Collaborative Learning Index (IEI)

• Collaborative Learning Index is a transparent metric that assigns Active, Semi-active, or Passive codes each second to capture individual engagement during group work.
• It aggregates audio and video sensor data into interpretable engagement profiles, supporting timely scaffolding and personalized feedback for learners.
• Empirical validation distinguishes prototypical profiles (Drivers vs Passengers), demonstrating its effectiveness in aligning subjective and performance outcomes.

The collaborative learning index described in this context is a transparent collaboration analytics construct for face-to-face group work, instantiated in Zhou, Suraworachet and Cukurova’s "Harnessing Transparent Learning Analytics for Individualized Support through Auto-detection of Engagement in Face-to-Face Collaborative Learning" (Zhou et al., 2024). In the reconstruction provided for that work, the construct is termed the Individual Engagement Index (IEI): a fully transparent, rule-based metric of each student’s moment-to-moment engagement during physical, face-to-face collaborative activity. It assigns one of three engagement codes—Active, Semi-active, or Passive—at one-second resolution and aggregates those codes into per-session engagement profiles. The index is intended both to make individual participation interpretable to instructors and learners and to support timely scaffolding of cognitive, behavioural, and socio-emotional dimensions of collaborative learning.

1. Definition and educational role

The IEI is defined as a triad of engagement codes assigned to each learner second by second during collaborative activity: Active, Semi-active, and Passive (Zhou et al., 2024). These codes are not merely descriptive labels. They are designed to surface an interpretable account of how each individual participates in a collaborative task, including distinctions such as who is speaking, who is listening, and who is off-task.

Its educational purpose is explicitly twofold. First, it provides an interpretable measurement of how each student participates as an individual within a group. Second, it enables individualized scaffolding of collaborative learning practice by making visible patterns that may warrant intervention, such as quieter students who might be invited to contribute or groups in which too many students are Passive. The underlying motivation is a critique of learning analytics approaches that rely on "black box" modelling and that focus only on group- and cohort-level analysis. In that critique, lack of transparency can obstruct educationally meaningful guidance, while aggregate analysis can limit the provision of specific support for individuals (Zhou et al., 2024).

This framing positions the index as an interpretability-first alternative to opaque prediction pipelines. A plausible implication is that the index is intended less as a hidden optimization device than as a pedagogical representation whose logic remains inspectable by teachers and learners.

2. Mathematical formulation

The IEI is formalized through normalized frequencies of the three engagement codes over a student’s collaborative session (Zhou et al., 2024). Let $T_i$ denote the total duration, in seconds, of student $i$’s session, and let $$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$ denote the engagement code at time $t$. The three frequency features are defined as

$$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$

$$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$

$$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$

The resulting profile is

$IEI_i = (f_i^a,\;f_i^s,\;f_i^p),$

with the simplex constraint

$f_i^a+f_i^s+f_i^p=1.$

No further weighting or dimension reduction is applied. The three frequencies themselves are the representation. This is methodologically significant because the index preserves direct semantic correspondence between observed behaviour and aggregate profile. The value of the index is therefore not hidden in latent components or transformed embeddings; it remains legible as time spent in each engagement state.

3. Behavioural inputs and derived interaction states

All behavioural inputs are drawn from two low-cost sensor streams: speech behaviours from audio and gaze behaviours from video (Zhou et al., 2024). Speech is identified per second via speaker-diarization using AWS Transcribe + manual voice–student mapping. Gaze is annotated per second in four categories: Peers, Laptop/Tablet, Tutor(s), and Other. The reported annotation agreement is Cohen’s $\kappa=0.98$ on a 1 000-frame sample.

From these micro-behaviours, seven group-interaction states are derived via sliding-window logic with window = 5 s. Each second is labelled as exactly one of the following states:

State	Description
IPC	Interacting with Peers by Communication
RF	Referring & Following; speaker’s gaze–object synchrony
PO	Peer Observation; gaze on peer who is manipulating materials
RM	Resource Management; gaze synchrony on same digital canvas
ITC	Interacting with Tutor by Communication
TO	Tutor Observation
NC	No Collaboration

These derived group states, together with raw gaze and speech, supply the observable substrate from which engagement is inferred. The architecture therefore joins individual-level behavioural traces with a shared group-level interaction context. This suggests that the index does not reduce engagement to speaking frequency alone; it operationalizes engagement as a structured combination of speech, gaze, and collaborative configuration.

4. Transparent modelling and rule-based assignment

The modelling approach is explicitly non–black-box (Zhou et al., 2024). Each second, a rule-based engine reads four elements: student $i$0’s speaking flag, student $i$1’s gaze direction, the shared group state, and the lookup specified in Table 1 of the paper. From these inputs it assigns $i$2.

