Undergraduate Research in Mathematics Education: Using Qualitative Data About Children’s Learning to Make Decisions About Teaching

Undergraduate research is increasingly prevalent in many fields of study, but it is not yet widespread in mathematics education. We argue that expanding undergraduate research opportunities in mathematics education would be beneficial to the field. Such opportunities can be impactful as either extracurricular or course-embedded experiences. To help readers envision directions for undergraduate research experiences in mathematics education with prospective teachers, we describe a model built on a design-based research paradigm. The model engages pairs of prospective teachers in working with faculty mentors to design instructional sequences and test the extent to which they support children’s learning. Undergraduates learn about the nature of systematic mathematics education research and how careful analyses of classroom data can guide practice. Mentors gain opportunities to pursue their personal research interests while guiding undergraduate pairs. We explain how implementing the core cycle of the model, whether on a small or large scale, can help teachers make instructional decisions that are based on rich, qualitative classroom data.

Footnotes

This article is based on the work supported by the National Science Foundation under Grant Nos. DRL-1356001 and DUE-1658968. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the author and do not necessarily reflect the views of the National Science Foundation.

Contributor Notes

Randall E. Groth, Jennifer A. Bergner, Jathan W. Austin, Claudia R. Burgess, Veera Holdai, Salisbury University, 1101 Camden Ave., Salisbury, MD 21801

(Corresponding author is Groth regroth@salisbury.edu)
Mathematics Teacher Educator
  • 1.

    Alexander, B., Foertsch, J., Daffinrud, S., & Tapia, R. (2000). The “spend a summer with a scientist” (SAS) program at Rice University: A study of program outcomes and essential elements 1991-1997. CUR Quarterly, 20(3), 127133.

    • Search Google Scholar
    • Export Citation
  • 2.

    Amador, J. M., Carter, I., & Hudson, R. A. (2016). Analyzing preservice mathematics teachers’ professional noticing. Action in Teacher Education, 38(4), 371383.

    • Search Google Scholar
    • Export Citation
  • 3.

    Bakker, A., & van Eerde, D. (2015). An introduction to design-based research with an example from statistics education. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Doing qualitative research: Methodology and methods in mathematics education (pp. 429466). Springer.

    • Search Google Scholar
    • Export Citation
  • 4.

    Banilower, E. R., Smith, P. S., Weiss, I. R., Malzahn, K. A., Campbell, K. M., & Weis, A. M. (2013). Report of the 2012 National Survey of Science and Mathematics Education. Horizon Research, Inc.

    • Search Google Scholar
    • Export Citation
  • 5.

    Bauer, K. W., & Bennett, J. S. (2003). Alumni perceptions used to assess undergraduate research experience. Journal of Higher Education, 74(2), 210230.

    • Search Google Scholar
    • Export Citation
  • 6.

    Beaulieu, R. J. (2013). Action research: Trends and variations. Canadian Journal of Action Research, 14(3), 2939.

  • 7.

    Boaler, J. (2016). Mathematical mindsets. Jossey-Bass.

  • 8.

    Cai, J., Morris, A., Hohensee, C., Hwang, S., Robinson, V., & Hiebert, J. (2018). Reconceptualizing the roles of researchers and teachers to bring research closer to teaching. Journal for Research in Mathematics Education, 49(5), 514520.

    • Search Google Scholar
    • Export Citation
  • 9.

    Campbell, A., & Skoog, G. (2004). Preparing undergraduate women for science careers. Journal of College Science Teaching, 33(5), 2426.

    • Search Google Scholar
    • Export Citation
  • 10.

    Chamberlain, L., & Mendoza, S. (2017). Design thinking as research pedagogy for undergraduates: Project-based learning with impact. Council on Undergraduate Research Quarterly, 37(4), 1822.

    • Search Google Scholar
    • Export Citation
  • 11.

    Corbin, A., & Strauss, J. (2008). Basics of qualitative research (3rd ed.). Sage Publications.

