Multidimensional Diagnostic Technique for Mathematical Proficiency with Automated Feedback Generation
Bibliographic record
Abstract
This research addresses the critical gap in the automated assessment of open-ended mathematical responses by developing a novel diagnostic technique that integrates multidimensional item response theory with real-time analysis of misconceptions and adaptive feedback generation. Unlike existing automated assessment systems limited to multiple-choice formats or binary scoring, this study pioneers the automated evaluation of subjective mathematical work in geometry and algebra while simultaneously diagnosing specific misconception patterns. The research analyzed 517 seventh-grade students’ responses across four Thai regions to establish empirically grounded cutoff points for five proficiency levels in two dimensions: mathematical processes (-2.37, -0.16, 0.89, 1.06) and conceptual structures (-2.69, 0.24, 0.46, 1.03). The innovative contribution lies in categorizing misconceptions into four distinct types (overgeneralization, defective mathematical understanding, mistranslation, and limited conception) and linking each to five differentiated feedback modes, creating a pedagogically-driven automated response system. The multidimensional model demonstrated superior psychometric properties compared to unidimensional approaches, with reliability coefficients of 0.83 and 0.80 for the respective dimensions. Implementation within the eMAT-Testing platform enabled real-time diagnostic capability, processing subjective responses containing mathematical expressions, and providing targeted feedback based on identified misconception patterns. This breakthrough enables the use of a scalable formative assessment technique previously requiring human expertise, with system evaluation showing the highest appropriateness ratings for user interaction (x̄ = 5.00, SD = 0.00) and responsibility aspects (x̄ = 4.89, SD = 0.58). The technique’s novelty extends the application of construct modeling theory to automated assessment practice, demonstrating how sophisticated psychometric frameworks can maintain rigor while delivering immediate, pedagogically-meaningful diagnostic information for differentiated instruction.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.071 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".