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Merging the Worlds of Undergraduate Research and Mathematics Teacher

Education

Merging the Worlds of Undergraduate Research and Mathematics Teacher

Education

Randall E. Groth, Ph.D.

NCTM 2015 Regional Conference

Atlantic City, NJ

Randall E. Groth, Ph.D.

NCTM 2015 Regional Conference

Atlantic City, NJ

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Two Challenges to Mathematics Education

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).

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).

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Addressing the Challenges Simultaneously

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).

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).

Birth of a Program: Bringing the Two Trends Together

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)

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)

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Mentoring StructureMentoring Structure

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Theoretical PremisesTheoretical 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).

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).

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PATHWAYS Process Reflection Undergraduate Research Cycle

PATHWAYS Process Reflection Undergraduate Research Cycle

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Ricks (2011) illustrated the application of process reflection to teacher education with Japanese Lesson Study

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Key Readings for Undergraduates

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)

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)

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Year 1 ProjectsYear 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).

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).

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Joseph

DuJuan

Shonice

Emily

Students’ beginning conceptions of “typical value”

Students’ beginning conceptions of “typical value”

Emily and Joseph described the typical birth weight in terms of the tallest “stack” on their graphs.

Shonice opted for the largest value in the data set.

DuJuan did 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.”

Emily and Joseph described the typical birth weight in terms of the tallest “stack” on their graphs.

Shonice opted for the largest value in the data set.

DuJuan did 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.”

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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

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Weeks 2-3: Building Aggregate Displays

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.

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.

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Weeks 4-5: Expanding Strategies for Typical Value

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.

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.

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Weeks 6-8: Choosing among Mean, Median, and Mode

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.

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.

Post-Assessment Responses 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.

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.

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Summary: Intersecting Learning Pathways

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ReferencesReferencesAmerican 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

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ReferencesReferencesDewey, 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.

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ReferencesReferencesRicks, 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.