Abstract:

The Erasmus+ funded project DiToM (Diagnostic Tool in Mathematics) developed screening instruments for early identification of students at-risk at key transitions in European school systems. The consortium comprises seven partners: Bielefeld University (Germany), University of Paris-Est Créteil (France), Linnaeus University (Sweden), Free University of Bozen-Bolzano (Italy), University of the Aegean (Greece), University of Rijeka (Croatia), and the Spanish Federation of Mathematics Teachers (Spain).

Initial Situation:
Across Europe, national and international large-scale assessments indicate that a growing proportion of students does not reach minimum standards in mathematics by the end of primary and in lower secondary education, highlighting the need for preventive support structures and defensible allocation of support resources.

Background:
Setting cut-off scores is a sensitive step in screening development because it directly controls which students are flagged for follow-up diagnostics and targeted support. Common approaches (e.g. expert-based standard setting, prevalence-based rules, criterion-based optimisation) often face limitations regarding feasibility, replicability or reliance on external reference standards.

Objective:
This contribution proposes and evaluates a model-based procedure for determining cut-off scores for the DiToM Screening 6+. The approach adapts latent class analysis for cut-off score identification to the screening context to obtain transparent and reproducible decision rules.

Method:
Data were collected in Germany (June 2025) from N = 1010 students at the end of Grade 6. The paper-and-pencil screening contains 73 dichotomously scored items covering mathematical key skills in basic arithmetic, understanding of fractions, decimals and proportions. A three-class latent class analysis was estimated at item level. Given the screening purpose, we prioritised stability and interpretability over purely statistical criteria, a three-class solution supported a practicable differentiation into at-risk, monitoring and not at-risk groups. Cut-off scores were derived from intersections of smoothed posterior class-probability curves along the total score. Robustness was evaluated via multistart estimation and non-parametric bootstrap resampling.

Results:
The three-class solution yielded ordered performance profiles across all content areas and predominantly monotonic item probabilities (72/73 items). Intersections between adjacent posterior curves indicated two stable cut-off scores at 33 and 53 points (max score = 73), separating a low-performing risk group, an intermediate monitoring group and an inconspicuous as expected-performing group. Stability analyses supported the reproducibility of both cut-off scores across starting values and bootstrap samples.

Discussion:
Model-based cut-off scores operationalise latent performance profiles into transparent decision rules for group screening. Previous work suggests the usefulness of latent class–based cut-off procedures when benchmarked against alternative standard-setting approaches. In the present data, the resulting cut-off scores showed close alignment with those derived from the combined reference standard, suggesting that the LCA-based approach yields defensible classifications while reducing discretionary decisions. Future work will compare cut-off scores across countries and examine predictive validity for later mathematics outcomes and support needs.

Keywords:

Screening, cut-off scores, latent class analysis, mathematical key skills, DiToM.