POSTER: A Validity Argument Approach to Collaborative Development of the Colleges Mathematics Assessment Program
Bibliographic record
Abstract
Introduction Ensuring that a test will produce results that are valid for the intended uses, such as the placement of students into community college mathematics courses, begins during test development. When test development is a collaboration among intended users, such as the community colleges within a province, communicating to all collaborators the implications of the many decisions that must be made about content, format, scoring, and reporting is especially important. Objectives This paper describes and illustrates a validity argument approach to support collaborative test development through the example of Ontario’s Colleges Mathematics Assessment Program (CMAP). Design/Methodology For mathematics tests, Schilling and Hill (2007) have proposed a variation on Kane’s (2002, 2013) validity argument approach. The assumptions required to support the proposed use of the test results and corresponding evidence for those assumptions are organized into three categories: (1) Elemental – concerning the performance of specific test items, (2) Structural – concerning the internal structure of the test, and (3) Ecological – concerning the external structure of the test. In this paper, we use Schilling and Hill’s (2007) three categories to relate the assumptions and evidence to decisions made in developing the test. Results The resulting validity argument makes explicit why each test development decision is important and what types of evidence might inform or support each decision. For use with collaborators with minimal test development experience or expertise, the elements of the argument are expressed in non-technical language. Conclusions In one of their critiques of Kane’s validity argument approach, Schilling and Hill (2007) note the scarcity of real-world examples using an interpretive argument approach. This study provides an illustration of this approach, with a particular emphasis on the use of non-technical language to support collaborative test development. References Kane, M. (2002). Validating high-stakes testing programs. Educational Measurement: Issues and Practice, 21 (1), 31-41. Kane, M. (2013). Validating the interpretations and uses of test scores. Journal of Educational Measurement, 50, 1-73. Schilling, S. G., & Hill, H. C. (2007). Assessing measures of mathematical knowledge for teaching: A validity argument approach. Measurement: Interdisciplinary Research & Perspectives, 5 (2/3), 70-80.
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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 | 0.059 | 0.094 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.010 | 0.013 |
| Scholarly communication | 0.012 | 0.008 |
| Open science | 0.004 | 0.010 |
| Research integrity | 0.007 | 0.006 |
| Insufficient payload (model declined to judge) | 0.049 | 0.005 |
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".