Design, Construction, Validation, and Standardization of a Psychometrically Reliable Mathematical Achievement Test for Grade X Students: An Empirical Study on Reliability, Validity, and Educational Measurement in Secondary Mathematics
Bibliographic record
Abstract
This study aimed to design, construct, and standardize a Mathematical Achievement Test (MAT) for Grade X students, ensuring that the instrument meets the psychometric standards of reliability, validity, and objectivity.Recognizing the growing importance of mathematics education in the 21st century-an era increasingly defined by data, computation, and problem-solving-the test was developed to measure students' mathematical understanding, conceptual application, and analytical reasoning.The preliminary version of the test contained 50 multiple-choice items derived from the official secondary school mathematics curriculum.After pilot testing on a sample of 810 students across diverse educational contexts, 40 items were retained through rigorous item analysis and expert review.The construction process followed standardized psychometric stages: item generation, content validation, pilot administration, item discrimination and difficulty index computation, test standardization, and reliability and validity estimation.Reliability was assessed using Cronbach's alpha (α = 0.881) and split-half reliability (r = 0.973), confirming internal consistency and stability.Validity evidence was obtained through intrinsic validity (r = 0.938) and criterionrelated validity (r = 0.882), indicating a high correlation with students' actual classroom performance.The findings affirm that the MAT is a scientifically robust, pedagogically relevant, and statistically valid tool for assessing mathematical proficiency among Grade X learners.This standardized instrument contributes to the body of research on educational measurement and offers teachers, curriculum developers, and educational policymakers a reliable means to evaluate mathematical learning outcomes and identify instructional gaps.
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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 | 0.028 | 0.049 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".