Bibliographic record
Abstract
Here is another collection of Fallacies, Flaws and Flimflam, mostly drawn from the column of this name in the College Mathematics Journal between 2000 and 2008. As in the first volume, there is a variety of items ranging from howlers (outlandish procedures that nonetheless lead to a correct answer) to errors that are deep or subtle often made by strong students. While some are provided for entertainment, others offer a challenge to the reader to determine exactly where things go wrong. There are many proposals to improve the quality of mathematics education, but they seldom address the need for students to pay careful attention to what they do and to check their work. It is through an engagement with meaning that students can avoid the pitfalls that come too naturally. Accordingly, this volume should be useful to teachers at all levels by giving them examples of flawed work they can use in the classroom. Encouraging students to find where someone else went wrong may help them avoid similar errors in the future. The items are sorted according to subject matter. Elementary teachers will not find much of use beyond Chapter 1, while middle and secondary teachers will find items in Chapters 1, 2, 3, 7, 8 that they might use. College teachers should find material in every part of the book. The mathematical topics covered include arithmetic, algebra, trigonometry, geometry, combinatorics, probability, and calculus.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.004 | 0.007 |
| Scholarly communication | 0.007 | 0.014 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.029 | 0.007 |
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".