The process consists of three stages. First, the rule-based engine performs per-second assignment. Second, the session-level aggregation computes $i$3. Third, k-means clustering is applied to $i$4 using Bregman divergences and $i$5. Because each rule is explicitly listed, users can trace why a student was coded as Active rather than Semi-active or Passive. The reconstruction further states that educational theory underpins each rule, for example that “Active” requires either speech or being directly observed/manipulated by peers.

A common misconception would be to treat this index as a conventional supervised classifier whose credibility rests on predictive accuracy. That is not how the construct is presented. Its transparency derives from explicit rule specification, and its empirical support is established through validity evidence rather than classifier metrics such as accuracy or AUC.

5. Engagement categories and empirical validity

Clustering on $i$6 yields two clusters, selected by the elbow method with average within-centroid distance –0.026 (Zhou et al., 2024). The two prototypical engagement tactics are Drivers and Passengers. Their reported mean IEI profiles are as follows:

Category	Mean IEI
Drivers $i$7	$i$8
Passengers $i$9	$$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$0

No hard numerical cutoff on $$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$1 is proposed beyond the $$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$2 clustering, although the reconstruction notes that one could, in principle, adopt a fixed threshold such as “Driver” $$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$3 and “Passenger” otherwise if a thresholded implementation were desired.

Validity is demonstrated through alignment with self-reports and outcomes rather than prediction accuracy. Two-sample $$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$4-tests between Drivers and Passengers show the following:

• Self-Reported Individual Engagement: Drivers $$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$5 ($$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$6); Passengers $$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$7 ($$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$8); $$E_i(t)\in\{\mathrm{Active}, \mathrm{Semi\text{-}active}, \mathrm{Passive}\}$$9, $t$0, Cohen’s $t$1
• Self-Reported Peer Engagement: Drivers $t$2 ($t$3); Passengers $t$4 ($t$5); $t$6, $t$7, $t$8
• Behavioural Challenges (lower = fewer problems): Drivers $t$9 ($$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$0); Passengers $$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$1 ($$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$2); $$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$3, $$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$4, $$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$5
• Cognitive Challenges: Drivers $$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$6 ($$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$7); Passengers $$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$8 ($$f_i^a = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Active}\bigr],$$9); $$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$0, $$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$1, $$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$2
• Socio-Emotional Challenges: Drivers $$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$3 ($$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$4); Passengers $$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$5 ($$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$6); $$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$7, $$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$8, $$f_i^s = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Semi\text{-}active}\bigr],$$9
• Final Assessment Scores: Drivers $$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$0 ($$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$1); Passengers $$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$2 ($$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$3); $$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$4, $$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$5 (one-tailed), $$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$6

All reported differences are significant at $$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$7. On that basis, the index is presented as reliably distinguishing students by self-perceived engagement, reported challenges, and learning gains. The significance of this result lies in the fact that a transparent rule-based index, rather than an opaque predictive model, is shown to align with both subjective and outcome-based measures.

6. Scaffolding, dashboards, and pedagogical implications

Because the IEI is computed in real time from video and audio, it can be embedded in an instructor dashboard or a student-facing display (Zhou et al., 2024). Three deployment patterns are explicitly described.

For an Instructor View, groups can be flagged when more than 40% of members are coded Passive—expressed as $$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$8—to inform in-room walk-arounds. For a Live Visual Cue aimed at students, a bar chart of each member’s Active, Semi-active, and Passive ratios can support co-regulation, illustrated by the example: “Alice is very Passive—let’s ask her what she thinks.” For Automated Prompts, if a student’s Active ratio $$f_i^p = \frac{1}{T_i}\sum_{t=1}^{T_i} 1\bigl[E_i(t)=\mathrm{Passive}\bigr].$$9 dips below $IEI_i = (f_i^a,\;f_i^s,\;f_i^p),$0 for more than $IEI_i = (f_i^a,\;f_i^s,\;f_i^p),$1 s during an IPC phase, the system suggests: “Would you like to share an idea?”

These deployments are characterized as lightweight interventions grounded in fully transparent rules. Teachers and learners can read and revise each rule, thereby maintaining agency over both the analytics and the pedagogical response. The discussion further states that the IEI can act as “eyes on the back” in busy classrooms, can empower socially shared regulation by making engagement visible to peers, and can guide timely scaffolds at the individual level.

A broader implication follows from the contrast with black-box learning analytics. The paper argues that interpretability is not merely a model property but a condition for actionable educational support. In that sense, the collaborative learning index is not only a measurement device; it is also a mechanism for linking observable participation patterns to individualized interventions in face-to-face collaborative learning.