Doctoral Courses in Mathematics Education:

Math 609 Research Methods in Mathematics Education Fall 2011

Time: 4.40 -7:30 pm
Place: Math 108
Instructor: Prof. Bharath Sriraman
Office: 301
Phone & E-mail: 243-6714; sriramanb@mso.umt.edu

Course Description
The course will address the nature of research in mathematics education, starting from philosophical/ epistemological perspectives. It will introduce and explore a range of research paradigms with associated qualitative and quantitative approaches and methods.

Key approaches and methods will be discussed in detail alongside examples of their use from real research studies. There will be a practical dimension in which approaches and techniques in data collection and analysis, including use of relevant software, will be discussed. Research ethics, validation of results and presentation of findings will be important considerations.
Participants will be expected to develop expertise in reading research that uses methods beyond those used in their own research. Participants will be encouraged to read centrally indicated key texts, to select for themselves from the wider list and to find their own articles by using established search techniques.

Text: Reading Lists Appended

Administrative Policies:

Important Dates:
Monday, Sept 5 Labor Day Holiday
Monday, Sept 19, 5.00 pm Last Day to Add/Drop by CyberBear.Also last day to select AUDIT option. After this date, a drop results in W on transcript and no refund is given.
Tuesday, Nov 1 Last Day to Drop by Paper Form. Transcript will show WP or WF. $10 fee.
Friday, Nov 11 Veterans Day, no classes
Wednesday, Nov 23 Student travel day, no classes
November 24-25 Thanksgiving Holiday, no classes
Friday, Dec 2, Last Day to withdraw from semester
December 10-11 Study Days

Academic misconduct is subject to an academic penalty by the course instructor and/or a disciplinary sanction by the University. Academic misconduct is defined as all forms of academic dishonesty and the Student Conduct Code. The Code is available for review online at http://life.umt.edu/vpsa/student_conduct.php
In particular, Student Conduct Code Section IV.a.5 identifies the following violations: Submitting false information: Knowingly submitting false, altered, or invented information, data, quotations, citations, or documentation in connection with an academic exercise

Grading Distribution:
Discussion leader (2) 30%
Article Critique(1) 20%
Research Assignment 1 25%
Research Assignment 2 25%

Grading Scale: 90-100 A ; 80-89.9 B ; 70-79.9 C ; 60-69.9 D ; Below 60 F

Reading Assignments:
August 29

  • None, Course Orientation

    • September 5
  • None, Labor Day Holiday

    • September 12
  • An array of errors. (2011, September 10).The Economist, 91-92.
  • Bauck Jensen, C. Preparing a study of mathematics in vocational education. (Unpublished Essay for MA607).Høgskolen i Sør-Trøndelag.
  • Burton, L. (2002).Methodology and Methods in Mathematics Education Research: Where is “The Why”? In Goodchild, S. & English, L. (Eds.) Researching Mathematics Classrooms: A critical examination of methodology (pp. 1-10). London: Praeger.

    • September 19
  • Amit, M. (2010).Commentary 1 on Re-conceptualizing Mathematics Education as a Design Science. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 147-149). New York: Springer.
  • Boote, D. N. (2010).Commentary 3 on Re-conceptualizing Mathematics Education as a Design Science. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 159-168). New York: Springer.
  • Goldin, G. A. (1997).Observing Mathematical Problem Solving through Task-based Interviews. In Teppo, A. (Ed.) Qualitative Research Methods in Mathematics Education, Monograph Number 9 (pp. 40-62). Reston, VA: National Council of Teacher of Mathematics.
  • Lee, K. H. &Sriraman, B. (2011). Conjecturing via reconceived classical analogy.Educational Studies in Mathematics, 76, 123-140.
  • Lesh, R., &Sriraman, B. (2010).Re-conceptualizing Mathematics Education as a Design Science. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 123-146). New York: Springer.
  • Michelsen, C. (2010). Commentary 2 on Re-conceptualizing Mathematics Education as a Design Science. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 151-157). New York: Springer.
  • Yuan, W. and Sriraman, B. (2011).An exploratory study of relationships between students’ creativity and mathematical problem-posing abilities: Comparing Chinese and U.S. Students. In Lee, K. H. &Sriraman, B. (Eds.) The Elements of Creativity and Giftedness in Mathematics (pp. 5-28). Boston: Sense Publishers.

