Discussion of Results
Firstly, it can be concluded that as all participants were in their final year of primary schooling, each would have had prior exposure to working in groups, and secondly, had a general understanding of the notion of collaboration. The pre-survey of students’ experiences with collaborative learning revealed that most boys enjoyed learning collaboratively. Of significance, however, were their generalised responses about what they felt effective collaboration looked like. The responses from boys, such as, “be kind,” “be positive,” and “work hard and help other group members,” suggest a lack of in-depth understanding of the nature of collaboration. Very few responses mentioned respect or listening. At the conclusion of the project, using a web-based word-cloud program, I entered all of the words from the students’ discussion during the focus group to achieve a visual representation of the most prevalent words used. See Figure 2.
Following the intervention, a number of themes emerged from the analysis of the data from the focus group meetings and a comparison of pre and post-survey responses:
Structured Face-to-Face Interactions
Emphasising the importance of roles within groups facilitated the development and improvement of the structure of learning groups during problem-solving sessions. Prior to the intervention, a divide and conquer approach occurred as students split up work according to their self-perceived abilities: A boy recounted, “When we first starting doing group problems solving, everyone was talking over each other and we couldn’t hear anything and we couldn’t get the job done.” He also noted, “At the beginning, everyone was fighting for control and like it was their opinion and nobody else’s.”
Following the intervention, the boys realised that respecting each other’s role was a key factor that facilitated the group’s efforts and allowed them to better share their ideas through turn taking. The same boy added, “Whereas now, people respect each other’s opinions, work together to use their skills to solve the problem.” Discussing the importance of their roles within the groups allowed boys to refocus their efforts during group problems solving. This was important to one particular boy who shared his thoughts on what he felt was an important collaborative skill: “Well respecting each other’s roles cause some of us were doing two roles at a time. For example, the facilitator was also the scribe. We had to stick to our roles, because it got messed up and it got confusing.” In many cases, boys felt they were doing the best for the group by taking over a role not assigned to them because they felt that they had better skills in the group, such as neater handwriting or could work out a group problem using algebra. As a result, boys had to let go of their natural urge to take control and ‘do it for them’. By doing so, each group developed a better empathetic understanding of other boys’ abilities within their groups. The comparison between the pre-survey and post-survey responses supports a positive change in how participants felt about sharing within their groups. See Figures 3, 4 and 5.
Positive interdependence promotes learning through others
Jones and Jones (2008) hold the view that positive interdependence “is the belief that the individual is dependent on the contributions, inclusion, and success of the others in the group in order to be successful” (p. 66). Prior to the intervention, students were allowed to freely work in groups to solve problems, which provided a staging point for the project. Initially, when each group received the problem they would all begin working at once in order to achieve an answer using different methods and then share their answers with each other. From observations made earlier in the year, I noticed that boys’ general approach to problem-solving showed a reliance on an iterative process of guessing and checking using a robust knowledge of retained mathematical concepts. Within the group, only a handful of students were able to consistently demonstrate success with their ability to formulate and reason mathematically using a range of more abstract strategies. When students were able to share their thinking about how they solved problems three further elements surfaced during the project: learning through others, sharing understandings, and an appreciation of each other’s abilities. One student expressed his sense of success commenting, “I enjoyed being able to see how other people got to work out the question and see how they find their solutions. So, you have more than one way to work out doing things. So, you have backup ideas and see how other people solve questions.” A comparison of pre and post surveys indicated that boys were developing a greater preparedness to use the strategies of other team members. See Figure 6.
Reflecting on his experiences one student stated, “I think it was a sense of satisfaction, not only individually but as the whole group, because I think from memory I used algebra for my two extra Olympiads [questions]. And I learnt that from my group, and so that showed that what we were doing was working.” He also went on to reflect, “When I think back on problem-solving at other schools, and last year as well, it was all really messy and it wasn’t as good as it was doing it this year. And now I think in the future it will be really easy, and instead of going ‘Oh, we’re doing group [problem] solving…’ it will be a bit like, ‘Oh yeah, I can learn about from this!’ Instead of having to somehow find the answer with other people and struggle with where we had to be.”
Interpersonal skills allow for the intersection of other minds.
To promote greater awareness of interpersonal understandings and social interactions, the action incorporated the explicit teaching of social and interpersonal skills, which included: making eye contact, leaning in, checking for understanding, listening attentively, paraphrasing, disagreeing politely and using first names (see Appendix 3). At the beginning of group problem-solving sessions boys set goals by identifying three collaborative skills they would use. They reflected on the effectiveness of their goals. A boy commented, “As we went along, we started making goals and these goals quite helped.” In effect, the process of goal setting acted as a conduit between the boys’ use of the collaborative skills taught and their individual creative solving problems skills. Further into the project, the positive nature of communication within groups changed significantly. Interactions between boys resulted in improved understandings and greater engagement during problem-solving work. Summarising his feelings about this change, a boy reflected, “When we were getting towards the end [of the project] our minds started to think more alike. So one person would say their suggestion on how to solve it [the problem] and another person would say, ‘I was also thinking that way.’ So our minds started out as separate, but slowly started to come together so we could think more alike.”
Gamification / Competition heightens students’ use of collaborative skills
After the group problem-solving sessions, boys individually attempted problems with similar mathematical concepts. The results of their individual improvement scores were collectively converted into an overall group score and presented on a leaderboard with teams awarded badges. Reichert and Hawley (2010a) state that interactive exchanges and competition are significant factors that contribute to the element of ‘transitivity’ and result in student engagement. Long (2016) uses the term “boyology” for boys’ engagement as a critical factor in the teaching of boys. The leaderboard and badges gamified the collaborative problem-solving process, serving to arouse boys’ awareness of to the importance of using collaborative skills taught. Highlighting the impact of these two elements on group and individual accountability, a boy reflected:
“The scoring system and having that game or competition element in boys, because we always need competition, really improved and gave people an incentive and it gave them something to work towards. Because you don’t want to look up to see that your score had let down your team to be one of the worst teams. So, it would make you perform better, and that lifted everybody.”
Similarly, another boy commented:
“Having the individual questions in the competition made us collaborate better. You gave us no choice, so you had to collaborate well to get everyone to have an understanding of the problem. Because you’d go to the individual problems which were usually similar to the group problem, you’d have to have and understanding of that problem, so it helped us collaborate greatly.”
Overall, I was pleasantly surprised to observe the deep impact gamification had on the boys’ use of collaborative skills and their problem-solving skills. A richness within these results has been achieved by presenting and preserving the boys’ voices. The findings show that gamification is a significant transitive factor that promotes the use of collaborative skills whilst also improving the problem-solving skills boys in Mathematics.