Group formation methods used across a semester and students' experiences

Abstract

‘Group work’ is a vague description of an instructional activity, because many factors shape its character and effect on students. One important factor is group formation, that is, how groups are formed by the instructor. In this paper, we sought to better understand the variation of group work with respect to group formation by addressing: How do university mathematics instructors form groups over the course of a semester? To this end, we examined eight instructors' methods of forming groups in one multi-section introduction to proof course. Our findings include a classification of group formation methods and descriptions of how instructors varied their formation methods across the semester. Further, we sought to understand: How do students experience different group formation methods? We analysed interviews with 29 students from the eight instructors' classes and identified central themes among students' experiences of different group formation methods. Finally, we discuss the sometimes conflicting research on (when) which group formation method is most appropriate and offer our thoughts on how the differences between typical undergraduate and K-12 mathematics classrooms may contribute to different recommendations.

KEYWORDS:

• Active learning
• group formation
• group work
• student experience

Acknowledgments

The authors gratefully acknowledge the data collection contributions of Sofía Abreu, Younggon Bae, Sarah Castle, and Robert Elmore, as well as the support offered by Mariana Levin and Shiv S. Karunakaran.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 One benefit of pseudo-random selection with private modifications is students’ ability to privately offer grouping suggestions to the instructor, for instance, if they do not feel safe working with a particular student. The instructor can then make these modifications before class (or during class with, for example, a rigged Excel sheet). Despite being pseudo-random, the instructor may present the selection method as random.

2 Liljedahl (2014) posited that some students who wish to work with their friends may cease collaborating when placed in a group of non-friends by their teacher.

3 All necessary approvals were obtained from the Human Research Protection Program at the institution at which the research was conducted.

4 In most classes, some students arrived late, and instructors would tell them to join a particular group. Thus, we were confronted with the question of whether to, for example, change a coding from random (public) selection to pseudo-random (public) selection. We chose not to make this change and, instead, coded for instructors’ intended group formation method. Further, sometimes students worked together even though the instructor had not asked students to work together or had asked students not to work together. We did not code this as group work.

5 Note that we are not using ‘random’ and ‘pseudo-random’ in the way statisticians use these terms. For instance, whereas Excel’s random number generating functions are considered pseudo-random by statisticians, we would consider using Excel’s randomisation function to compose groups a random selection method. For us, what makes a group formation method pseudo-random is if the method has some semblance of randomness with the instructor still conceivably manipulating groups (e.g. grouping students by height which is more likely to create homogeneously gendered groups).

6 In different countries, the birth rate peaks at different points of the year. This is also true for the two countries that most of the students originated from: the U.S.A. and China. Thus, the likelihood – however small – was increased that a U.S. student would work with another U.S. student and a Chinese student would work with another Chinese student. Although this increase in probability is likely negligible, we choose to include selection by birthday as a pseudo-random method to highlight how seemingly random methods may not actually be random.

7 We wish to acknowledge that although changing groups each week may have led to changing interactions and positions, dominant personalities may have still found a way to dominate their groups. Group work norms such as determining the group’s writer via ‘first come, first served’ (e.g. N2) may still benefit dominant personalities.

8 As many surveys of university mathematics (e.g. the College Board of the Mathematical Sciences [CBMS] surveys, the Characteristics of Successful Programs in College Calculus [CSPCC] survey) have presented gender as a binary category, we do not know the proportion of non-binary students in U.S. university mathematics classrooms. Further, we know very little about the experience of non-binary students during group work. We do have reports, however, of binary gender being used as a group forming criterion, which devalues the experiences of non-binary students (Francis & Monakali, 2021).

Additional information

Funding

This material is based on the work supported by the National Science Foundation [grant number 1835946] (Shiv S. Karunakaran, PI; Mariana Levin, Co-PI; John Smith III, Co-PI).