Creating Problem Taxonomies for WeBWorK in Mechanical Engineering
Bibliographic record
Abstract
Abstract WeBWorK is an open-source, online homework system widely used in mathematics at the post-secondary level, with a number of institutions developing WeBWorK problems for use in engineering. The WeBWorK Open Problem Library (OPL) contains around 33,000 problems that are freely available to instructors to use within their courses (currently, around 200 mechanical engineering problems are available). The OPL problems are organized under a taxonomy structure of “subject”, “chapter”, and “section”, where subject is an area of study (e.g. linear algebra, probability, etc.), and chapter and section locate a particular problem within the subject (e.g. linear algebra – matrices – inverses), analogous to a textbook structure. Having an easily understandable and comprehensive taxonomy available makes it simpler for contributors to correctly designate their new problems, and for instructor-users to find appropriate problems to assign to their students. While there are some engineering problems available on the OPL, the taxonomies are either not extensive (few problems) or do not truly adhere to the structure above. As well, engineering instructors interested in building a few problems for their classes have the daunting task of creating a taxonomy structure in order to share them. We have created comprehensive proposed taxonomies in three core mechanical engineering subjects (statics, dynamics, mechanics of materials) and a partial taxonomy in a fourth (vibrations) for discussion and approval, and eventual use by future contributors. We have not found any literature that outlines practices for the creation of a new taxonomy, so we have documented our process and provide guidance for the creation of future OPL taxonomies in engineering. Finally, we outline suggestions for the systematic use of searchable keywords in OPL problems that can provide consistency across engineering subject areas and institutions. This work will lay the foundation for educators to more easily contribute to and utilize the growing body of open-source mechanical engineering problems in WeBWorK.
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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 | 0.007 | 0.041 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.019 | 0.011 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.008 | 0.012 |
| Open science | 0.003 | 0.007 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.019 | 0.008 |
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".