Case topology arranges opportunities; it does not create effects

Figure 1 shows four generic arrangements. They are analytic patterns rather than product features or evaluated treatments. Each moves control to a different place and therefore makes a different kind of learner work possible to observe.

Table 1. Each arrangement makes one reasoning opportunity visible while leaving its quality unproven

Source and note: Authors’ conceptual classification, adapted from the mechanism and non-claim distinctions in HS-WP-2026-05. The rows are design hypotheses ordered by where control sits. They do not rank arrangements or report completed comparative results.

The single-guide pattern has the closest adjacent evidence because worked examples have been studied directly. A mathematics meta-analysis reported a positive average, Hedges’ g = 0.48, 95% CI [0.36, 0.60], but extreme heterogeneity, I² = 93.72%, and a literature dominated by structured tasks and immediate accuracy (Barbieri et al., 2023). The result supports inspectable worked structure under conditions. It does not show that one humanlike guide is the best social arrangement.

Support also has to change with knowledge. Across 60 experiments, higher assistance favored learners with lower prior knowledge and lower assistance favored those with higher prior knowledge, but both estimates were highly heterogeneous (Tetzlaff et al., 2025). A small law experiment found worked cases useful for first- and third-year students alike. Topology cannot substitute for diagnosing what has become redundant on the focal task.

Evidence for several perspectives is narrower. In Hayashi’s laboratory rule-discovery experiments, a coherent dissenting perspective could prompt integration, while three dissenters were not better than one in the first experiment. The partners were scripted conversational agents, but there was no human, text or alternative-interface comparison; the immediate artificial task did not test retained professional judgment (Hayashi, 2018). The study supports task-relevant dissent under a constructive interaction climate. It does not validate an anchored or learner-directed topology.

Simulation evidence likewise supports rehearsal packages rather than a particular handoff structure. A synthesis of 145 higher-education studies reported favorable estimates for objectively assessed complex skills, including g = 0.63, 95% CI [0.38, 0.89], for role-play or standardized-patient formats, with I² = 87.02% and strong concentration in medical education (Chernikova et al., 2020). Practice, feedback and reflection were usually bundled. A separate direct comparison found no reliable overall advantage for trained standardized patients over peer role-play (Xiao & Fu, 2025). Realism can improve confidence or experience without improving objective performance.

The common lesson is that the instructional work occurs inside the arrangement: comparison, explanation, responsibility, feedback, calibrated support and a later criterion task. The topology allocates opportunities for that work. It does not perform the work for the learner.

The strongest directly relevant higher-education transfer study held exposure constant. Eighty-eight management master’s students studied the same two negotiation cases. One condition explicitly compared them and derived their shared principle; the other analyzed each protagonist separately. One week later, 14 of 22 comparison-trained dyads (64%) used the target contingency contract, compared with 5 of 22 dyads (23%) in the other condition, χ²(1, N = 44) = 7.503, p < .01; no confidence interval was reported (Thompson, Gentner, & Loewenstein, 2000). Overall monetary gain differed by only 2% and not significantly.

That result is valuable because it identifies an activity rather than a surface format. Two cases were not enough. Learners had to align their structure and articulate a common strategy. The behavioral transfer was bounded to one negotiation task and did not produce a general economic advantage.

The implication for topology is precise. Holding an arrangement constant across an initial comparison can reduce irrelevant variation. Changing the arrangement on a later case can then test whether the learner acquired the decision structure or merely learned how to navigate one pattern. The claim belongs to guided comparison and aligned transfer, not to multiplicity itself.

A credible study would hold the case content, relevant evidence, time, feedback and decision opportunity constant while varying only the arrangement of roles and information. Prior knowledge would be measured in the target domain rather than inferred from academic year. Outcomes would distinguish immediate assisted performance from a new unaided decision, delayed retention and a structurally aligned transfer case.

The observation model would matter too. An arrangement creates different opportunities: learner-directed consultation permits an information-seeking choice, while a fixed handoff may not. Missing behavior therefore cannot be interpreted without knowing whether the task made that behavior possible. Independent reviewers would need to judge the reasoning and decision, not merely count consultations, turns or roles.

Such a design could compare an arrangement with a simpler baseline and identify mediators: relevant information sought, constraints integrated, unwarranted certainty revised or handoffs justified. It could also test whether accessibility, disciplinary culture or prior experience changes who benefits. Until then, a topology remains a reasoned design hypothesis.