Bibliographic record
Abstract
The title of this article is borrowed from a panel presentation at a recent conference. [1] At the close of our annual meeting, four members of the Canadian mathematics education community were invited share their thoughts on the topic of why mathematics is taught. My contributions this discussion were similar the arguments I made some years ago in an article in this journal (Davis, 1995), in which I attempted bring enactivist thought (Varela, 1999; Varela, Thompson and Rosch, 1991) bear on the question of why we teach mathematics. Through the session, though, some inadequacies with that thinking were highlighted. In particular, the seemingly innocuous phrase to all students, tacked the end of the question Why teach mathematics?, occasioned considerable response at the conference around matters of changes formal education over the past century, Western tendencies toward cultural imperialism and popular assumptions concerning a transcendent mathematics. Further issues have been raised by Peter Huckstep (2000) in his recent contribution the expanding debate around rationales for teaching mathematics. Among other matters, Huckstep argues that the utility of mathematics remains as viable a basis for teaching the subject as it ever was. He further suggests that other rationales which are more grounded in psychological and sociological discourses, while worthy of discussion, are not as compelling as those that are built on an acknowledgment of the usefulness of the subject matter. While I agree with Huckstep on the former point, I think that I disagree on the latter. In any case, prompted by my conference presentation and Huckstep 's discussion, I find that I am no longer comfortable with many aspects of my earlier article on the issue, and so I offer this account. With regard that past piece, this one might be seen as part elaboration, part clarification and part abdication.
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 | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.005 | 0.005 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.026 | 0.010 |
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".