  • 12.

    Council on Undergraduate Research. (2014). Expanding the conversation: 2012-2014. Washington, DC: Author. https://www.cur.org/assets/1/7/triennialreport672015.pdf

    • Search Google Scholar
    • Export Citation
  • 13.

    Council on Undergraduate Research. (2018a). History. Washington, DC: Author. https://www.cur.org/who/organization/history/

  • 14.

    Council on Undergraduate Research. (2018b). Integrating undergraduate research into teacher education programs and related fields institute. Washington, DC: Author. https://www.cur.org/what/events/institutes/education/

    • Search Google Scholar
    • Export Citation
  • 15.

    DeCuir-Gunby, J. T., Marshall, P. L., & McCulloch, A. W. (2011). Developing and using a codebook for the analysis of interview data: An example from a professional development project. Field Methods, 23(2), 136155.

    • Search Google Scholar
    • Export Citation
  • 16.

    DeVore, S., & Munk, D. (2015). Undergraduate research in teacher education: A rationale for broader engagement. CUR Quarterly, 35(4), 1217.

    • Search Google Scholar
    • Export Citation
  • 17.

    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. https://www.nsf.gov/pubs/2011/nsf11076/nsf11076.jsp

    • Search Google Scholar
    • Export Citation
  • 18.

    Foertsch, J., Alexander, B., & Penberthy, D. (2000). Summer research opportunity programs (SROPs) for minority undergraduates: A longitudinal study of program outcomes 1986-1996. CUR Quarterly, 20(3), 114119.

    • Search Google Scholar
    • Export Citation
  • 19.

    Gafney, L. (2005). The role of the research mentor/teacher: Student and faculty views. Journal of College Science Teaching, 34(4), 5257.

    • Search Google Scholar
    • Export Citation
  • 20.

    Groth, R. E. (2017). Classroom data analysis with the Five Strands of Mathematical Proficiency. The Clearing House: A Journal of Educational Strategies, Ideas, and Issues, 90(3), 103109. https://doi.org/10.1080/00098655.2017.1301155

    • Search Google Scholar
    • Export Citation
  • 21.

    Groth, R. E., & McFadden, J. (2016). Identity development during undergraduate research in mathematics education. Mathematics Education, 11(2), 357375. https://www.iejme.com/download/identity-development-during-undergraduate-research-in-mathematics-education.pdf

    • Search Google Scholar
    • Export Citation
  • 22.

    Herbel-Eisenmann, B. A., & Breyfogle, M. L. (2005). Questioning our patterns of questioning. Teaching Children Mathematics, 10, 484489.

    • Search Google Scholar
    • Export Citation
  • 23.

    Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Heinemann.

    • Search Google Scholar
    • Export Citation
  • 24.

    Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372400.

    • Search Google Scholar
    • Export Citation
  • 25.

    Hoffer, W. W. (2016). Developing literate mathematicians: A guide for integrating language and literacy instruction into secondary mathematics. National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 26.

    Hoffman, J., & Manak, J. (2016, September). Developing teacher candidates’ data literacy through undergraduate research . 2016 Fall Council for the Accreditation of Educator Preparation (CAEP) Conference, Washington, DC.

    • Export Citation
  • 27.

    Hunter, A. B., Laursen, S. L., & Seymour, E. (2006). Becoming a scientist: The role of undergraduate research in students’ cognitive, personal, and professional development. Science Education, 91(1), 3674.

    • Search Google Scholar
    • Export Citation
  • 28.

    Ishiyama, J. (2002). Does early participation in undergraduate research benefit social science and humanities students? College Student Journal, 36(3), 380386.

    • Search Google Scholar
    • Export Citation
  • 29.

    Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169202.

    • Search Google Scholar
    • Export Citation
  • 30.

    Jacobs, V. R., & Spangler, D. A. (2017). Research on core practices in K-12 mathematics teaching. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 766792). Reston, VA: National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 31.

