Research into the Development of Mathematical Ideas
Graduate School, New Brunswick
Rutgers University,
College Avenue Campus
Spring 2005
16:300:563
Mondays, 4:50 to 7:30
GSE, Room 211
Instructor: Arthur B.
Powell
Associate Professor, Department of
Urban Education, Newark Campus
973.353.3530 (office), abpowell@andromeda.rutgers.edu
Associate Director, Robert B.
Davis Institute for Learning, GSE
eCompanion online course supplement: http://rutgersonline.net
The purpose of this course is to enable you to develop further your understanding and experience in conducting video-facilitated fieldstudy in mathematics education. Fieldstudy is a research genre in the social sciences that is also known, among other labels, as naturalistic research, ethnography, or qualitative study. A specific arena in which to hone your capacity to do ethnography will be investigating the development of students' mathematical ideas and reasoning. This is a line of research within the Robert B. Davis Institute for Learning (RBDIL) of the Graduate School of Education, Rutgers University, that enjoys international recognition. Over the years, through many fieldstudies, an ethnographic methodology for the use of videodata has evolved within the RBDIL. It has been documented and is receiving increased attention among researchers in mathematics education. You will study documents—dissertations and journal articles—of video-facilitated research that have emerged from the work of the RBDIL. You will also read and summarize documents that report on video-facilitated fieldstudy conducted by investigators from other institutions.
Besides studying the ethnographic work of investigators in mathematics education, you will engage two of three components of fieldstudy. In general, ethnographic investigations contain three non-linear, overlapping, and interweaving components: (1) gathering or collecting and assembling data, (2) focusing or asking questions about these data, and (3) analyzing or developing and presenting evidence-based interpretations of these data. Despite having to gather data before asking questions and analyzing them, it is also the case that researchers unavoidably pose questions about and interpret their data as they gather them. In this course, you will study and implement the second and third components of conducting fieldstudy.
1. Successful completion
of Human Subjects Certification Program of the Institutional Review Board for
the Protection of Human Subjects in Research. This can be done either online
http://orsp.rutgers.edu/HSCPLetter.asp
or equivalently attending both parts of the Certification Film in its
entirety. The Film consists of two
videotapes, each approximately an hour and 15 minutes in length. The first videotape, "Basics of Human
Subjects Research", provides a general overview of the regulations and ethical
considerations that must be addressed for such research. The second videotape, "Advanced
Topics", covers regulatory and ethical guidance for vulnerable research
populations, such as pregnant women and fetuses, children, and prisoners.
2. Complete
all readings and associated assignments.
3. Initiate
and contribute to threaded discussions at the course's eCompanion site <http://rutgersonline.net>.
4. Read,
summarize, and report on three doctoral dissertations that involve the use of
video-facilitated fieldstudy. The
specific format of the dissertation summary and report of method will be
detailed in class. The report will
focus on methodological issues related to the investigator's use of
videorecordings for gathering, focusing, and analyzing data. Dissertations are available at the
following Web site: http://wwwlib.umi.com/dissertations/. You will also have access to many dissertations
through our course Web site: http://rutgersonline.net.
5. Code
and analyze video-portfolio data.
You will have access to video-portfolio data from a current,
longitudinal project, "Research on Informal Mathematical Learning" (IML) of the
RBDIL, which is supported by a research grant from the National Science
Foundation (REC-0309062).
6. Write
a paper detailing your focusing and analyzing processes and the results of your
analysis of video-portfolio data.
Required Readings
Charmaz, K., & Mitchell, R. G. (2001).
Grounded theory in ethnography. In P. Atkinson, A. Coffey & S. Delamont
(Eds.), Handbook of ethnography (pp.
160-174). London: Sage.
Lofland, J., & Lofland, L. H. (1995). Analyzing
social situations: A guide to qualitative observation and analysis (Third ed.). Belmont, CA: Wadsworth. (Chapter 6:
Thinking Topics; and Chapter 7: Asking Questions)
Davis, R. B., Maher, C., & Martino, A.
(1992). Using videotapes to study the construction of mathematical knowledge of
individual children working in groups. Journal of Science, Education, and
Technology, 1(3), 177-189.
Maxwell, J. A. (2005). Qualitative
research design: An interactive approach
(2nd ed.). Thousand Oaks: Sage. (Chapter 6: Methods: What will you actually
do?)
Pirie, S. (1998). Working toward a design
for qualitative research. In A. R. Teppo (Ed.), Qualitative research methods
in mathematics education (Monograph Number
9, pp. 79-97). Reston, VA: National Council of Teachers of Mathematics.
Powell, A. B., Francisco, J. M., &
Maher, C. A. (2003). An analytical model for studying the development of
mathematical ideas and reasoning using videotape data. Journal of
Mathematical Behavior, 22(4), 405-435.
Stohl, H., & Tarr, J. E. (2002). Developing
notions of inference with probability simulation tools. Journal of
Mathematical Behavior, 21(3), 319-337.
