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Merging Undergrad Research & Math Teacher Education Conference - Addressing Challenges and Promoting Growth

This conference explores the challenges in mathematics education and presents a program that combines undergraduate research and teacher education to address these challenges. The focus is on developing content knowledge and pedagogical skills and meeting the demand for graduate programs in mathematics education.

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Merging Undergrad Research & Math Teacher Education Conference - Addressing Challenges and Promoting Growth

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  1. Merging the Worlds of Undergraduate Research and Mathematics Teacher Education Randall E. Groth, Ph.D. NCTM 2015 Regional Conference Atlantic City, NJ

  2. Two Challenges to Mathematics Education • Developing prospective mathematics teachers’ content knowledge and pedagogical skill against a backdrop of “learning rules and practicing procedures” (Stigler & Hiebert, 2009) in many U.S. classrooms. • Growing graduate programs in mathematics education to meet university-level demand (Reys, Reys, & Estapa, 2013).

  3. Addressing the Challenges Simultaneously • One trend: Increasing use of performance assessments that require teacher candidates to assess the impact of their instruction on students’ learning (e.g., American Association of Colleges for Teacher Education & Stanford Center for Assessment, Learning, and Equity, 2015). • Another, complementary, trend: commitments from funding agencies such as the National Science Foundation (NSF) to support undergraduate research and the growing number of publication and presentation venues devoted to undergraduate research (Council on Undergraduate Research, 2015).

  4. Birth of a Program: Bringing the Two Trends Together • NSF issued a “Dear Colleague” letter requesting proposals for undergraduate research sites focusing on mathematics and science education (Ferrini-Mundy, 2011). • Our program: Preparing Aspiring Teachers to Hypothesize Ways to Assist Young Students (PATHWAYS)

  5. Mentoring Structure

  6. Theoretical Premises • Growth as a teacher and as an undergraduate researcher both depend on a reflective cycle of hypothesis formulation and testing (Dewey, 1933; Schön, 1983). • Process reflection is “an active form of reflection that extends and links together separate reflective incidents into cohesive mental continuums as ideas through action” (Ricks, 2011, p. 252).

  7. PATHWAYS Process Reflection Undergraduate Research Cycle Ricks (2011) illustrated the application of process reflection to teacher education with Japanese Lesson Study

  8. Key Readings for Undergraduates • Research compliance: CITI modules • Designing instruction: Learning progressions for assigned content area (Confrey et al., 2012) • Collecting data: Interviewing and video recording (Ellemor-Collins & Wright, 2008) • Analyzing data: Five strands of mathematical proficiency (Kilpatrick, Swafford, & Findell, 2001)

  9. Year 1 Projects • Group 1: Fourth-graders’ learning of multiplication • Group 2: Fourth-graders’ learning of fractions • Group 3: Fifth graders’ learning of decimals • Group 4: Sixth graders’ learning of statistics (we will zoom in on Group 4 as an example next).

  10. Shonice Emily Joseph DuJuan

  11. Students’ beginning conceptions of “typical value” • Emily and Joseph described the typical birth weight in terms of the tallest “stack” on their graphs. • Shoniceopted for the largest value in the data set. • DuJuandid not examine the data but instead used only his personal background knowledge: “When a dog is born – when a dog is a puppy – it weighs 5 pounds.”

  12. Joseph and Shonice both focused on the closeness of each statistic to the main cluster of data. For example, for Theatre A, Joseph chose the median, saying, “All of these numbers are closer to 90.” Emily looked for the statistic that was closest to the maximum value in each data set. DuJuan did not take the lists of data into consideration at all, but instead chose the median because it “orders the data from least to greatest.” Source: 1996 NAEP

  13. Weeks 2-3: Building Aggregate Displays • Developing ideas for children: • Using dotplots as aggregate data displays • Analyzing qualitative features of aggregate displays (talk about places where the data were “squished together”; location of tallest stack) • Developing ideas for undergraduates: • Producing a dotplot is normally not an end in itself in statistics. • Multiple ways to describe typical – draw students’ attention toward clusters.

