This study provides a framework for utilizing artificial intelligence (AI) in the college mathematics classroom. First, it reviews current trends in mathematics education, as they relate to active learning. Historically, much mathematics instruction has been done in the traditional mode of a non-interactive lecture given by a faculty member, a format where the learner behaves passively while the lecturer delivers information in recent years, more student-focused instructional methods have gained some popularity. The review of the literature provided herein includes an examination of the use of various techniques in college mathematics instruction. We look at instructional techniques that can be used in addition to or instead of purely didactic lecture-based methods. In contrast to the prior format, the lesson examples provided toward the end of this study present approaches that shift the learning paradigm from a model where the teacher is in complete authority to a participatory model where learners and educators together decide how curriculum is delivered and how learning outcomes are assessed by identifying, examining, and selecting modes of delivery and assessment. Following this, we look at topics related to the use of AI in the mathematics classroom. Since the use of AI, especially in the classroom, is a relatively new development, the literature in this area is still in its early stages. Next, this study develops a theoretical framework offering educators the ability to structure lessons on a variety of mathematical topics with both AI and more traditional instructional methods. This study concludes with three sample lessons, with the latter presenting examples of the utilization of the framework at various levels of college mathematics: developmental, core, and upper-level math major courses. The lessons each include an objective, procedures (including both AI-based and non-AI based instructional methods), and a listing of the knowledge, skills, and values acquired in the lesson.
Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM Mathematics Education, 45(6), 797-810.
Berry, M. W. (2005). The paradigm shift in mathematics education: Explanations and implications of reforming conceptions of teaching and learning. The Mathematics Educator, 7, 7-17.
Burton, D. M. (2007). The history of mathematics (7th ed.). McGraw-Hill.
Cengage. (2024). Faces of faculty: The higher education instructor experience 2023. Cengage.
Chamberlin, M., & Powers, R. (2010). The promise of differentiated instruction for enhancing the mathematical understandings of college students. Teaching Mathematics and Its Applications: An International Journal of the IMA, 29(3), 113-139.
Croom, L. (1997). Mathematics for all students. In Multicultural and gender equity in mathematics: The gift of diversity (pp. 1-9). NCTM.
Khasawneh, E., & G. C. (2021). What impact does math anxiety have on university students? BMC Psychology, 9, 1-9.
Engelbart, D. (1962). Augmenting human intellect: A conceptual framework. Air Force Office of Scientific Research.
Gardner, H. (2023, September 5). Chat GPT: First musings. MI Oasis. https://www.multipleintelligencesoasis.org/blog/2023/9/5/chat-gpt-first-musings
Goldenberg, P. (2000). Thinking (and talking) about technology in math classrooms.
Gay, G. (2018). Culturally responsive teaching: Theory, research, and practice. Teachers College Press.
Halmos, P. B. (1958). Innovation in mathematics. Scientific American, 199(3), 66-73.
Harvard Graduate School of Education. (2023, February 9). Educating in a world of artificial intelligence. Harvard Graduate School of Education. https://www.gse.harvard.edu/ideas/edcast/23/02/educating-world-artificial-intelligence
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, 1-24.
Furner, J. M., & L. M. (2022). Addressing math anxiety in a STEM world: Preventative, supportive, and corrective strategies for the inclusive classroom. European Journal of STEM Education, 7(1), 11.
Van, K. G., Morton, B. A., Liu, H. Q., & Kline, J. (2006). Effects of web-based instruction on math anxiety, sense of mastery, and global self-esteem: A quasi-experimental study of undergraduate statistics students. Teaching Sociology, 34(4), 370-388.
Kaushik, R., Parmar, M., & Jhamb, S. (2021, December). Roles and research trends of artificial intelligence in mathematics education. In 2021 2nd International Conference on Computational Methods wherein Science & Technology (ICCMST) (pp. 202-205). IEEE.
Keynes, H. B., & Olson, A. M. (2002). Professional development for changing undergraduate mathematics instruction. In The teaching and learning of mathematics at university level: An ICMI study (pp. 113-126).
Kopzhassarova, U., Akbayeva, G., Eskazinova, Z., Belgibayeva, G., & Tazhikeyeva, A. (2015, November 30). Enhancement of students’ independent learning through their critical thinking skills development. International Journal of Environmental and Science Education. https://eric.ed.gov/?id=EJ1121248
Higgins, K., & L. D. (2017). Effects of technology in mathematics on achievement, motivation, and attitude: A meta-analysis. Journal of Educational Computing Research, 57(2), 283-319.
Laursen, S. L., & Rasmussen, C. (2019). I on the prize: Inquiry approaches in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education, 5, 129-146.
Leyva, L. A., Quea, R., Weber, K., Battey, D., & López, D. (2021). Detailing racialized and gendered mechanisms of undergraduate precalculus and calculus classroom instruction. Cognition and Instruction, 39(1), 1-34.
Lucas, A. F. (2000). Leading academic change: Essential roles for department chairs. Jossey-Bass.
Munro, F. B. (2008). Why hasn’t technology disrupted academics’ teaching practices? Understanding resistance to change through the lens of activity theory. Computers & Education, 50(2), 475-490.
Orzel, C. (2010, July 23). Real math doesn’t use calculators. Science Blogs. https://scienceblogs.com/principles/2010/07/23/real-math-doesnt-use-calculato
Phillips, C. J. (2016). The new math: A political history (Reprint ed.). University of Chicago Press.
Prensky, M. (2012). From digital natives to digital wisdom: Hopeful essays for 21st century learning (1st ed.). Corwin.
Millis, B. (Ed.). (2023). Cooperative learning in higher education: Across the disciplines, across the academy. Taylor & Francis.
Møgelvang, A., & Nyléhn, J. (2022). Co-operative learning in undergraduate mathematics and science education: A scoping review. International Journal of Science and Mathematics Education, 1-25.
Rappaport, D. (1976). The new math and its aftermath. School Science and Mathematics (SSM), 76(7), 563-570.
Rasmussen, C., & Kwon, O. N. (2007). An inquiry-oriented approach to undergraduate mathematics. The Journal of Mathematical Behavior, 26(3), 189-194.
Daker, R. J., & U. S. (2021). First-year students’ math anxiety predicts STEM avoidance and underperformance throughout university, independently of math ability. NPI Science of Learning, 6(1).
Boyle, R., & F. I. (2015). The effect of calculator use on college students’ mathematical performance. International Journal of Research in Education and Science, 1(2), 95-100.
Roy, R. (2021). The calculus of Newton and Leibniz. In C. University (Ed.), In series and products in the development of mathematics (pp. 143-164). Cambridge University Press.
Tapscott, D. (2009). Grown up digital: How the net generation is changing your world. McGraw-Hill.
Qawaqneh, H., Ahmad, F. B., & Alawamreh, A. R. (2023). The impact of artificial intelligence-based virtual laboratories on developing students’ motivation towards learning mathematics. International Journal of Emerging Technologies in Learning (Online), 18(14), 105.
Toth, L. S., & Montagna, L. G. (2002). Class size and achievement in higher education: A summary of current research. College Student Journal, 36(2), 253+. Gale Academic OneFile. https://link.gale.com/apps/doc/A89809976/AONE?u=anon~1a707b62&sid=googleScholar&xid=9d4caba8
U.S. Census Bureau. (2023, August 16). American Community Survey (ACS) data. U.S. Census Bureau. https://www.census.gov/programs-surveys/acs/data.html
Williams, D. D., Cook, P. F., Quinn, B., et al. (1985). University class size: Is smaller better? Research in Higher Education, 23, 307–318. https://doi.org/10.1007/BF00973793
8 November 2024
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