Inquiry-Based Learning in College Mathematics

This comprehensive study investigated student outcomes of inquiry-based learning (IBL) in undergraduate mathematics and linked these outcomes to students’ and instructors’ experiences of IBL. Based at four research universities that have been developing IBL courses, the mixed-methods study examined outcomes including skills, cognitive gains, attitudes and beliefs, and education and career paths. The study also sought to understand how these outcomes come about, using a combination of surveys, classroom observations, interviews, tests, and student academic records. Finally, we examined the recruitment and participation of IBL instructors, their professional development, and the institutionalization of these approaches in their departments.

  • Laursen, S. (2020, June 11). What does the research say? ÌýLearning and teaching in inquiry-based undergraduate mathematics. A summary for educators. Video:ÌýYoutube.Ìý(23 minute video presentation)Ìý[video:http://www.youtube.com/watch?v=m_HK6b3RGOc]
  • Laursen, S. L., Hassi, M.-L., & Hough, S. (2016).Ìý .ÌýÌýInternational Journal of Mathematical Education in Science and Technology,Ìý47(2), 256-275. Published online 25 July 2015. doi: 10.1080/0020739X.2015.1068390 [Abstract]
  • Hassi, M.-L., & Laursen, S. L. (2015). .ÌýJournal of Transformative Education 13(4), 316-340.ÌýPublished online before printÌýMay 24, 2015, doi:Ìý10.1177/1541344615587111 [Abstract]Ìý
  • Laursen, S. L., Hassi, M.-L., Kogan, M., & Weston, T. J. (2014). . ÌýJournal of Research in Mathematics Education,Ìý45(4), 406-418. [Abstract]
  • Laursen, S. L. (2013).ÌýÌýFrom innovation to implementation:ÌýMulti-institution pedagogical reform in undergraduate mathematics.Ìý In D. King, B. Loch, L. Rylands (Eds.),Ìý, Kiama, New South Wales, Australia, 24-29 November 2013. ÌýSydney:Ìý University of Western Sydney, School of Computing, Engineering and Mathematics, on behalf of the International Delta Steering Committee.
  • Kogan, M., & Laursen, S. L. (2014).Ìý .ÌýÌýInnovative Higher Education,Ìý39(3), 183-199 (published online August 13, 2013).ÌýDOI 10.1007/s10755-013-9269-9. [Open access]
  • Laursen, S., & Hassi, M.L. (2012). Outcomes of inquiry-based learning for pre-service teachers: A multi-site study. In (Eds.) S. Brown, S. Larsen, K. Marrongelle, and M. Oehrtman,ÌýÌýpp. 88-94, Portland, Oregon.
  • Hassi, M.-L., Kogan, M., & Laursen, S. L. (2011). Student outcomes from inquiry-based college mathematics courses: Benefits of IBL for students from under-served groups. In (Eds.) S. Brown, S. Larsen, K. Marrongelle, and M. Oehrtman,ÌýÌýpp. 73-77, Portland, Oregon.
  • Laursen, S., Hassi, M.-L., & Hunter, A.-B. (2011). Navigating the straits: Critical instructional decisions in inquiry-based college mathematics classes. In (Eds.) S. Brown, S. Larsen, K. Marrongelle, and M. Oehrtman,ÌýÌýpp. 101-104, Portland, Oregon.
  • Hassi, M.-L. (2009).ÌýEmpowering undergraduate students through mathematical thinking and learning. In G. Fitzsimons (Ed.),ÌýA Declaration of Numeracy: Empowering Adults through Mathematics Education, Proceedings of the 15th International Conference of Adults Learning Mathematics (ALM), 53-69.Ìý Lancaster, PA:Ìý DEStech Publications.
  • Hassi M.-L., & Laursen, S. (2009).ÌýÌýIn S.L. Swars, D.W. Stinson, & S. Lemons-Smith (eds.),ÌýProceedings of the 31st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA), pp.113-121. Atlanta, GA: Georgia State University.

