Bibliographic record
Abstract
Recent trends in mathematics education emphasize discovery learning over drill. This has proven to be a bad idea in some cases, for the simple reason that practice is required to learn basic arithmetic skills. Drills in arithmetic skills can be made interesting through gamification. This study proposes a family of puzzles that gamify arithmetic practice. The puzzles are designed with an evolutionary algorithm forming an instance of automatic content generation. Two methods of evolutionary puzzle design are presented and discussed. The first method used transformed the problem into an almost trivial optimization. The second algorithm was designed to avoid the flaws of the first and produced a huge variety of puzzles. A hardness measure, based on the difficulty experienced by the evolutionary puzzle generator, is employed. The hardness measure is tested on a large collection of puzzles produced with the evolutionary automatic content generation system. An initial assumption, that all the pieces in the puzzle must be used to achieve a maximum score, was shown to be incorrect in puzzles located via automatic search. Two classes of puzzle are defined: those where the optimal solution uses all pieces and those where the optimal solution fails to use at least one piece. The latter sort of puzzle were found to be far more common in the search space.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.019 | 0.002 |
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".