  14. Weeks 4-5: Expanding Strategies for Typical Value • Developing ideas for children: • Attending to clusters of data rather than just the tallest stack • Developing ideas for undergraduates: • Need to purposefully design contexts to generate data sets that produce features related to targeted student learning objectives.

  15. Weeks 6-8: Choosing among Mean, Median, and Mode • Developing ideas for children: • Existence of multiple measures for describing what is “typical” in a data set. • Some measures are more reasonable than others in certain contexts. • Developing ideas for undergraduates: • Formal measures are not necessarily better than informal analysis of data. • Need to move beyond procedural objectives for statistical measures.

  16. Post-Assessment Responses • Uniform use of aggregate displays • Consistent examination of relevant features to describe what is “typical” (modal stacks, main clusters) rather than purely context knowledge, maximum values, or procedural justifications.

  17. Summary: Intersecting Learning Pathways

  18. References American Association of Colleges for Teacher Education & Stanford Center for Assessment, Learning, and Equity. (2015). edTPA. Retrieved from http://edtpa.aacte.org/ Beijaard, D. (1995). Teachers’ prior experiences and actual perceptions of professional identity. Teachers and Teaching: Theory and Practice, 1(2), 281-294. doi: 10.1080/1354060950010209 Chong, S., Low, E.L., & Goh, K.C. (2011). Emerging professional identity of pre-service teachers. Australian Journal of Teacher Education, 36(8), 50-64. Clift, R.T., & Brady, P. (2005). Research on methods courses and field experiences. In M. Cochran-Smith & K.M. Zeichner (Eds.), Studying teacher education: The report of the AERA Panel on Research and Teacher Education (pp. 309-424). Mahwah, NJ: Erlbaum. Council on Undergraduate Research. (2015). Student events. Retrieved from http://www.cur.org/conferences_and_events/student_events/ Confrey, J., Maloney, A.P., Nguyen, K.H., Mojica, G., & Myers, M. (2012). TurnOnCCMath.net: Learning trajectories for the K-8 Common Core math standards. Retrieved from https://www.turnonccmath.net

  19. References Dewey, J. (1933). How we think: A restatement of the relation of reflective thinking to the educative process. Boston: Heath. Ellemor-Collins, D.L., & Wright, R.J. (2008). Assessing student thinking about arithmetic: Videotaped interviews. Teaching Children Mathematics, 15, 106-111. Ferrini-Mundy, J. (2011). Dear colleague letter: Opportunity for Research Experiences for Undergraduates (REU) sites focusing on STEM education research. Arlington, VA: National Science Foundation. Retrieved from http://www.nsf.gov/pubs/2011/nsf11076/nsf11076.jsp Forbes, C.T., & Davis, E.A. (2008). The development of pre-service elementary teachers’ curricular role identity for science teaching. Science Education, 92, 909-940. doi: 10.1002/sce.20265 Kilpatrick, J., Swafford, J. and Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Pillen, M., Beijaard, D., & den Brok, P. (2013). Tensions in beginning teachers’ professional identity development, accompanying feelings and coping strategies. European Journal of Education, 36(3), 240-260. doi: 10.1080/02619768.2012.696192 Reys, Robert, Barbara Reys, and Anne Estapa. 2013. "An Update on Jobs for Doctorates in Mathematics Education at Institutions of Higher Education in the United States." Notices of the AMS 60: 470-473.

  20. References Ricks, T.E. (2011). Process reflection during Japanese Lesson Study experiences by prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 14, 251-267. doi: 10.1007/s10857-010-9155-7 Sammons, P., Day, C., Kington, A., Gu, Q., Stobart, G., & Smees, R. (2007). Exploring variations in teachers’ work, lives and their effects on pupils: Key findings and implications from a longitudinal mixed-methods study. British Educational Research Journal, 33, 681-701. doi: 10.1080/01411920701582264 Schön, D.A. (1983). The reflective practitioner: How professionals think in action. New York: Basic Books. Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14-22. doi: 10.3102/0013189X034004014 Stigler, James W., and James Hiebert. 2009. The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom. New York: Simon and Schuster.

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