Using the Attribute Hierarchy Method to Make Diagnostic Inferences about Examinees' Cognitive Skills in Algebra on the SAT.
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Bibliographic record
Abstract
The purpose of this study is to apply the attribute hierarchy method (AHM) to a sample of SAT algebra items administered in March 2005.The AHM is a psychometric method for classifying examinees' test item responses into a set of structured attribute patterns associated with different components from a cognitive model of task performance.An attribute is a description of the procedural or declarative knowledge needed to perform a task.These attributes form a hierarchy of cognitive skills that represent a cognitive model of task performance.The study was conducted in two steps.In step 1, a cognitive model was developed by having content specialists, first, review the SAT algebra items, identify their salient attributes, and order the item-based attributes into a hierarchy.Then, the cognitive model was validated by having a sample of students think aloud as they solved each item.In step 2, psychometric analyses were conducted on the SAT algebra cognitive model by evaluating the model-data fit between the expected response patterns generated by the cognitive model and the observed response patterns produced from a random sample of 5000 examinees who wrote the items.Attribute probabilities were also computed for this random sample of examinees so diagnostic inferences about their attribute-level performances could be made.We conclude the study by describing key limitations, highlighting challenges inherent to the development and analysis of cognitive diagnostic assessments, and proposing directions for future research. Note: This is a multimedia articleAll multimedia components are enclosed in blue.Acrobat Reader 8.0 and Acrobat Flash Player 9.0 or higher are required.These programs, which are free, can be accessed and installed from the Adobe website (www.adobe.com).This article contains "mouse-over" actions in Figure 1 to illustrate how the attributes are measured with sample algebra items from the SAT.This article also contains multimedia clips.We present the reader with three embedded videos in Figures 2 to 4 to illustrate how a student actually solves an item.Figures 5 to 10 contain embedded audio clips so the reader can hear how a student solves an item .These video and audio clips supplement our text descriptions of the attributes to provide the reader with more concrete examples about the cognitive skills that constitute each attribute and how attributes are hierarchically related.
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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 | 0.004 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.000 | 0.001 |
| 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 it