Laursen, S. (2015, June). From innovation to implementation: Multi-institution pedagogical reform in undergraduate mathematics. A summary of research results. Â鶹ӰԺ, CO: Â鶹ӰԺ, Ethnography & Evaluation Research. [A two-page digest of key findings]

Laursen, S., Hassi, M. L., Kogan, M., Hunter, A. B., & Weston, T. (2011).ÌýEvaluation of the IBL Mathematics Project: Student and Instructor Outcomes of Inquiry-Based Learning in College Mathematics. (Report to the Educational Advancement Foundation and the IBL Mathematics Centers) Â鶹ӰԺ, CO: Â鶹ӰԺ, Ethnography & Evaluation Research, Assessment & Evaluation Center for Inquiry-Based Learning in Mathematics.

Study methodsÌý-Ìýall appendices

  • Appendix A1Ìý- Overview of Research Methods for the Mixed-Methods Study

  • Appendix A2Ìý- Study Methods: Classroom Observation

  • Appendix A3Ìý- Study Methods: Student Surveys

  • Appendix A4Ìý- Study Methods: Linking Classroom Observation and Student Survey Data

  • Appendix A5Ìý- Study Methods: Mathematics Tests

  • Appendix A6Ìý- Study Methods: Student Academic Records

  • Appendix A7Ìý- Study Methods: Student and Instructor Interviews

Assessment & Evaluation Center for Inquiry-Based Learning in Mathematics (2009). (Reports to the IBL Mathematics Project) Â鶹ӰԺ, CO: Â鶹ӰԺ, Ethnography & Evaluation Research.

  • Inquiry Brief 1: Validation of mathematical proofs. First findings from a proof test.
  • Inquiry Brief 2: Mathematical knowledge for teaching. First findings from MKT measures of students’ cognitive gains.
  • Inquiry Brief 3: Differences between IBL and non-IBL classroom practices. First findings from observations of classroom activity, leadership, and questioning behaviors.
  • Inquiry Brief 4: Variations in classroom practice among IBL courses. First findings from observations of classroom activity, leadership, and questioning behaviors.

In related work, we are evaluating professional development workshops that support college mathematics instructors in using inquiry-based learning in their own courses. See our Professional Development page for our most recent reports.

We are currently studying how people, structures, and ideas are important to the past development, current growth, and future sustainability of an educational community that promotes inquiry-based learning in college mathematics.

Some of this work reveals opportunities and challenges for the IBL Math community in defining itself. To learn more from the research team and from IBL community members, visit the IBL Community page.

The study of the IBL Math community is supported by the National Science Foundation under award 1347669. Any opinions, findings, conclusions or recommendations expressed in these reports are those of the researchers, and do not represent the official views, opinions, or policy of the National Science Foundation.

Interested in inquiry-based learning in math? We recommend the following resources:

Assessment

The SALG-M is a form of the Student Assessment of their Learning Gains (SALG) survey instrument that is customized for undergraduate mathematics courses. We have used this survey to examine students' learning gains across a range of cognitive, affective, and social domains (e.g. Hassi & Laursen, 2009) and are making it available to instructors and researchers. To examine or use the SALG-M, please downloadÌýthese instructionsÌýand visitÌýÌýto set up and customize a copy for your own use. To review the questions, viewÌýthis copy of the instrument.

Ways to Learn Â鶹ӰԺ Inquiry Teaching in College Mathematics

  • TheÌýÌý(AIBL) supports mathematics instructors in applying inquiry-based learning within their own classrooms and building a practitioner community. AIBL offers many instructor resourcesÌýand sometimes hostsÌýintensive summer workshops and shorter, traveling workshops for college instructors.
  • AIBL director Stan Yoshinobu writes about inquiry instruction at the IBLÌýBlog and curates collections of blog posts about core topics.
  • TheÌýÌýhas gatheredÌýpractitioners of inquiry-based learning in mathematics annually.
  • The hosts regional communities of inquiry teachers... check to see if there is a group in your part of North America!
  • The Mathematical Association of America has aÌýÌý(SIGMAA). .
    • .

Materials for Inquiry-Based College Mathematics Courses

  • TheÌýÌýpublishes course notes that instructors can use to design an inquiry-based math course.
  • Ìýoffers a variety of resources to support mathematical inquiry for non-STEM majors.
  • The Mathematical Association of American publishes texts for and about inquiry-based learning in mathematics.
    • , Katz & Starbird
    • , Marshall, Odell & Starbird
    • , Coppin, Mahavier, May & Parker
  • The IBL Mathematics Centers have shared some materials from courses they have developed.
  • Inquiry-oriented curriculum materials for and Ìýinclude student activities and instructor support.Ìý