Formative Assessment Linked to Perceived Math Achievement Through Cognitive Activation

Students in Ghanaian senior high schools who reported more frequent experiences of formative assessment in their mathematics classrooms also tended to report higher perceptions of their own mathematical achievement, according to a new quantitative survey study published in Frontiers in Education. The research, led by Anatu Buffiama Issah of the Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development in Kumasi, Ghana, together with Joseph Frank Gordon and Benjamin Obeng Adu, went a step further than most earlier work by testing whether cognitively activating instruction, in which students are pushed to explain reasoning, justify solutions and connect mathematical ideas, statistically accounts for part of that association.

The study surveyed 320 senior high school students drawn from two public schools through a multistage sampling procedure. From an accessible population of 1,200 students, the researchers first purposively selected the two schools, then used proportionate stratified sampling to allocate participants across programme categories, and finally simple random sampling to pick individual respondents. The sample spanned six academic programmes, with Home Economics the largest group at 93 students (29.1 percent), followed by General Science with 79 (24.7 percent), General Arts with 55 (17.2 percent), Visual Arts with 48 (15.0 percent), Technical with 29 (9.1 percent) and Business with 16 (5.0 percent). Just over half of the respondents, 171 students (53.4 percent), were male, and 281 (87.8 percent) were aged between 16 and 20 years.

All three constructs in the model were measured through a structured questionnaire using five-point Likert scales, and the authors are explicit that these are student self-reports rather than objective measures. Formative assessment practices captured students’ reported experiences of feedback, questioning, self-assessment, peer feedback, monitoring of understanding and instructional adjustment. Cognitive activation-oriented instruction covered experiences such as being encouraged to explain why a solution is correct, compare different solution methods, connect new ideas with previous knowledge and justify answers. Perceived students’ mathematical achievement reflected self-reported understanding of topics, confidence in solving problems, learning progress, examination confidence and overall performance beliefs, a construct the authors deliberately distinguish from achievement measured through examinations or standardized tests.

On the technical side, the team screened the data in IBM SPSS Statistics version 23 and then ran confirmatory factor analysis and structural equation modelling in AMOS version 23. Exploratory factor analysis with the full sample produced a Kaiser-Meyer-Olkin value of 0.904 and a significant Bartlett’s test of sphericity (chi-square = 3,498.745, df = 120, p < .001), with three factors explaining 68.458 percent of the total variance and item loadings ranging from 0.741 to 0.885. The measurement model fit the data well, with CMIN/DF = 1.649, TLI = .968, NFI = .932, CFI = .972, SRMR = .036 and RMSEA = .042. Composite reliabilities of 0.838 to 0.929 and average variances extracted of 0.561 to 0.685 supported convergent validity, while the Fornell-Larcker criterion supported discriminant validity among the three constructs. Cronbach’s alpha values were 0.836 for cognitive activation, 0.883 for formative assessment and 0.928 for perceived achievement.

The structural results were consistent across all four hypotheses. Formative assessment practices showed a positive, statistically significant relationship with perceived mathematical achievement (β = .174, S.E. = .084, C.R. = 2.071, p = .012). The association between formative assessment and cognitive activation-oriented instruction was considerably stronger (β = .541, S.E. = .063, C.R. = 8.587, p < .001), suggesting that students reporting greater exposure to feedback and monitoring practices also reported more cognitively demanding lessons. Cognitive activation-oriented instruction was itself positively associated with perceived achievement (β = .199, S.E. = .088, C.R. = 2.261, p = .005). Age, gender and programme of study were included as control variables and were not significant predictors.

The mediation test, conducted with bootstrapping in AMOS, yielded a standardized indirect association of β = .131 with a 95 percent confidence interval of (.013, .278) and p = .031. Because the interval excluded zero, the indirect pathway was statistically significant, and since the direct path from formative assessment to perceived achievement remained significant (β = .174, p = .012), the pattern indicates statistical partial mediation. In plain terms, students who reported richer formative assessment experiences tended to report both more cognitively activating instruction and higher perceived mathematical achievement, with part of the association running through the instructional pathway. The authors caution that, given the cross-sectional design, these are statistical indirect associations rather than evidence of a causal mechanism.

The study was grounded in an integrated framework drawing on Assessment for Learning Theory, the cognitive activation perspective on instructional quality and Constructivist Learning Theory. Within this framework, formative assessment is conceptualised as eliciting and using evidence of learning, while cognitive activation concerns the cognitive demand of the mathematical activity generated during instruction. The authors note that although questioning can support both processes, the two constructs are treated as distinct, and the theoretical model proposes that formative assessment relates to perceived achievement both directly and indirectly through cognitively activating instruction. Because the design is cross-sectional, the hypothesized pathways represent statistical relationships rather than causal effects.

The findings sit within a Ghanaian context where mathematics achievement at the senior high school level remains a persistent concern, with successive West African Examinations Council reports indicating fluctuating and generally unsatisfactory performance. Prior Ghanaian studies cited by the authors suggest that teachers are often aware of formative assessment principles but apply them inconsistently, and that mathematics instruction frequently emphasizes procedural learning at the expense of conceptual understanding and higher-order reasoning. The new results, interpreted at the level of student perceptions, add evidence that reported formative assessment experiences are positively interrelated with reported cognitively activating instruction and perceived achievement in this setting.

The authors also tested for common method bias, a concern whenever all variables come from the same respondents at the same time. Harman’s single-factor test showed the first unrotated factor accounted for 34.45 percent of the total variance, below a majority share, so common method bias was not considered a dominant concern, although the authors acknowledge it cannot be completely ruled out. They further note that CFA confirmed the measurement structure within the present sample rather than providing independent cross-validation, and that students were nested within shared school and classroom contexts, a potential clustering that was not explicitly modelled in the analysis.

The limitations section is candid. Beyond the cross-sectional design and reliance on self-reported perceptions, the study measured perceived rather than objective mathematical achievement, and the two purposively selected schools limit generalisability beyond the participating institutions. The authors recommend that future research employ longitudinal or experimental designs, incorporate objective achievement measures, classroom observations and teacher data, include larger numbers of schools and classrooms with multilevel analytical approaches where appropriate, and examine additional mediating or moderating variables such as mathematics self-efficacy, mathematics anxiety or learning engagement. Within those boundaries, the study’s contribution is to show that students’ reported experiences of formative assessment, cognitive activation-oriented instruction and perceived mathematical achievement are significantly interrelated, and that cognitive activation-oriented instruction statistically accounts for part of the link between assessment experiences and students’ perceptions of their own mathematical achievement.

Subject of Research: The relationship between formative assessment practices and perceived mathematics achievement among Ghanaian senior high school students, with cognitive activation-oriented instruction as a statistical mediator.

Article Title: Formative assessment practices and perceived students’ mathematical achievement in senior high schools: the mediating role of cognitive activation-oriented instruction

Article References: Issah, A. B., Gordon, J. F., & Adu, B. O. (2026). Formative assessment practices and perceived students’ mathematical achievement in senior high schools: the mediating role of cognitive activation-oriented instruction. Frontiers in Education, 11, 1953835. https://doi.org/10.3389/feduc.2026.1953835

Image Credits: AI Generated

DOI: 10.3389/feduc.2026.1953835

Keywords: formative assessment, cognitive activation, mathematics achievement, Ghana, senior high school, structural equation modelling, student perceptions, instructional quality, cross-sectional survey, mediation analysis, Formative, assessment