Modified IBL Method with an Oral Defense

Abstract

Topic/Problem Statement: This talk focuses on the learning outcome of “do the students have a deeper understanding of the given material or are they going through the motions without really understanding?” Using writing alone does not truly reflect student understanding. This talk will lay out a structure that tries to answer this question at the advanced course level. Context: The primary courses of focus are Analysis and Abstract Algebra. The average class size is currently about 6 students. Class makeup is about 50-50 pure mathematics majors and education majors. The outcomes are: better understanding and application of course material, and the student’s ability to communicate mathematical ideas, especially oral communication. Inquiry-Based Learning (IBL) has a lot of evidence supporting its effectiveness in mathe- matical classrooms [3, 4, 1, 5]. Furthermore, in 2017 the Conference Board of the Mathemat- ical Sciences has endorsed IBL [8]. The Fall of 2017 Analysis course was taught as a 50-50 Inquiry-Based Learning (IBL) and traditional lecture. Though there were some successes with the class structure, it did have its draw backs. There were still glaring gaps of understanding the course material because of the lack of time students had to defend their work. Approach: In the Fall of 2018, the Abstract Algebra took on a more tradition IBL proof based course drawing elements from [2, 6, 9, 5, 10]. A book from the Journal of Inquiry-Based Learning in Mathematics was adopted [7]. The overall structure had a brief discussion of new definitions which quickly lead into computation like questions and examples. As proficiency in definitions were acquired the students move on to proofing/disproving theorems which required defending their work in front of their peers. After each exam, students must complete a one-on-one oral defense of their exam. The grading structure of class, rubric for the defense, and anecdotal evidence will be discussed. Reflection: This change to almost full IBL resulted in several positive things. First, the level of difficultly in exam questions increased dramatically while not negatively affecting grades. Second, students have become more critical of not only their classmate’s proofs but their own as well. Finally, conversational mathematics at this level is becoming easier than it has been in past classes. Unfortunately, this process is slow in nature. Specifically the overall structure on how homework is handled, though worked well, needs to be adjusted to manage expectations. This is to ensure students stay on an appropriate pace. References D. Bressoud, Evidence for inquiry based learning, Retrieved from http://launchings.blogspot.com/2011/07/the-worst-way-to-teach.html. D. Ernst, A. Hodge, and S. Yoshinobu, What is inquiry-based learning?, Notices of the AMS 64 (2017), no. 6, 570{574. S. Freeman, S. L. Eddy, M. McDonough, M. K. Smith, N. Okoroafor, Hannah Jordt, and M. P. Wenderoth, Active learning increases student performance in science, engineering, and mathematics, Proceedings of the National Academy of Sciences 111 (2014), no. 23, 8410{8415, DOI: 10.1073/pnas.1319030111. M. Kogan and S. Laursen, Assessing long-term effects of inquiry-based learning: A case study from college mathematics, Innovative Higher Education 39 (2014), 183{199, https://doi.org/10.1007/s10755-013-9269-9. G. Kuster, E. Johnson, K. Keene, and C. Andrews-Larson, Inquiry-oriented instruction: A conceptualization of the instructional principles, PRIMUS (2017), no. 26. S. Laursen, M. L. Hassi, M. Kogan, and A. B. Hunter, Evaluation of the ibl mathematics project: Student and instructor outcomes of inquiry-based learning in college mathematics, Retrieved from https://www.colorado.edu/eer/sites/default/_les/attached-_les/iblmathexecsumm050511.pdf. M. L. Morrow, Introductory abstract algebra, Journal of Inquiry-Based Learning in Mathematics (May 2012), no. 26. Conference Board of the Mathematical Sciences, Active learning in post-secondary mathematics education, Retrieved from http://www.cbmsweb.org/Statements/Active Learning Statement.pdf. C. Rasmussen and O. N. Kwon, An inquiry-oriented approach to undergraduate mathematics, Journal of Mathematical Behavior (2007), no. 26, 189{194, DOI: 10.1080/10511970.2017.1338807. C. Rasmussen, K. Marrongelle, O. N. Kwon, and A. Hodge, Four goals for instructors using inquiry-based learning, Manuscript submitted for publication.