Skip to main content
SpringerLink
Log in

“I use IBL in this course” may say more about an instructor’s beliefs than about their teaching

  • Published:
International Journal of Research in Undergraduate Mathematics Education Aims and scope Submit manuscript

Abstract

Inquiry-Based learning (IBL) is a fairly well-known term in the United States (US) describing a range of student-centered or active pedagogical approaches in mathematics. However, the ‘big tent’ definitions of IBL mean that there is much variation in IBL users’ instructional practices, variation which we set out to codify. Cluster analysis of self-reported data from a survey of postsecondary calculus instructors across the US reveals three instructional profiles among self-declared users of IBL: (a) heavy users of group work; (b) users of a variety of mixed approaches; and (c) heavy users of didactic lecture. The instructional profile of this third group is indistinguishable from that of calculus instructors who report never having heard of IBL. We further investigate the relationship of these instructional profiles to certain beliefs about teaching and learning. All groups agree that inquiry supports learning; the groups who spend a minority of time in didactic lecture disagree with statements that there are benefits to lecturing. Implications for research and adoption of IBL are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. That 30% of our participants declare that they use IBL suggests increased usage of the approach in the last five years. Though not directly comparable, university mathematics departments reported IBL was in use in 3% of their Calculus 1 courses (Apkarian, N., & Kirin, D. 2017).

References

  • Academy of Inquiry Based Learning (2021). Supporting instructors, empowering students, transforming mathematics learning. http://www.inquirybasedlearning.org

  • Apkarian, N., & Kirin, D. (2017). Progress through calculus: Census survey technical report. Mathematical Association of America. http://bit.ly/PtC_Reporting

  • Apkarian, N., Smith, W. M., Vroom, K., Voigt, M., Gehrtz, J., PtC Project Team, & SEMINAL Project Team. (2019). X-PIPS-M Survey Suite. Retrieved from https://www.maa.org/sites/default/files/XPIPSM%20Summary%20Document.pdf

  • Aragón, O. R., Eddy, S. L., & Graham, M. J. (2018). Faculty beliefs about intelligence are related to the adoption of active-learning practices. CBE - Life Sciences Education, 17(ar47), 1–9. https://doi.org/10.1187/cbe.17-05-0084

    Article  Google Scholar 

  • Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM-The International Journal on Mathematics Education, 45(6), 797–810. https://doi.org/10.1007/s11858-013-0506-6

    Article  Google Scholar 

  • Borgen, F. H., & Barnett, D. C. (1987). Applying cluster analysis in counseling psychology research. Journal of Counseling Psychology, 34(4), 456–468. https://doi.org/10.1037/0022-0167.34.4.456

    Article  Google Scholar 

  • CBMS (2016). Active learning in post-secondary mathematics education. Conference Board of the Mathematical Sciences. Available: http://www.cbmsweb.org/Statements/Active_Learning_Statement.pdf

  • Chan, K. W., & Elliott, R. G. (2004). Relational analysis of personal epistemology and conceptions about teaching and learning. Teaching and Teacher Education, 20(8), 817–831. https://doi.org/10.1016/j.tate.2004.09.002

    Article  Google Scholar 

  • Dweck, C. S., Chiu, C., & Hong, Y. (1995). Implicit theories and their role in judgements and reactions: A world from two perspectives. Psychological Inquiry, 6(4), 267–285. https://doi.org/10.1207/s15327965pli0604_1

    Article  Google Scholar 

  • Ebert-May, D., Derting, T. L., Hodder, J., Momsen, J. L., Long, T. M., & Jardeleza, S. E. (2011). What we say is not what we do: Effective evaluation of faculty professional development programs. BioScience, 61(7), 550–558. https://doi.org/10.1525/bio.2011.61.7.9

    Article  Google Scholar 

  • Engeln, K., Euler, M., & Maass, K. (2013). Inquiry-based learning in mathematics and science: A comparative baseline study of teachers’ beliefs and practices across 12 European countries. Zdm Mathematics Education, 45, 823–836. https://doi.org/10.1007/s11858-013-0507-5

    Article  Google Scholar 

  • Ernst, D. C., Hodge, A., & Yoshinobu, S. (2017). What Is Inquiry-Based Learning? Notices of the American Mathematical Society, 570–574. https://doi.org/10.1090/noti1536

  • Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., & Jordt, H. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410–8415. https://doi.org/10.1073/pnas.1319030111

  • Gibbons, R. E., Villafañe, S. M., Stains, M., Murphy, K. L., & Raker, J. R. (2018). Beliefs about learning and enacted instructional practices: An investigation in postsecondary chemistry education. Journal of Research in Science Teaching, 55(8), 1111–1133. https://doi.org/10.1002/tea.21444

  • Haberler, Z., Laursen, S. L., & Hayward, C. N. (2018). What’s in a Name? Framing Struggles of a Mathematics Education Reform Community. International Journal of Research in Undergraduate Mathematics Education, 4(3), 415–441. https://doi.org/10.1007/s40753-018-0079-4

    Article  Google Scholar 

  • Hayenga, A. O., & Corpus, J. H. (2010). Profiles of intrinsic and extrinsic motivations: A person-centered approach to motivation and achievement in middle school. Motivation and Emotion, 34(4), 371–383. https://doi.org/10.1007/s11031-010-9181-x

    Article  Google Scholar 

  • Hayward, C. N., Kogan, M., & Laursen, S. L. (2016). Facilitating instructor adoption of inquiry-based learning in college mathematics. International Journal of Research in Undergraduate Mathematics Education, 2(1), 59–82. https://doi.org/10.1007/s40753-015-0021-y

    Article  Google Scholar 

  • Henderson, C. & Dancy, M. (2009) The Impact of Physics Education Research on the Teaching of Introductory Quantitative Physics in the United States, Physical Review Special Topics: Physics Education Research, 5(2), 020107. (Auxiliary Appendix to accompany article.) http://dx.doi.org/10.1103/PhysRevSTPER.5.020107

  • Hoyles, C. (1992). Mathematics teaching and mathematics teachers: A meta-case study. For the Learning of Mathematics, 12(3), 32–44

    Google Scholar 

  • Johnson, E. (2019). Chapter 6. Undergraduate mathematics instruction: Not as bad as you’d think? S. Laursen & B. Ruedi (Eds.), Levers for change: An assessment of progress on changing STEM instruction. American Association for the Advancement of Science. Washington, DC.

  • Johnson, E., Keller, R., & Fukawa-Connelly, T. (2018). Results from a Survey of Abstract Algebra Instructors across the United States: Understanding the Choice to (Not) Lecture. International Journal of Research in Undergraduate Mathematics Education, 4(2), 254–285. https://doi.org/10.1007/s40753-017-0058-1

  • Johnson, E., Keller, R., Peterson, V., & Fukawa-Connelly, T. (2019). Individual and situational factors related to undergraduate mathematics instruction. International Journal of STEM Education, 6(1), 23. https://doi.org/10.1186/s40594-019-0175-2

  • Kogan, M., & Laursen, S. L. (2014). Assessing long-term effects of inquiry-based learning: a case study from college mathematics. Innovative Higher Education, 39(3), 183–199. https://doi.org/10.1007/s10755-013-9269-9

    Article  Google Scholar 

  • Krosnick, J. A. (1999). Survey research. Annual Review of Psychology, 50, 537–567. https://doi.org/10.1146/annurev.psych.50.1.537

    Article  Google Scholar 

  • Laursen, S. L., Hassi, M. L., Kogan, M., & Weston, T. J. (2014). Benefits for women and men of inquiry based learning in college mathematics: a multi-institution study. Journal for Research in Mathematics Education, 45(4), 406–418. https://doi.org/10.5951/jresematheduc.45.4.0406

    Article  Google Scholar 

  • Laursen, S. L., & Rasmussen, C. (2019). I on the Prize: Inquiry Approaches in Undergraduate Mathematics. International Journal of Research in Undergraduate Mathematics Education, 5(1), 129–146. https://doi.org/10.1007/s40753-019-00085-6

    Article  Google Scholar 

  • Leatham, K. R. (2006). Viewing mathematics teachers’ beliefs as sensible systems. Journal of Mathematics Teacher Education, 9(1), 91–102. https://doi.org/10.1007/s10857-006-9006-8

