Blog Twenty-Six - Group Sizes in Mathematics Classrooms (Group Work Part 2)
Collaboration is often cited as one of the major changes being made to mathematics classrooms, with a focus on discussion based learning and increased peer-to-peer discourse. Part of these reforms call for an increased amount of small group work for a number of reasons. For starters, smaller groups allow for more targeted help rather than having to address the wide variety of content mastery levels of a large group of learners, thus allowing the teacher to place focus on students more effectively. Additionally, smaller groups promote more active participation and engagement from all students, as they are less likely to be able to blend in and simply observe during group discussions. Of course, as with any implementation, group work has its own downsides. However, the focus of this article is the optimal group size for mathematics classrooms. While each classroom has its own specific needs, a scale between larger and smaller groups can grow to have their own general pros and cons as one moves from one end to another. The optimal group size for mathematics classrooms can vary depending on several factors, including the specific learning objectives, the level of the students, and the nature of the task at hand.
Starting off with smaller groups, they allow for more emphasis on each student in the group, as there are fewer people sharing out. This can foster a sense of individual accountability and responsibility, encouraging participation from all students in the group and not giving students a route to hide as they could in a larger group. A smaller number of students also allows for students to come to a consensus faster as there are fewer ideas to consider. However, this may backfire as the small number of students may put unnecessary pressure on individuals, potentially scaring non-confident learners if they are not ready to share yet. Additionally, with smaller groups, if students do end up not participating, there is more burden on the other members of the group, especially if the group is especially small like a pair of two or a group of three.
Larger groups, on the other hand, set a floor for a wider array of ideas to be shared, leading to richer and more nuanced discussions. There are more students to provide a diverse range of perspectives, and, in a subject like mathematics where there are many different ways to interpret and solve a problem, these discussions can help students build their critical thinking skills by exposing them to different thinking patterns. Students are taught to work with many different personalities, which is parallel to what they will experience after graduation and in the workplace. Of course, larger groups also come with their own set of challenges. As the number of students in a group increases, it becomes more difficult to ensure that all members are actively participating and contributing to the discussion. This can lead to some students feeling marginalized or disengaged, which can ultimately hinder the learning process. There is a higher risk of some students not participating as actively or some students dominating the conversation, leading to an unequal distribution of sharing and ultimately, an uneven learning experience for all group members.
A research study was published in the Journal of Personality and Social Psychology that examined the relationship between group size and performance on various letters-to-numbers equations. These equations are similar to the critical thinking needed in mathematics classrooms, so some of the group dynamics found in the study would likely apply to classroom small groups as well. The study found that pairs only performed as well as their best member, but groups of 3-5 members showed improved performance over the best individual group member. The lack of difference in performance between the pairs and the best individual indicates that the pair dynamic may not have enough people to encourage rich discussion and fully utilize the potential of small group collaboration.
As for group sizes in mathematics classrooms, there are many factors that need to be considered to determine the optimal group size. And this depends on the dynamics of the classroom as well, as what works perfectly for one classroom may appear to be disastrous for another. However, in most cases, a group size of 3-5 students seems to strike a reasonable balance, allowing for sufficient discourse and collaborative problem-solving without becoming too unmanageable or risking some students disengaging.
