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 ( = 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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.015 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".