Feeling able is not the same as solving the problem

Steven Watson | EdgeLab | Research and Scholarship | 19 September 2026

What helps a student persist with an unfamiliar probability problem: explanation, encouragement, confidence, or some combination of all three? The question matters because probability asks learners to reason about uncertainty, not merely substitute numbers into a formula. A new Ghanaian study examines whether students who experience more teacher support also report greater self-efficacy and a stronger sense that they can solve probability problems.

What the study found

Lord Ampofo Adusei and colleagues surveyed 265 undergraduates at one public university in Ghana during the 2024–25 academic year. The sample comprised 101 first-year Mathematics Education students and 164 second-year Information Technology Education students, selected from departmental lists using proportionate stratified random sampling. All selected students completed an online questionnaire.

The open-access study measured three things on five-point scales: perceived teacher support, students’ belief in their own mathematical capability, and self-perceived probability problem-solving. This last distinction is crucial. The students rated statements about breaking down problems, choosing formulae, checking answers and interpreting results; they did not sit an independently scored probability test.

The authors used structural equation modelling to test their proposed relations. Perceived teacher support was positively associated with self-efficacy (standardised coefficient .559) and, more modestly, with self-perceived probability problem-solving (.218). Self-efficacy was also associated with self-perceived problem-solving (.190). A bootstrapped indirect path from teacher support through self-efficacy was statistically significant (.106, 95% confidence interval .052 to .164), while the direct path remained significant. The authors describe this as partial mediation.

The measurement work is a strength. The team piloted the questionnaire with 40 students outside the final sample, reported good internal consistency, and used exploratory and confirmatory factor analyses. The reported fit indices were strong: the comparative fit index was .978 and the root mean square error of approximation was .056. The study also gives valuable attention to probability learning in Ghanaian higher education, a setting too rarely represented in internationally visible educational research.

Association is not a learning pathway

The statistical pattern is plausible, but its interpretation needs care. All three variables came from the same questionnaire at the same moment. Structural equation modelling can estimate whether the observed responses fit a proposed directional model; it cannot supply the missing temporal sequence. The data therefore show associations consistent with mediation, not that teacher support caused confidence, which then caused better probability reasoning.

Reciprocal explanations remain possible. Students who already feel confident may interpret ordinary teaching more favourably, participate more visibly and elicit more support. A generally positive view of the course could also lift all three ratings. The authors apply Harman’s single-factor test and find that one factor explains 39% of the variance, below their 50% threshold. That check does not remove the basic same-source, self-report problem.

There is a second, more substantive gap. Feeling able to solve a probability problem is not the same as solving one. The article sometimes moves from “self-perceived probability problem-solving” to claims about performance, ability and higher-order thinking. Yet no scored problems, explanations or misconception probes were collected. Confidence may help students attempt a task, but accurate confidence and successful reasoning must still be demonstrated.

The study’s scope also limits generalisation. It covers one institution, two programmes and two different academic levels. Its strong completion rate is useful, but the design cannot separate programme, year or local teaching effects. The authors appropriately call for longitudinal, multi-institution and intervention studies.

An AE interpretation: support as a capacity to recover

The following is my interpretation, not the authors’ theoretical claim. Autopoietic ecology asks whether an arrangement merely produces an accepted output or renews the capacity to continue acting. In learning, teacher support matters not only when a student reports confidence or submits a correct answer. It matters when feedback, challenge and opportunities to revise help the learner recover from error and approach the next unfamiliar problem with more discriminating resources.

This reframes support as a relation rather than a dose delivered by a teacher. A mathematically useful classroom must make it possible to risk a conjecture, expose a mistaken assumption and revise a strategy without treating error as personal failure. Self-efficacy can then be understood as one condition of continued participation. But it should not be treated as evidence that the learner’s reasoning is already adequate.

EdgeLab’s Research Programme distinguishes the renewal of capacity from immediate performance. Applied here, the important question is whether supportive teaching changes what students can do later, especially when the surface features of a probability problem change. Does a student recognise conditional structure, challenge an equiprobability assumption and explain why a result is reasonable? Those observations would connect confidence with the development of mathematical judgement.

The AE Concept Guide also draws attention to mediation between forms of representation. A student’s rating, a solved problem, a teacher’s feedback and an institutional assessment are not interchangeable records of learning. Each preserves some distinctions and loses others. Treating confidence as competence collapses that chain too early.

What should come next?

A stronger follow-up would retain the relational insight while adding evidence over time. Students could complete probability tasks that reveal their reasoning, receive documented forms of instructional and emotional support, and repeat matched transfer tasks later. Classroom observation could distinguish encouragement, error clarification, worked examples, autonomy support and opportunities for revision. Interviews could then show how students interpret those encounters.

An alternative reading should remain live: teacher support may chiefly change students’ willingness to report confidence, while gains in probability reasoning depend on other features such as task design, prior knowledge and explicit attention to misconceptions. A longitudinal or classroom experiment could test these competing explanations rather than assuming the direction represented by the model.

Adusei and colleagues provide a useful account of how social support and self-belief travel together in an under-researched context. Its practical lesson is not simply “make students confident”. It is to build support that keeps students engaged with difficulty, while measuring whether that engagement becomes accurate, transferable mathematical reasoning.

Reference

Adusei, L. A., Agyebi, C. O., Enninful, S. E. K., and Arthur, Y. D. (2026). “Teacher support and university students’ self-perceived probability problem-solving: a mediation analysis of self-efficacy.” Frontiers in Education, 11, 1854658. Published 18 September 2026. https://doi.org/10.3389/feduc.2026.1854658. The publisher lists Jabeen Fayyaz as editor and John Mark R. Asio and Recep Bindak as reviewers.