    • September 26
  • Pimm, D. (2010). Commentary on Knowing More Than We Can Tell. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 613-618). New York: Springer.
  • Polanyi, M. (1966).Tacit Knowing.The Tacit Dimension. New York: Doubleday & Company, Inc.
  • Roscoe, M &Sriraman, B. (2011).A quantitative study of the effects of informal mathematics activities on the beliefs of preservice elementary school teachers.ZDM Mathematics Education, 43, 601-615. Doi: 10.1007/s11858-011-0332-7
  • Sinclair, N. (2010). Knowing More Than We Can Tell. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 595-612). New York: Springer.

    • October 3
  • Bulut, S., Gür, B. S., &Sriraman, B. (2010).Commentary 2 on Feminist Pedagogy and Mathematics. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 455-466). New York: Springer.
  • Jacobs, J. E. (2010). Feminist Pedagogy and Mathematics. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 435-446). New York: Springer.
  • Leder, G. C. (2010).Commentary 1 on Feminist Pedagogy and Mathematics. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 447-454). New York: Springer.
  • Pálsdóttir, G. &Sriraman, B. (2010).Commentary 3 on Feminist Pedagogy and Mathematics. In B. Sriraman& L. English (Eds.), Theories of Mathematics Education: Seeking New Frontiers (pp. 467-475). New York: Springer.
  • Sriraman, B. (2004). Gifted Ninth Graders’ Notions of Proof: Investigating Parallels in Approaches of Mathematically Gifted Students and Professional Mathematicians. Journal for the Education of the Gifted, 27(4), 267-292.
  • Steinthorsdottir, O. B. &Sriraman, B. (2009).Icelandic 5th-Grade Girls’ Developmental Trajectories in Proportional Reasoning.Mathematics Education Research Journal, 21(1), 6-30.

    • October 17
  • Gutstein, E. (2007). Connecting Community, Critical, and Classical Knowledge in Teaching Mathematics for Social Justice.The Montana Mathematics Enthusiast, Monograph 1, The Montana Council of Teachers of Mathematics, 109-118.
  • Lesh, R., Hoover, M, Hole, B., Kelly, A. E., & Post, T. (2000).Principles for Developing Through-Revealing Activities for Students and Teachers. In Kelly, A. E. &Lesh, R. A. (Eds.) Handbook of Research Design in Mathematics and Science Education (pp. 591-645). Mahwah, NJ: Lawrence Erlbaum Associates.

    • October 24
  • Borko, H., Frykholm, J., Pittman, M., Eiteljorg, E., Nelson, M, Jacobs, J., Koellner-Clark, K., & Schneider, C. (2005).Preparing Teachers to Foster Algebraic Thinking.ZDM Mathematics Education, 37(1), 43-52.
  • Diefes-Dux, H. A., Hjalmarson, M. A., Miller, T. K., &Lesh, R. (2008).Model-Eliciting Activities for Engineering Education. In Zawojewski, J. S., Diefes-Dux, H. A., & Bowman, K. J. (Eds.) Model and Modeling in Engineering Education, Designing Experiences for All Students (pp. 17-35). Rotterdam: Sense publishers.
  • Zawojewski, J. S., Hjalmarson, M. A., Bowman, K. J., &Lesh, R., (2008).A Modeling Perspective on Learning and Teaching in Engineering Education. In Zawojewski, J. S., Diefes-Dux, H. A., & Bowman, K. J. (Eds.) Model and Modeling in Engineering Education, Designing Experiences for All Students (pp. 1-15). Rotterdam: Sense publishers.

    • October 31
  • Hiedemann, B., & Jones, S. M. (2010). Learning Statistics at the Farmers Market? A Comparison of Academic Service Learning and Case Studies in an Introductory Statistics Course.Journal of Statistics Education, 18(3), 1-21.
  • Pais, A. (2011).Criticisms and contradictions of ethnomathematics.Educational Studies in Mathematics, 76, 209-230.Doi: 10.1007/s10649-010-9289-7
  • Vilela, D. S. (2010). Discussing a philosophical background for the ethnomathematical program. Educational Studies in Mathematics, 75, 354-358.

    • November 14
  • Sriraman, Bharath (2004). Reflective abstraction, uniframes and the formulation of generalizations.Journal of Mathematical Behavior, 23, 205-222.doi: 10.1016/j.jmathb.2004.03.005
  • Lesh, R.&Sriraman, B.(2009). Models-modeling perspectives and the philosophy of pragmatism. Manuscript submitted to ZDM, The International Journal on Mathematics Education, 7-28.

    • November 21
  • Haverhals, N., & Roscoe, R. (2010). The history of mathematics as a pedagogical tool: Teaching the integral of the secant via Mercator’s projection. The Montana Mathematics Enthusiast, 7(2&3), 339-368.
  • McGinn, M. K., &Boote, D. N. (2003).A First-Person Perspective on Problem Solving in a History of Mathematics Course.Mathematical Thinking and Learning, 5(1), 71-107.
  • Sriraman, B. (2005). Letter to the editor.Mathematical Thinking and Learning, 7(4), 345-348.