Bibliography of Video-Facilitated Dissertation
From Rutgers University
Bellisio, C. W. (1999). A study of elementary
students' ability to work with algebraic notation and variables. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Bulgar, S. (2002). Through a teacher's
lens: Children's constructions of division of fractions. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Francisco, J. M. (2004). Students'
reflection on mathematical learning: Results from a longitudinal study. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Glass, B. H. (2001). Mathematical
problem solving and justification with community college students. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Kiczek, R. D. (2000). Tracing the
development of probabilistic thinking: Profiles from a longitudinal study. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Martino, A. M. (1992). Elementary
students' construction of mathematical knowledge: Analysis by profile. Unpublished doctoral dissertation, Rutgers, the
State University of New Jersey, New Brunswick.
Muter, E. M. (1999). The development of
student ideas in combinatorics and proof: A six-year study. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Powell, A. B. (2003). "So let's
prove it!" Emergent and elaborated mathematical ideas and reasoning in the
discourse and inscriptions of learners engaged in a combinatorial task. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Steencken, E. P. (2001). Tracing the
growth of understanding of fraction ideas: A fourth grade case study. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Tarlow, L. D. (2004). Tracing students'
development of ideas in combinatorics and proof. Unpublished doctoral dissertation, Rutgers, The State University of
New Jersey, New Brunswick.
Uptegrove, E. B. (2005). To symbols from meaning:
Students' long-term investigations in counting. Unpublished doctoral dissertation, Rutgers, The State University of
New Jersey, New Brunswick.
Walter, J. G. (2004). Tracing
mathematical inquiry: High school students mathematizing a shell. Unpublished doctoral dissertation, Rutgers, The
State University of New Jersey, New Brunswick.
Warner, L. B. (2005). Behaviors that indicate
mathematical flexible thought. Unpublished
doctoral dissertation, Rutgers, The State University of New Jersey, New
Brunswick.
From other universities
Choppin, J. M. (2004). How teachers' discourse
practices affect student engagement in the context of mathematics reform. Unpublished doctoral dissertation, The University of
Wisconsin, Madison.
Doyle, J. A. (2003). Student voice: The
influence of complex instruction on fifth grade students' mathematical problem
solving performance. Unpublished doctoral
dissertation, Boston College, Boston.
Goos, M. (1999). Metacognition in context: A study
of metacognitive activity in a classroom community of mathematical inquiry. Unpublished doctoral thesis, University of
Queensland.
Herbst, P. G. (1998). What works as
proof in the mathematics class. Unpublished
doctoral dissertation, University of Georgia.
Horn, I. S. (2002). Learning on the job:
Mathematics teachers' professional development in the contexts of high school
reform. Unpublished doctoral dissertation,
University of California, Berkeley.
John, A. S. (2001). Generalizing in interaction:
Students making and using mathematical generalizations in design projects. Unpublished doctoral dissertation, University of
California-Berkeley, Berkeley.
Larsen, S. P. (2004). Supporting the
guided reinvention of the concepts of group and isomorphism: A developmental
research project. Unpublished doctoral
dissertation, Arizona State University.
Magidson, S. (2002). Teaching, research, and
instructional design: Bridging communities in mathematics education. Unpublished doctoral dissertation, University of
California, Berkeley.
Martin, L. C. (1999). The nature of the
folding back phenomenon within the Pirie-Kieren theory for the growth of
mathematical understanding and the associated implications for teachers and
learners of mathematics. Unpublished
doctoral dissertation, University of Oxford, Oxford, England.
Raman, M. J. (2002). Proof and
justification in collegiate calculus.
Unpublished doctoral dissertation, University of California, Berkeley.
Seymour, J. R. (2004). Tracing the evolution of
pedagogical content knowledge as interanimated discourses. Unpublished doctoral dissertation, The University of
Wisconsin-Madison, Madison.
Sherin, M. G. (1996). The nature and dynamics of
teachers' content knowledge. Unpublished
doctoral dissertation, University of California, Berkeley.
Smith, S. P. (1999). Children, learning theory,
and mathematics: An analysis of the role of language and representations in
children's mathematical reasoning.
Unpublished doctoral dissertation, Michigan State University, East Lansing.
Comparing Units of Analyses & Issues of
Reform-Oriented Teaching and Equity
Boaler, J. (1998). Open and closed mathematics:
Student experiences and understandings. Journal for Research in Mathematics
Education, 29(1), 41-62.
Boaler, J. (2002). Learning from teaching: Exploring
the relationship between reform curriculum and equity. Journal for Research
in Mathematics Education, 33(4), 239-258.
Lubienski, S. T. (2000). Problem solving as a means
toward mathematics for all: An exploratory look through the class lens. Journal
for Research in Mathematics Education, 31(4),
454-482.
Articles Involving Video-Facilitated Research in
Mathematics Education
Goos, M. (2004). Learning mathematics in a classroom
community of inquiry. Journal for Research in Mathematics Education, 35(4), 258-291.
Jacobson, C., & Lehrer, R. (2000). Teacher
appropriation and student learning of geometry through design. Journal for
Research in Mathematics Education, 31(1),
71-88.
Simon, M. A., Tzur, R., Heinz, K., Kinzel, M., & Schwan
Smith, M. (2000). Characterizing a perspective underlying the practice of
mathematics teachers in transition. Journal for Research in Mathematics
Education, 31(5), 579-601.
Stohl, H., & Tarr, J. E. (2002). Developing
notions of inference with probability simulation tools. Journal of
Mathematical Behavior, 21(3), 319-337.
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