Rethinking How Students Judge Their Own Abilities: A Classic Psychology Model Gets a Mathematical Overhaul

For nearly four decades, one of the most celebrated ideas in educational psychology has rested on a seemingly simple observation: students judge how good they are at math partly by comparing themselves with classmates, and partly by comparing their math skills with their verbal skills. This framework, known as the internal/external frame of reference model, has generated hundreds of studies and two meta-analyses covering more than 200,000 participants. But a new systematic investigation published in Educational Psychology Review by Fabian Wolff, Jennifer Schumacher, and Jens Möller suggests that the field may have been reading the model’s statistical fingerprints incorrectly—and that the true power of social comparison on student self-concept may be substantially smaller than textbooks have long claimed.

The classic model, proposed by Herbert Marsh in 1986, makes two elegant predictions. First, students who perform well in math tend to develop strong math self-concepts, because they compare their grades or test scores with those of peers—a so-called external, or social, comparison. This produces a positive within-domain effect. Second, a student who excels in math often feels comparatively worse at English, even with decent English grades, because the two abilities are contrasted internally. This dimensional comparison produces a negative between-domain effect: high math achievement actually suppresses verbal self-concept, and vice versa. Meta-analytic results have confirmed both patterns with striking consistency across countries, age groups, and school types, making the model one of the most robust findings in the discipline.

The trouble, as Wolff first argued in 2021, lies in how the model’s coefficients are interpreted. In the standard specification, a student’s math self-concept is regressed on both math achievement and verbal achievement. Researchers have traditionally labeled the math-achievement coefficient a pure social comparison effect. But dimensional comparison theory defines dimensional comparisons as contrasts between one’s own achievements in two domains. If that is what students actually do, then the verbal achievement coefficient in the classic model does not capture the contrast itself—it captures only the part of the contrast that remains after the shared variance between the two achievement measures is partitioned. The contrast, in other words, leaks into the within-domain coefficient, inflating it.

To fix this, Wolff proposed the difference I/E model, a reparameterization in which self-concept in one domain is predicted by achievement in that same domain plus the difference between achievement in that domain and achievement in the other. Algebraically, the two models contain exactly the same information: they fit the data identically and explain the same variance. The between-domain effects are equal in magnitude and differ only in sign. But the within-domain effect in the classic model equals the sum of the within- and between-domain effects in the difference model. Using meta-analytic estimates, the authors calculate that the genuine within-domain effect on math self-concept might be around β = .37 rather than .57, and on verbal self-concept around β = .29 rather than .46—shifting the ratio of within- to between-domain effects from roughly 2.8 to about 1.8.

What was missing until now was a direct empirical test. The new research delivers one across six pre-registered studies. In the first, the team reanalyzed PISA 2000 data from 55,582 students in 26 countries—the same dataset Marsh and K.T. Hau used in their landmark 2004 cross-cultural validation. The logic was subtle. If the classic model’s within-domain effect already contains a between-domain component, then explicitly adding the other domain’s achievement as a predictor should increase the within-domain effect, because the shared contribution is now being counted twice. Conversely, in the difference model, adding the achievement difference should decrease the within-domain effect, because the dimensional component is being removed from it. Both patterns appeared exactly as predicted, and the changes scaled with the strength of the between-domain effects: in the Netherlands, where the negative between-domain effect on math self-concept was strong, the within-domain effect jumped by more than a quarter of a standard unit when the classic model was fully specified.

Study 2 brought in something the models alone cannot provide: students’ own reports of the comparisons they make. Nearly 950 German ninth- and tenth-graders rated how they judged their math and German achievement relative to classmates and relative to each other. When these explicit ratings were added to the models, the results were decisive. Controlling for social comparison ratings shrank the within-domain effects in both model versions while leaving the between-domain effects untouched. Controlling for dimensional comparison ratings reduced all four effects in the classic model, but only the between-domain effects in the difference model. Strikingly, the explicit comparison ratings were stronger predictors than the objective grades themselves, and the within-domain effects dropped by more than 60 percent—up to 85 percent in the difference model—once the ratings were accounted for.

Study 3 attacked the question from a third angle using moderator variables. Two beliefs—the conviction that math and verbal abilities are negatively related, and the perceived dissimilarity of the two subjects—should, on theoretical grounds, strengthen dimensional comparisons but have no reason to affect social comparisons. In the classic model, both beliefs significantly amplified all four effects, including the supposedly social within-domain effects. In the difference model, they amplified only the between-domain effects. This is precisely the signature one would expect if the classic model’s within-domain coefficients are contaminated by dimensional comparison processes, and it echoes earlier findings that had puzzled researchers who lacked the difference-score framework to interpret them.

The remaining three studies asked whether relative achievement information—the difference between grades in two subjects—is actually salient to students when they evaluate themselves. University students studying to become teachers reported relying on the difference between their math and German grades more than twice as strongly as on their grade in the other subject alone when reflecting on their school-day self-concepts. A replication with 229 secondary school students assessing their current self-concepts showed the same pattern, albeit with smaller effect sizes. In a deliberately exploratory sixth study, the authors posed the same forced choice to ChatGPT-5 across 145 prompts per domain; the language model chose the achievement difference in every single case, reasoning that the contrast between grades offers a more direct index of relative strength. The authors are careful to note that LLM responses reflect patterns in training data rather than human cognition, but the unanimous preference is at least consistent with the conceptual plausibility of difference-based self-evaluation.

The implications ripple outward. Prior studies that labeled the classic model’s within-domain effects as social comparison effects now require qualification, since those coefficients bundle together social and dimensional processes. Group comparisons—across ages, countries, ability levels, or teacher knowledge—may have drawn premature conclusions when between-domain effects differed alongside within-domain effects. Intervention research faces a parallel challenge: programs designed to boost self-concept in one domain can inadvertently depress it in another, as one study found when a math-values intervention lowered students’ German values. Promisingly, an intervention that explicitly taught students about dimensional comparisons raised math self-concept without harming verbal self-concept, with effects lasting at least six months.

The authors stop short of declaring the difference model superior. Both specifications encode identical information, and neither directly isolates psychological mechanisms; the difference model’s real contribution is interpretive transparency, making a theoretically grounded contrast explicit rather than hidden in algebraic cross-talk. Their practical recommendation is pragmatic: researchers can keep estimating the classic model within a single statistical framework, then use modern software to decompose the within-domain effects along difference-score lines. What the six studies establish is that the field’s most trusted coefficients deserve a more cautious reading—and that a 40-year-old model still has the capacity to surprise the scientists who know it best.

Subject of Research: The role of social and dimensional comparisons in academic self-concept formation within the internal/external frame of reference model

Article Title: Revisiting the Role of Social and Dimensional Comparisons in the Internal/External Frame of Reference Model: A Systematic Comparison of the Classic and the Difference I/E Model

Article References: Revisiting the Role of Social and Dimensional Comparisons in the Internal/External Frame of Reference Model: A Systematic Comparison of the Classic and the Difference I/E Model. (n.d.). https://doi.org/10.1007/s10648-026-10212-w

Image Credits: AI Generated

DOI: 10.1007/s10648-026-10212-w

Keywords: academic self-concept, internal/external frame of reference model, dimensional comparisons, social comparisons, educational psychology, difference I/E model, achievement, self-concept formation, PISA, meta-analysis, regression models, student motivation