    Kardash, C. M. (2000). Evaluation of an undergraduate research experience: Perceptions of undergraduate interns and their faculty mentors. Journal of Educational Psychology, 92(1), 191201.

    • Search Google Scholar
    • Export Citation
  • 32.

    Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.

    • Search Google Scholar
    • Export Citation
  • 33.

    Kuh, G. D. (2008). High-impact educational practices: What they are, who has access to them, and why they matter. Association of American Colleges and Universities.

    • Search Google Scholar
    • Export Citation
  • 34.

    Lesseig, K., Casey, S., Monson, D., Krupa, E. E., & Huey, M. (2016). Developing an interview module to support secondary PST’s noticing of student thinking. Mathematics Teacher Educator, 5(1), 2946. https://www.nctm.org/Publications/Mathematics-Teacher-Educator/2016/Vol5/Issue1/Developing-an-Interview-Module-to-Support-Secondary-PST_s-Noticing-of-Student-Thinking/

    • Search Google Scholar
    • Export Citation
  • 35.

    Lester, F. K., & Wiliam, D. (2002). On the purpose of mathematics education research: Making productive contributions to policy and practice. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 489506). Erlbaum.

    • Search Google Scholar
    • Export Citation
  • 36.

    Lewis, J. (2016). Learning to lead, leading to learn: How facilitators learn to lead lesson study. ZDM Mathematics Education, 48(4), 527540. https://doi.org/10.1007/s11858-015-0753-9

    • Search Google Scholar
    • Export Citation
  • 37.

    Lopatto, D. (2004). Survey of undergraduate research experiences (SURE): First findings. Cell Biology Education, 3(4), 270277.

  • 38.

    Lopatto, D. (2008). Exploring the benefits of undergraduate research: The SURE survey. In R. Taraban & R. L. Blanton (Eds.), Creating effective undergraduate research programs in science (pp. 112132). Teachers College Press.

    • Search Google Scholar
    • Export Citation
  • 39.

    Lopatto, D. (2009). Science in solution: The impact of undergraduate research on student learning. Tucson, AZ: Research Corporation for Science Advancement.

    • Search Google Scholar
    • Export Citation
  • 40.

    Lopatto, D. (2010). Undergraduate research as a high-impact student experience. Peer Review, 12(2), 27. https://www.aacu.org/publications-research/periodicals/undergraduate-research-high-impact-student-experience

    • Search Google Scholar
    • Export Citation
  • 41.

    Manak, J. A., & Young, G. (2014). Incorporating undergraduate research into teacher education: Preparing thoughtful teachers through inquiry-based learning. CUR Quarterly, 35(2), 3538.

    • Search Google Scholar
    • Export Citation
  • 42.

    Mandinach, E. B., & Gummer, E. S. (2016). Every teacher should succeed with data literacy. Phi Delta Kappan, 97(8), 4346.

  • 43.

    Moyer, P. S., & Milewicz, E. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5(4), 293315.

    • Search Google Scholar
    • Export Citation
  • 44.

    Nazaire, D. W., & Usher, B. M. (2015). Leveraging federal work-study to support undergraduate research. CUR Quarterly, 36(2), 917.

  • 45.

    Osborn, J. M., & Karukstis, K. K. (2009). The benefits of undergraduate research, scholarship, and creative activity. In M. Boyd & J. Wesemann (Eds.), Broadening participation in undergraduate research: Fostering excellence and enhancing the impact (pp. 4153). Council on Undergraduate Research.

    • Search Google Scholar
    • Export Citation
  • 46.

    Ramirez, M., McNicholas, J., Gilbert, B., Saez, J., & Siniawski, M. (2015). Creative funding strategies for undergraduate research at a primarily undergraduate liberal arts institution. Council on Undergraduate Research Quarterly, 36(2), 58.

    • Search Google Scholar
    • Export Citation
  • 47.

    Reys, R., Reys, B., & Estapa, A. (2013). An update on jobs for doctorates in mathematics education at institutions of higher education in the United States. Notices of the American Mathematical Society, 60, 470473.

