The decisions between the answers

The argument becomes confused when “learning” is allowed only one meaning.

Anna Sfard described two enduring metaphors in educational research. The acquisition metaphor treats learning as something an individual comes to possess. The participation metaphor treats learning as changing engagement in a practice. Her point was not to choose a winner; it was that each reveals something the other hides.

The acquisition view asks an essential question: what can the learner do later, independently, in a new situation, after time has passed? The participation view asks another: how is the learner beginning to see, speak, decide, and act within the practice now?

A human working with AI belongs initially to the second frame. The learner is participating in a mediated cognitive activity. The AI supplies information, language, alternatives, and prompts; the learner notices, requests, accepts, modifies, combines, or rejects them. Those choices are not merely residue around the “real” learning. They are part of learning as activity.

Salomon, Perkins, and Globerson gave educational technology a useful distinction more than three decades ago: effects with a technology are properties of joint performance, while effects of a technology remain when the support is gone. A reasoning graph can begin as a record of the first and later be tested against the second.

That yields three claims rather than one.

First, the graph may be an activity record: a faithful account of reasoning elements observed in defined episodes. Second, it may be a learning-process representation: evidence that strategy selection and coordination are changing across those episodes. Third, it may support a learning-outcome inference: a prediction of what the learner can later do without the same assistance.

The first does not automatically prove the second. The second does not automatically prove the third. But the third is not the only form of educational meaning.

Expertise is not simply having more ideas. It is knowing what bears on a decision and how considerations constrain one another.

A novice may know that base rates matter and know that alternative explanations should be tested, yet fail to bring those ideas together when evaluating a causal claim. Another learner may begin to coordinate them across cases. A list of mastered items misses that difference. A relational process record is designed to preserve it.

This approach has substantial precedent. Epistemic Network Analysis already constructs networks from co-occurring knowledge, skills, values, and practices in discourse and action. Process-mining researchers already examine how self-regulatory strategies unfold in sequence. In a recent chemistry study, 300 upper-secondary students completed 86 tasks across a 10–12-week unit. Researchers built individual networks from knowledge elements co-enacted in students’ work. Combined network summaries accounted for R² = .51, adjusted .47, in an immediate end-of-unit test.

The result did not say “more edges means more learning.” In phase-level regressions, the area under the density trajectory related negatively to later performance in the first phase and positively in the second. The result concerned accumulated density across each phase, not density at one moment. Unfocused connections and integrated understanding can look similar if time and content are ignored. The study’s contribution was subtler: an evolving individual network of enacted knowledge can be educationally informative, but its structure needs interpretation.

That is close to the heart of a heuristic graph. It is also a warning against turning connection into a universal good.

What non-use can mean

The contrast between what was available and what was enacted makes the record more revealing—and more dangerous.

An unused heuristic may be unknown. It may also be irrelevant, redundant, poorly presented, too costly, silently incorporated, or deliberately rejected. An expert sometimes uses a heuristic less often precisely because the expert recognizes its boundary conditions.

Strategy researchers have dealt with this problem for years. They distinguish the strategies in a person’s repertoire from how often each is selected, how efficiently each is executed, and how adaptively the person chooses. Choice/no-choice experiments were invented because ordinary choice data cannot reveal how an unchosen strategy would have performed.

Xu and colleagues demonstrated the distinction with 158 seventh-grade equation solvers. The students’ capacity to produce and recognize alternative strategies correlated only r = .27 with choosing an innovative strategy on the first attempt. In 38% of item-level cases, students answered accurately and demonstrated the alternative strategy when prompted without having chosen it initially. The study was cross-sectional and domain-specific, but it directly shows that an available strategy and an enacted strategy are not the same observation.

Available-versus-enacted evidence is therefore not a simple knowledge test. It is evidence about opportunity, attention, selection, uptake, and restraint. Repeated non-use becomes interpretable only when a task genuinely called for the heuristic, the learner could perceive and understand it, enactment was observable, and legitimate alternatives were represented.

Under those conditions, non-use can be part of the learning record rather than a penalty. A learner who moves from invoking a principle everywhere to using it only where it fits may be learning its scope.

Bayesian Knowledge Tracing has maintained person-specific estimates of skill mastery since the 1990s. Its canonical form assigns each tagged skill a hidden learned-or-unlearned state. Correct and incorrect opportunities update the probability of mastery, and a transition represents the modeled chance of learning.

BKT establishes the broad idea of a longitudinal probabilistic learner model. That foundation is not new.

Its usual question, however, is about a learner–skill node: how likely is it that this learner has mastered this skill? A heuristic process graph asks about relations: how are expert reasoning resources being selected and coordinated in this learner’s work with AI?

Relational modeling also has substantial precedent. Researchers have learned prerequisite graphs, fitted Bayesian networks over skills, inferred person-specific semantic associations from retrieval, and built changing networks of enacted knowledge. U-INVITE, for example, Bayesianly inferred individual semantic networks from repeated fluency lists. COMMAND learned a cohort skill graph while estimating student mastery. The chemistry study built changing learner-level co-enactment networks.

What has not appeared in the reviewed literature is the full combination: expert heuristics, human–AI decision traces, available-versus-enacted evidence, and longitudinal probabilistic relations estimated for the individual learner.

That is a narrower contribution than “the first graph of learning.” It is also a more credible one.

The immediate educational value is formative visibility, not another high-stakes label.

A faculty member could see that students repeatedly invoke a familiar principle but rarely connect it to an important boundary condition. A teaching-and-learning team could discover that a case sequence elicits one reasoning pattern while leaving another nearly invisible. A learner could inspect a model of their visible reasoning trajectory and challenge a relation that the record has misread.

Open learner-model research suggests that inspectability can support cognition and metacognition, but it also identifies unresolved questions about granularity, learner control, and transparency. The graph should remain a claim that can be examined, not an identity assigned to a person.

The validation program follows from the three layers. Human coding must test whether the recorded heuristic was introduced by the learner or supplied by AI, and whether it was repeated, transformed, or rejected. Process evidence must show that graph movement is not explained by exposure, verbosity, session count, task mix, or the interface. Relational models must add information beyond simple counts and node-level mastery estimates.

Then, for the stronger outcome claim, the support must disappear. Can the learner reconstruct the relation without seeing it? Use it beneath new surface features? Still use it after a meaningful delay?

The distinction is not academic hair-splitting. In Gajos and Mamykina’s nutrition experiments, assistance format changed both immediate decisions and incidental learning: requiring participants to reason from an explanation without a recommended answer produced gains that merely presenting advice did not reliably reproduce. In a four-session trial at one private high school in Turkey, generic GPT assistance improved mathematics-practice performance by about 48% while performance on the immediate unassisted examination was about 17% lower than control. These conditions do not establish a general effect of generative AI. Jointly successful work and learning carried forward are empirically separable.