    Article  Google Scholar 

  • Leatham, K. R. (2007). Pre-service secondary mathematics teachers’ beliefs about the nature of technology in the classroom. Canadian Journal of Math Science & Technology Education, 7(2–3), 183–207. https://doi.org/10.1080/14926150709556726

    Article  Google Scholar 

  • Landrum, R. E., Viskupic, K., Shadle, S. E., & Bullock, D. (2017). Assessing the STEM landscape: The current instructional climate survey and the evidence-based instructional practices adoption scale. International Journal of STEM Education, 4(1), https://doi.org/10.1186/s40594-017-0092-1

  • Lombardi, D., & Shipley, T. F. (2021). The Curious Construct of Active Learning. Psychological Science in the Public Interest, 22(1), 8–43. https://doi.org/10.1177/1529100620973974

    Article  Google Scholar 

  • Lund, T. J., & Stains, M. (2015). The importance of context: An exploration of factors influencing the adoption of student-centered teaching among chemistry, biology, and physics faculty. International Journal of STEM Education, 2(1), 13. https://doi.org/10.1186/s40594-015-0026-8

  • Meyers, S. A., Lansu, M. L., Hundal, J. S., Lekkos, S. K., & Prieto, L. R. (2007). Preparing new psychology instructors to teach undergraduates: Developing Confidence and Competence. Journal of Faculty Development, 21(1), 45

    Google Scholar 

  • Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. Second handbook of research on mathematics teaching and learning, 1, 257–315

    Google Scholar 

  • Rasmussen, C., & Kwon, O. N. (2007). An inquiry-oriented approach to undergraduate mathematics. The Journal of Mathematical Behavior, 26(3), 189–194. https://doi.org/10.1016/j.jmathb.2007.10.001

    Article  Google Scholar 

  • Rasmussen, C., Marrongelle, K., Kwon, O. N., & Hodge, A. (2017). Four Goals for Instructors Using Inquiry-Based Learning. Notices of the American Mathematical Society, 64(11), 1308–1311. https://doi.org/10.1090/noti1597

    Article  Google Scholar 

  • Rocard, M. (2007). Science education NOW: A renewed pedagogy for the future of Europe.European Commission. https://ec.europa.eu/research/science-society/document_library/pdf_06/report-rocard-on-science-education_en.pdf

  • Saxe, K., & Braddy, L. (2015). A common vision for undergraduate mathematical science programs in 2025. Washington, DC: Mathematical Association of America

    Google Scholar 

  • Scanlon, E., Roman, B. Z., Ibadlit, E., & Chini, J. J. (2019). A method for analyzing instructors’ purposeful modifications to research-based instructional strategies. International Journal of STEM Education, 6(1), 1–18. https://doi.org/10.1186/s40594-019-0167-2

    Article  Google Scholar 

  • Shultz, M. C. (2022). The Rationality of Undergraduate Mathematics Instructors: The Choice to Use Inquiry-Oriented Instructional Practices. Journal for Research in Mathematics Education, 53(3), 227–246

    Google Scholar 

  • Smith, M. K., Vinson, E. L., Smith, J. A., Lewin, J. D., & Stetzer, M. R. (2014). A campus-wide study of STEM courses: New perspectives on teaching practices and perceptions. CBE-Life Sciences Education, 13(4), 624–635. https://doi.org/10.1187/cbe.14-06-0108

    Article  Google Scholar 

  • Speer, N. M. (2008). Connecting beliefs and practices: A fine-grained analysis of a college mathematics teacher’s collections of beliefs and their relationship to his instructional practices. Cognition and Instruction, 26(2), 218–267. https://doi.org/10.1080/07370000801980944

    Article  Google Scholar 

  • Stains, M., & Vickrey, T. (2017). Fidelity of Implementation: An Overlooked Yet Critical Construct to Establish Effectiveness of Evidence-Based Instructional Practices. CBE—Life Sciences Education, 16(1), rm1. https://doi.org/10.1187/cbe.16-03-0113

  • Sztajn, P. (2003). Adapting Reform Ideas in Different Mathematics Classrooms: Beliefs Beyond Mathematics. Journal of Mathematics Teacher Education, 6(1), 53–75. https://doi.org/10.1023/A:1022171531285