    • Search Google Scholar
    • Export Citation
  • 48.

    Ricks, T. E. (2011). Process reflection during Japanese lesson study experiences by prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 14(4), 251267. https://doi.org/10.1007/s10857-010-9155-7

    • Search Google Scholar
    • Export Citation
  • 49.

    Russell, S. H., Hancock, M. P., & McCullough, J. (2007). Benefits of undergraduate research experiences. Science, 316(5824), 548549.

    • Search Google Scholar
    • Export Citation
  • 50.

    Schuster, M. (2018). Undergraduate research at two-year community colleges. Journal of Political Science Education, 14(2), 276280. https://doi.org/10.1080/15512169.2017.1411273

    • Search Google Scholar
    • Export Citation
  • 51.

    Seymour, E., Hunter, A., Laursen, S., & DeAntoni, T. (2003). Establishing the benefits of research experiences for undergraduates: Findings from a three-year study. Science Education, 88(4), 493534.

    • Search Google Scholar
    • Export Citation
  • 52.

    Shanahan, J. O., Liu, X., Manak, J., Miller, S. M., Tan, J., & Yu, C. W. (2015). Research-informed practice, practice-informed research: The integral role of undergraduate research in professional disciplines. CUR Quarterly, 35(4), 616.

    • Search Google Scholar
    • Export Citation
  • 53.

    Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. Routledge.

    • Search Google Scholar
    • Export Citation
  • 54.

    Silver, E. A. (2003). Border crossing: Relating research and practice in mathematics education. Journal for Research in Mathematics Education, 34, 182184.

    • Search Google Scholar
    • Export Citation
  • 55.

    Smit, J., & van Eerde, H. A. A. (2011). A teacher’s learning process in dual design research: Learning to scaffold language in a multilingual mathematics classroom. ZDM – The International Journal on Mathematics Education, 43(6-7), 889900. https://doi.org/10.1007/s11858-011-0350-5

    • Search Google Scholar
    • Export Citation
  • 56.

    Stanford, J. S., Rocheleau, S. E., Smith, K. P. W., & Mohan, J. (2017). Early undergraduate research experiences lead to similar learning gains for STEM and non-STEM undergraduates. Studies in Higher Education, 42(1), 115129. https://doi.org/10.1080/03075079.2015.1035248

    • Search Google Scholar
    • Export Citation
  • 57.

    Staub, N. L., Blumer, L. S., Beck, C. W., Delesalle, V. A., Griffin, G. D., Merritt, R. B., … Mader, C. M. (2016). Course-based science research promotes learning in diverse students at diverse institutions. Council on Undergraduate Research Quarterly, 37(2), 3646.

    • Search Google Scholar
    • Export Citation
  • 58.

    Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313340.

    • Search Google Scholar
    • Export Citation
  • 59.

    Tarr, J. E. (2002). The confounding effects of “50-50 chance” in making conditional probability judgments. Focus on Learning Problems in Mathematics, 24(4), 3553.

    • Search Google Scholar
    • Export Citation
  • 60.

    Watson, J. M. (2005). The probabilistic reasoning of middle school students. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 145168). Springer. https://doi.org/10.1007/0-387-24530-8_7

    • Search Google Scholar
    • Export Citation
  • 61.

    Wentzel, T. J. (1997). What is undergraduate research?. CUR Quarterly, 17, 163.

  • 62.

    Weston, T. J., & Laursen, S. L. (2015). The undergraduate research student self-assessment (URSSA): Validation for use in program evaluation. CBE–Life Sciences Education, 14, 110.

    • Search Google Scholar
    • Export Citation
  • 63.

    Yesiclay, Y. (2000). Research project in statistics: Implications of a case study for the undergraduate statistics curriculum. Journal of Statistics Education, 8(2), 114. ww2.amstat.org/publications/jse/secure/v8n2/yesilcay.cfm

    • Search Google Scholar
    • Export Citation

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