    • November 28
  • Peter, G. Indebted. Unpublished manuscript.

    • December 5
  • Berg, C. V., Fuglestad, A. B.,Goodchild, S., Sriraman, B (2011). Extrapolation and Expansion: Characteristics of Change Occurring in Mathematics Teaching Development Projects.Unpublished manuscript. UM technical report #25,2011 available at http://www.umt.edu/math/reports/sriraman/2011_abstract_25.html
  • Wood, D. (1988).How Children Think and Learn, pp. 1-36. Oxford: Basil Blackwell.

    • December 12
  • English, L. D., Jones, G. A., Bussi, M. B., Lesh, R. A., Tirosh, D., &Sriraman, B. Moving Forward in International Mathematics Education Research.Pre-print of chapter to appear in English, L. (Ed.) Handbook of International Research in Mathematics Education (2nd edition), Taylor and Francis.

    • Bibliography
    This list is being updated continually throughout the course. If there is something youhave found valuable which is not on the list please let me know to add it.We do not try to keep this list short. In any study at doctoral level you have to use a rangeof sources and make your own choices as to where to focus. There is no intention herethat you will read all of everything in the list!
    We will begin with 2 chapters that lay some theoretical foundations for mathematics education before looking at specific methodologies. Readings will be selected from books in bold among other.

    List starts here: Part of this List is also borrowed from co-numbered course at The University of Agder, Norway in which I serve as the Expert External Evaluator/ Sensor, appointed on a yearly basis by faculty, to evaluate papers in my areas of expertise, namely Learning Theories of Mathematics (Math 602); and Methodologies of Mathematics Education (Math 607) at University of Agder taught by Professor Simon Goodchild

    American Psychological Association (APA) (2009) Publication Manual of the American Psychological Association (6th ed.). Washington, DC.APA.

    Bassey, M. (1999) Case Study Research in Educational Settings.Buckingham: Open University Press

    Bond, T. G. & Fox, C. M. (2001) Applying the Rasch model: fundamentalmeasurement in the human sciences. Mahwah, NJ. Lawrence Erlbaum Associates.

    Bryman, A. (2008) Social Research Methods (3rd ed.). Oxford: OxfordUniversity Press.

    Carr, W. and Kemmis, S. (1986) Becoming Critical: Education,Knowledge and Action Research. London: Falmer Press

    Carspecken, P. F. (1996) Critical Ethnography in Educational Research: ATheoretical and Practical Guide. London: Routledge

    Clough, P. (2002) Narratives and Fictions in Educational Research.Buckingham: Open University Press

    Cohen, L. And Manion, L. (1980) Research Methods in Education.London: Routledge. (There should be a new edition of this.)

    Cooper, B. and Dunne, M(2000) Assessing Children’s MathematicalKnowledge: Social class, sex and problem solving. Buckingham:Open University Press.

    Cooper, P. and McIntyre, D. (1996) Effective teaching and learning:teachers’ and students’ perspectives. London, Open University Press

    Davis, R. B., Maher, C. A. and Noddings, N. (1990) Constructivist Views on the Learning and Teaching of Mathematics. Journal for Researchin Mathematics Education, Monograph Number 4. Reston, Va: National Council of Teachers of Mathematics.

    Denzin, N. K. & Lincoln, Y. S. (Eds.) (2005)The Sage handbook of qualitative research (3rd ed.) London, Sage

    Donaldson, M. (1978) Children's Minds. London: Fontana.(Good read. Good introduction to and critique of Piaget's stagetheory.)

    Elliott, J. (1991) Action Research for Educational Change. Buckingham: Open University Press

    Ely, M., Vinz, R., Downing, M. and Anzul, M. (1997) On WritingQualitative Research. London: Falmer Press

    Ernest, P. (1991) The Philosophy of Mathematics Education. London: Falmer Press

    Field, A. (2005) Discovering statistics using SPSS (2nd edition) London,Sage.

    Glaser, B. G. And Strauss, A. L. (1967) The Discovery of GroundedTheory: Strategies for Qualitative Research. New York: Aldine deGruyter

    Goodchild, S. and English, L. (2002) Researching MathematicsClassrooms: A critical examination of methodology. London: Praeger [Especially Chapter 1]

    Gorard, S. (2001) Quantitative Methods in Educational Research. London:Continuum

    Green, S. B. and Salkind, N. J. (2005) Using SPSS for windows andMacintosh: analyzing and understanding data 4th Edition. Upper Saddle River N.J.: Pearson Prentice Hall.