    Article  Google Scholar 

  • Tollerud, T. (1990). The perceived self-efficacy of teaching skills of advanced doctoral students and graduates from counselor education programs (Doctoral dissertation). University of Iowa

  • Walczyk, J. J., & Ramsey, L. L. (2003). Use of learner-centered instruction in college science and mathematics classrooms. Journal of Research in Science Teaching: The Official Journal of the National Association for Research in Science Teaching, 40(6), 566–584. https://doi.org/10.1002/tea.10098

    Article  Google Scholar 

  • Walter, E. M., Henderson, C. R., Beach, A. L., & Williams, C. T. (2016). Introducing the Postsecondary Instructional Practices Survey (PIPS): A concise, interdisciplinary, and easy-to-score survey. CBE—Life Sciences Education, 15(4), ar53. https://doi.org/10.1187/cbe.15-09-0193

  • Walter, E. M., Beach, A. L., Henderson, C., Williams, C. T., & Ceballos-Madrigal, I. (2021). Understanding Conditions for Teaching Innovation in Postsecondary Education: Development and Validation of the Survey of Climate for Instructional Improvement (SCII). International Journal of Technology in Education, 4(2), 166-199.

  • Wang, C. K. J., & Biddle, S. J. (2001). Young people’s motivational profiles in physical activity: A cluster analysis. Journal of Sport & Exercise Psychology, 23, 1–22. https://doi.org/10.1123/jsep.23.1.1

    Article  Google Scholar 

  • Yik, B. J., Raker, J. R., Apkarian, N., Stains, M., Henderson, C., Dancy, M. H., & Johnson, E. (2022). Evaluating the impact of malleable factors on percent time lecturing in gateway chemistry, mathematics, and physics courses. International Journal of STEM Education, 9(1), 15. https://doi.org/10.1186/s40594-022-00333-3

  • Yoshinobu, S., & Jones, M. G. (2012). The coverage issue. PRIMUS, 22(4), 303–316. https://doi.org/10.1080/10511970.2010.507622

    Article  Google Scholar 

Download references

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant Nos. 1726042, 1726281, 1726126, 1726328, 2028134.

Author information

Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, 24060, Blacksburg, VA, United States

    Madhavi Vishnubhotla & Estrella Johnson

  2. Department of Mathematics, George Mason University, 22030, Fairfax, VA, United States

    Ahsan Chowdhury

  3. School of Mathematical and Statistical Sciences, Arizona State University, 85287, Tempe, AZ, United States

    Naneh Apkarian

  4. The Evaluation Center, Western Michigan University, 49006-5444, Kalamazoo, MI, United States

    Melissa Dancy

  5. Department of Physics and Mallinson Institute for Science Education, Western Michigan University, 49006-5444, Kalamazoo, MI, United States

    Charles Henderson

  6. Center for Research on Instructional Change in Postsecondary Education , Western Michigan University, 49008, Kalamazoo, MI, United States

    Alexandra Claire Lau

  7. Department of Chemistry, University of South Florida, 33620, Tampa, FL, United States

    Jeffrey R. Raker & Marilyne Stains

Authors
  1. Madhavi Vishnubhotla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahsan Chowdhury
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Naneh Apkarian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Estrella Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Melissa Dancy
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Charles Henderson
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Alexandra Claire Lau
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Jeffrey R. Raker
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Marilyne Stains
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Estrella Johnson.

Ethics declarations

Statements and Declarations

 This material is based upon work supported by Evaluating the Uptake of Research-Based Instructional Strategies in Undergraduate Chemistry, Mathematics, & Physics is an NSF-funded (DUE Grant Nos. 1726042 , 1726281, 1726126, 1726328, 2028134). .

Informed consent

Was provided by all survey participants, in accordance with Western Michigan University’s Institutional Review Board.

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vishnubhotla, M., Chowdhury, A., Apkarian, N. et al. “I use IBL in this course” may say more about an instructor’s beliefs than about their teaching. Int. J. Res. Undergrad. Math. Ed. (2022). https://doi.org/10.1007/s40753-022-00186-9

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40753-022-00186-9

Keywords

Search

Navigation