The State of IBL
By David Bressoud @dbressoud
As of 2024, new Launchings columns appear on the third Tuesday of the month.
I talked about inquiry-based learning (IBL) in my Launchings column of April 2019, “Recent Research into IBL Mathematics.” Of particular importance was the article by Laursen and Rasmussen that had recently appeared, “I on the prize: Inquiry approaches to undergraduate mathematics.” It described IBL as a grassroots movement, contrasting it with Inquiry Oriented Instruction, a product of the research community. Significantly, this article recognized the commonalities and showed how to bring the two together.
What has this meant in practice? A recent report of results from an NSF grant, “ ‘I use IBL in this course’ may say more about an instructor’s beliefs than about their teaching”, has shed light on the answer to this question. In the Spring of 2019, the authors queried 1349 Calculus I instructors at 851 postsecondary institutions about their classroom practices. Of these, 963 instructors responded to all of target items related to IBL. Of these only 77 (8%) claimed never to have heard of inquiry-based learning, while 289 (30%) said that were currently using IBL in their Calculus I class.
To delve deeper into what “using IBL” means in practice, instructors were asked about their degree of agreement or disagreement with seven statements. They were also asked about how class time was typically divided among individual work, small group work, whole class discussions, and listening to lecture. For the division of class time, the variation was large. The authors did a cluster analysis of the responses from those using IBL and found three clear clusters:
o Mostly Lecture (ML): those who, on average, spent more than 60% of the time lecturing. There were 127 instructors in this category, 44% of those using IBL
o Mixed Ways (MW): those who on average spent less than a third of the time lecturing and more than a third in whole class discussions. There were 80 instructors in this category, 28% of those using IBL.
o Mostly Small Group (MSG): those who spent more than half the time in small group work. There were 82 instructors in this category, also rounding to 28% of those using IBL.
The average percentages for each group as well as for those who had never heard of IBL is shown in Figure 1.
Figure 1. Bar charts of the percentage of class time spent in each of four pedagogical activities by group.
It is striking that there is very little difference between those who never heard of IBL and those who claimed to be practicing it but still spent most of their class time lecturing. The one noticeable difference lies in how much time is spent in small group work. For a 50-minute class, small group work would take up less than 5 minutes for non-IBL instructors and almost 8 minutes for those who claimed to be IBL but mostly lectured. It is not clear how significant that difference is.
Instructors were also asked about their degree of agreement or disagreement with the following seven statements on a Likert scale that ranged from 1 (strongly disagree) to 6 (strongly agree).
1. I think lecture is the best way to teach.
2. Students learn best from lectures, provided they are clear and well-organized.
3. I think lecture is the only way to teach that allows me to cover the necessary content.
4. The major role of a teacher is to transmit knowledge to students.
5. I think students learn better when they struggle with the ideas prior to me explaining the material to them.
6. Making unsuccessful attempts is a natural part of problem-solving.
7. Learning means students have ample opportunities to explore, discuss, and express their ideas.
The average responses of the four groups are shown in Figure 2. It is interesting that all groups of instructors agree with the last three statements. For these statements, there are no significant differences in the degree of agreement among the instructors using IBL. We also see that there are clear attitudinal differences between the non-IBL instructors and those who still rely primarily on lecture. The IBL instructors who rely primarily on lecture do not disagree with the first four statement as strongly as the other IBL instructors, but there is a very real difference between them and those who have not heard of IBL.
Figure 2. Mean and 95% CI of the mean of each instructional group’s responses (vertical axis) to each of the seven selected Likert items (horizontal axis). Scores correspond to a six-point Likert scale, 1 = Strongly disagree; 6 = Strongly agree; there was no neutral option. The horizontal line at 3.5 corresponds to a “neutral” average response on the Likert scale. The vertical line separates the four positive statements about lecture and the three positive statements about learning through inquiry. Group order from top to bottom: nIBL (no exposure to IBL; n = 77), ML (IBL-mostly lecture; n = 127), MW (IBL-mixed ways; n = 80), MSG (IBL-mostly small group; n = 82).
The authors conclude with the following warning:
“Given our findings, we suggest caution when using the term IBL to describe instruction – for researchers and practitioners. This is particularly critical for those seeking to study or leverage the effects of IBL instruction on student experiences and/ or outcomes. For researchers, our findings imply that it would be a mistake to assume a consistency between IBL courses or even to assume that in all “IBL classrooms” the majority of class time is spent in student-centered activities.”
While we do need to be careful about self-characterization of instruction as IBL, I am encouraged by these findings. This study has identified a critical mass of faculty who are aware that lecture is not always the most effective method of teaching and who are expanding their use of small group explorations. Few faculty are equipped to plunge directly into full-scale adoption of IBL with recognition of the demands of Inquiry Oriented Instruction (IOI). As has been documented through the history of so many innovations, full-scale adopters are rare and liable to burnout. But we can work with those who are finding small and easy successes in partial adoptions of the ideas and methods of IBL/IOI. I see this study as evidence that we are moving in the right direction.
References
Laursen, S. L. & Rasmussen, C. (2019). I on the prize: Inquiry approaches in undergraduate mathematics. International Journal for Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-019-00085-6
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. 10, 87–106 (2024). https://doi.org/10.1007/s40753-022-00186-9
David Bressoud is DeWitt Wallace Professor Emeritus at Macalester College and former Director of the Conference Board of the Mathematical Sciences. Information about him and his publications can be found at davidbressoud.org