrance to student learning, depends on the knowledge gained during a teacher preparation program (Lee & Hollenbrands, 2008). In order to enable their future students to understand mathematical concepts, teacher candidates need to capitalize on the power of technology to create meaningful lessons during their teacher preparation programs. Providing an instructional framework that enables solving mathematical tasks using technology, and to reflect on their experiences can assist teacher candidates to develop an understanding of how technology can be integrated into math instruction (Lee & Hollenbrands).

Extending from Shulman’s original framework of pedagogical content knowledge (Shulman, 1986, 1987), the framework of Technological Pedagogical Content Knowledge (TPACK) (Koehler & Mishra, 2009; Mishra & Koehler, 2006) moved educators to consider the connections, interactions, affordances, and constraints between and among technology, pedagogy, and content. In this model, knowledge about technology (T), pedagogy (P), and content (C) is central for developing good teaching.

What is important within this framework is not only the separate components, but also the interaction between and among these three components (Koehler & Mishra; Niess, 2005, 2008). Teachers need to possess technological knowledge (how to use the technology), pedagogical knowledge (how to teach students) and content knowledge (what to teach). Additionally, to effectively integrate technology teachers also need to develop technological content knowledge (the alignment of the content with the appropriate technology) and technological pedagogical knowledge (the alignment of the content with the appropriate technology to instruct students). (Sprague & Katradis, in press)

With regards to mathematics education, the C in TPACK represents mathematics; specifically the content strands such as algebra, numbers and operations, and geometry.

Soon after TPACK was introduced, the Association of Mathematics Teacher Educators (AMTE, 2009) released a statement about Mathematics TPACK stating that mathematics educators have an important role in serving their teacher candidates by planning and modeling 21st century digital tools. The framework that was shared with mathematics educators not only elaborated on the TPACK Model and the International Society for Technology in Education (ISTE) Standards for Teachers (ISTE, 2008), but was also designed to inform mathematics teachers, university educators, professional development facilitators and researchers “to plan, examine, improve, and evaluate mathematics instruction at all levels” (AMTE, p. 1). The framework delineated four essential components for enhancing teachers’ mathematical learning experiences via technology:

  • 1.

    Design and develop technology-enhanced math learning environments and experiences;

  • 2.

    Facilitate mathematics instruction with technology as an integrated tool;

  • 3.

    Assess and evaluate technology enriched mathematics teaching and learning; and

  • 4.

    Engage in ongoing professional development to enhance their TPACK (AMTE).

Key Terms in this Chapter

TPACK: Technological Pedagogical Content Knowledge (TPACK) ( Koehler & Mishra, 2009 ; Mishra & Koehler, 2006 ) considers what teachers need to know to be able to integrate technology; focuses on three main components of teacher knowledge: technology, pedagogy, and content knowledge.

David Letterman’s Top Ten: David Letterman hosted the Late Night with David Letterman for 22 years, which aired on channel CBS (Columbia Broadcasting System) in the United States. Each episode included a “Top Ten List,” which was a comedy routine around news stories or issues of the day.

SMARTboard: SmartBoard is a brand of interactive whiteboards (IWB); these IWBs are large interactive displays that connect to a computer where data can be manipulated by using a stylus on the SmartBoard surface or from the computer itself.

PBA: Performance-based assessment is the signature assignment within each of our courses. For example, in the EMMC, the teacher candidates conduct a one-on-one interview with a student to purposefully identify understandings and possible student misconceptions, and develop an instructional plan.

Differentiation: Differentiation is a framework we use for providing a diverse range of students with different avenues for learning.

Field Placements: K-12 school field placements are where preservice teachers practice their teaching skills under the supervision of a practicing teacher.

iPads: iPads are tablet computers produced by Apple Inc. with a user interface built around a multi-touch screen.

EMTIC: Elementary mathematics technology integration course is a one credit course for preservice teacher candidates focused on effective ways to integrate technology in mathematics and is taught in conjunction with the EMMC.

ISTE: International Society for Technology in Education is an organization that sets the standards for what teachers should know about and be able to do with technology.

EMMC: Elementary mathematics method course is three credit course for preservice teacher candidates focused on effective ways to teach mathematics to K-6 students.

Teacher Candidates: Teacher candidates are preservice students who are studying to become teachers and seeking licensure.

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