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Connecting Preservice Teachers’ Knowledge of Mathematics, Pedagogy, and Technology through Learning Object Design

Connecting Preservice Teachers’ Knowledge of Mathematics, Pedagogy, and Technology through Learning Object Design. Jennifer Kosiak Becky LeDocq. Outline. Learning Object Design PCK & MKT TPCK Our Study Conclusion Questions. Learning Object Design.

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Connecting Preservice Teachers’ Knowledge of Mathematics, Pedagogy, and Technology through Learning Object Design

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  1. Connecting Preservice Teachers’ Knowledge of Mathematics, Pedagogy, and Technology through Learning Object Design Jennifer Kosiak Becky LeDocq

  2. Outline • Learning Object Design • PCK & MKT • TPCK • Our Study • Conclusion • Questions

  3. Learning Object Design • A LO is a self-contained learning unit. • LO’s can transform the traditional classroom environment. (Kay & Knaack 2005; NRC 1999) • The LO Design predicates learning from technology. (Reeves 1998)

  4. PRAXIS Wisconsin Project • The primary purpose was to involve mathematics faculty and preservice elementary and secondary teachers as designers of digital learning objects for mathematics. • Initially, the components of the learning objects were intended to help prepare educators for the mathematics portion of the Educational Testing Service’s Praxis II: Elementary Education and Middle School Content Knowledge Tests.

  5. PRAXIS Learning Objects • Statement of the Question with possible Answers and mistake-specific feedback • Hint to help them remember a key detail • Sandbox, a place to “play and learn” • Tutorial, a careful presentation of the solution (shockwave movie) • Chalk-Talk to hear and see a solution • Additional Self-Check Questions to Assess Understanding

  6. ExampleFind this example at http://www.uwlax.edu/mathematics/praxis/los/prelim_results.htm

  7. Lesson Study Development Model Team structure: • exchange ideas about student difficulties and/or misconceptions regarding the content of the learning object; • discuss multiple solution strategies of the mathematical task and multiple representations of the key mathematical concepts embedded in the learning object; and • provide constructive feedback during the design process.

  8. Pedagogical Content Knowledge Teaching requires a structured knowledge network of specific subject matter facts, skills, and concepts that are intimately connected. (Schulman 1986, p. 9)

  9. Mathematics Knowledge for Teaching (MKT) In the context of teaching math, PCK requires: • a conceptual understanding of the core knowledge; • fluency in carrying out procedures; • strategic competencies in planning effective instruction; • adaptive reasoning in justifying and explaining one’s instructional practices; and • a productive disposition towards mathematics, teaching, learning, and the improvement of practices. (Hill & Ball 2004, NRC 2001)

  10. Technological Pedagogical Content Knowledge (TPCK) Educators must not only be proficient in subject matter and pedagogical knowledge, but they must also develop an “overarching conception of their subject matter with respect to technology and what it means to teach with technology”. (Niess 2005, p. 510).

  11. Technological Pedagogical Content Knowledge (TPCK) Effective teaching with technology requires “understanding the mutually reinforcing relationships between all three elements taken together to develop appropriate, context specific strategies and representations”. (Mishra & Koehler 2006, p. 27).

  12. Participants • 21 preservice elementary and secondary teachers voluntarily elected to participate in the extra-curricular PRAXIS Wisconsin Project. • Preservice teachers were recruited by six faculty mentors from three UW-System campuses.

  13. Research Questions • What are the perceived benefits relating to the development of participants’ technology, pedagogy, and content knowledge through designing digital learning objects for mathematics? • How does this professional development program depict the nature of preservice teachers’ Technological Pedagogical Content Knowledge for teaching mathematics? • In which ways do the specific components of the digital learning objects reflect preservice teachers’ Mathematics Knowledge for Teaching?

  14. Instrument • Participants completed a Project Exit-Survey. • The open-endedness of the survey was designed to allow the researchers to obtain a snapshot of the participants TPCK at the end of the project.

  15. Methods • Two qualitative methodologies were used: • Typology of the Responses: A classification scheme was developed to describe general themes regarding the benefits of participation. (Patton 2002) • Content Analysis: TPCK was used as an analytic framework. (Mishra &Koehler 2006)

  16. Question 1 Perceived Benefits

  17. TPCK as an Analytic Framework Sixty exit-survey responses were independently categorized into three overlapping categories: • Content Knowledge – A response that was mathematics content specific; • Pedagogical Knowledge – A response that emphasized the general methods of teaching and learning; and • Technological Knowledge – A response encompassing the use of technology.

  18. Content Knowledge Pedagogical Knowledge Technological Knowledge TPCK as an Analytic Framework

  19. TPCK as an Analytic Framework Intersecting categories were exclusively recorded as: (4) Pedagogical Content Knowledge; (5) Technological Content Knowledge; (6) Technological Pedagogical Knowledge; and (7) Technological, Pedagogical, Content Knowledge.

  20. TPCK as an Analytic Framework Content Knowledge Pedagogical Knowledge Technological Knowledge

  21. TPCK as an Analytic Framework Technological Content Knowledge would provided evidence of an understanding of how technology influence mathematical knowledge including, but not limited to, the varied representations of a concept or procedure through technology. Pedagogical Content Knowledge would reflect the interplay between mathematics subject knowledge and the ways to represent and explain this knowledge to others. All responses were categorized using one of the seven exclusive descriptors to describe the level of TPCK knowledge.

  22. Example of Coding The project was a great experience, both in terms of the valuable information I gained about the process of problem solving as well as the ability to teach problem solving procedures with the use of technology. I feel the portion of the project which benefited me the most, in preparing to create learning objects, was exploring the several approaches students take when solving a problem and being able to represent this with technology.

  23. Question 2 TPCK

  24. Question 2 TPCK * Number of Categorized Responses = 60

  25. Question 3 Evidence of MKT

  26. Question 3 Evidence of MKT

  27. Conclusions A 3-D TPCK DevelopmentalFramework

  28. Conclusions A 3-D TPCK Developmental Framework

  29. Closing Remarks from Preservice TeachersListen to these at http://www.uwlax.edu/faculty/kosiak/projects/index.html Maren Kelly Kristin

  30. Connecting Preservice Teachers’ Knowledge of Mathematics, Pedagogy, and Technology through Learning Object Design Jennifer Kosiak Becky LeDocq kosiak.jenn@uwlax.eduledocq.rebe@uwlax.edu http://www.uwlax.edu/faculty/kosiak/ For more information on the PRAXIS Wisconsin Project please visit http://www.uwlax.edu/mathematics/praxis/los/assets/project_intro.htm

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