    Hammersley, M. (1990) Classroom Ethnography. Buckingham: Open University Press

    Hardy, M. &Bryman, A. (Eds.) (2004) Handbook of data analysis. London,Sage.

    Hollingsworth, S. (1997) (Ed.) International Action Research: ACasebook for Educational Reform. London: Falmer Press

    Hostetler, K. (2005). What is “good” educational research?Educational Researcher, 34(6), 16-21.

    Kelly, A. E. &Lesh, R. A. (Eds) (2000) Handbook of research design in mathematics and science education.Mahwah NJ Lawrence Erlbaum Associates.

    Maddy, P. (1990) Realism in Mathematics. Oxford: Clarendon Press.

    May, T. (1997) Social Research: Issues, Methods and Process.Buckingham: Open University Press

    Miles, M. B. and Huberman, A. M. (1994) Qualitative Data Analysis: An expanded sourcebook. London: Sage

    Punch, K. F. (1998) Introduction to Social Research. London: Sage.

    Seale, C., Gobo, G., Gubrium, J. F. & Silverman, D. (Eds.) (2004)Qualitative research practice. London, Sage.

    Silverman,D. (2000) Doing Qualitative Research - A Practical Handbook.London: Saga Publications

    Sriraman, B., & English, L. (Eds) (2010).Theories of Mathematics Education- Seeking New Frontiers.Springer Science & Business.Available Free at Springer Link [through UM- Mansfield Library]

    Stake, R. E. (1995) The Art of Case Study Research. London: Sage

    Strauss, A and Corbin, J. (1998) Basics of qualitative research.Techniquesand procedures for developing grounded theory. London, Sage.

    Teppo, A. (1998) (Ed.) Qualitative Research Methods in Mathematics Education.Journal for Research in Mathematics Education, Monograph Number 9. Reston, Va: National Council of Teacher of Mathematics.

    Wellington, J. (2000) Educational Research: Contemporary Issues and Practical Approaches. London: Continuum.

    Wood, D. (1988) How Children Think and Learn. Oxford: BasilBlackwell. (Excellent, easy, introduction to Piaget, Bruner and Vygotsky) (There's probably a new edition.)

    Yin, R. K. (1994) Case Study Research.Design and Methods.London:Sage.

    Description of Assignments

    Discussion Leader: The selected readings for the week will need to be synthesized into four pages of themes and issues, and a list of questions for discussion. This will be provided to all the participants in the class.
    This should include

    Iteration 1:
    About 700 words outlining the ‘methodology’ of the research: explain why the “researcher” has taken a particular focus, a rationale for the design of the study, what types of methods were used and why – what alternatives might have been used (and why they are rejected).

    Iteration 2
    About 700 words outlining the paradigm within which the researcher(s) are working – how the paradigm is consistent in terms of ontology, epistemology and methodology. What are the consequences of the paradigm regarding the type of ‘knowledge’ or ‘knowing’ that might be the outcome of the research and what the paradigm suggests about the warrants that might be sought for the knowledge gains claimed.
    For Iteration 2, a data set will be provided.

    Article Critique:

    Students will be given one article to critique. They will take on the role of a reviewer in this task.
    The critique should include elements of Iteration 1 and 2, and in addition include:

    About 700 words explaining the details of the methods used.
    About 700 words explaining the process of analysis and attempts to ensure validity and reliability – and trustworthiness of interpretations.

    Also include a discussion about potential threats to trustworthiness.


    Research Assignment 1

    Conduct a task based “problem solving” session with a group based on a research question involving student understanding of proof

    Research Assignment 2
    Conduct a task based “problem solving” interview with a peer based on a research question involving problem solving heuristics/strategies

    Exact parameters on howto write up these two assignments will be given later in the semester.
    The write up will include

    about 700 words critically examining the ethical issues of the research proposed and what measure must be taken to protect informants (and potential users and abusers of the research).

    about 700 words – an introduction to the research as a whole, and a summary/conclusion that addresses the issue of whether the research is ‘good’ research – in the sense of Hostetler 2005.

    AN INDIAN COGNITIVE TASK FROM A BOOK ENTITLED THINK WITHOUT INK

    A Task
    A man and his will
    A man paranoid of his untimely death prepared a will immediately after his marriage. He willed his wife ¼th of his property, and the remaining 3/4th to his daughter, should one be born, but in case of a son being born, ½ of the property was willed to the wife and the remaining to his son. Shortly after the man’s death, twins were born, a boy and a girl. How should the property be divided in order to carry out the arithmetical relationships prescribed in the will?