# Collaborative Learning Groupings Incorporating Deep Knowledge Tracing Optimization Strategies
## 5 Evaluation of Student Groups
### Collaborative Learning Groupings Effectiveness Comparison
#### 5.4.2 Heterogeneity of the Grouping Approach  
Heterogeneity refers to the need for groups to be as heterogeneous as possible and must be measured by the variability of student knowledge acquisition data within each group. An analysis of the data in Tables 4-6 shows that the groupings based on raw scores and the DINA model will place many homogeneous students in the same group. For instance, in group 3 of the groupings based on raw scores, S18 and S24 are both students with relatively good mastery of circuit operating conditions (K2), resistor type and parameters (K5), and average mastery of other knowledge. Similarly, in group 5, formed based on the DINA model, S7 and S10 were both students with relatively good knowledge of resistor basics (K3), resistor type and parameters (K5), electrical power (K9), and Ohm's law (K11), and their knowledge structures showed a high degree of homogeneity. To quantify the heterogeneity of group compositions, we calculated the Gini Index (GI) for each knowledge point within groups. The Gini Index, ranging from 0 (perfect homogeneity) to 1 (maximal heterogeneity), provides a standardized measure of diversity. The groups formed by DKVMN-EKC achieved significantly higher GI values (mean GI = 0.42) compared to the raw-score-based (GI = 0.28) and DINA-based (GI = 0.31) groups, confirming enhanced intra-group diversity. For example, in Group 1 formed by DKVMN-EKC, the GI for knowledge points K2 (circuit operating state) and K5 (resistor type and parameters) were 0.48 and 0.45, respectively, indicating substantial variability in student mastery levels. In contrast, the corresponding GI values for raw-score-based groups were 0.32 and 0.29, reflecting lower diversity. While our method achieved higher intra-group diversity than the baseline approaches, it is important to contextualize these results. Prior studies on collaborative learning grouping (e.g., [PERSON] & [PERSON], 2019; [PERSON] et al., 2020) [13; 14] typically involved 100-500 participants across multiple institutions. Our smaller sample (N = 30) may amplify random variations in group composition, as seen in the wider confidence intervals for heterogeneity metrics. Future work should prioritize scaling to cohorts of similar size to the established literature. To better illustrate the variability in the degree of knowledge mastery of the group members, Figure 8 shows Group 1, formed based on our model, as an example. The horizontal coordinates indicate the knowledge points, the vertical coordinates indicate the students, and the height indicates the knowledge mastery. In this study group, S10 can tutor group members on knowledge points related to the working state of a circuit (K2), resistor type and parameters (K5), electrical power (K9), and Ohm's law (K11); S21 can help group member S16 to tutor knowledge points related to the basic knowledge of resistance (K3), electrical power (K9), and electrical energy (K10); and S16 can teach S21 about basic elements of circuit composition (K1), circuit operating state (K2), and other relevant knowledge points. There is a clear difference in the degree of mastery of each knowledge point among the group members, reflecting the heterogeneity of the group. Students in the same group have different advantageous knowledge points, which can improve positive interactions among students by learning others' knowledge to effectively improve students' knowledge points. The analysis of fairness and heterogeneity revealed that the collaborative learning grouping strategy based on the DKVMN-EKC model effectively established learning teams characterized by enhanced inter-group fairness and intra-group heterogeneity in terms of knowledge structure, and that the approach had good learning group formation performance, which was analyzed with the following in mind:  
1. The conventional grouping approach, which relies solely on raw scores as a measure of students' knowledge level and is widely employed in related research [13; 14], has significant limitations.