Mathematics education (research) liberated from teaching and learning: Towards (the future of) doing mathematics
Bibliographic record
Abstract
Now, what do you make of that? We want to discuss mathematics education, and research in mathematics education (we don’t really need to specify, hence the parenthesis). And we want to address teaching and learning (mathematics, but we skipped the parenthesis this time around because we used the word just before) in terms of not-being. You will notice, however, the provocative presence of “liberated”, a strong verb which alludes to the idea of freedom while acknowledging certain constraints: captivity, dependence, and even liability. Its selection was a bold choice. But having made such a suggestive statement (without actually saying things upfront), we hastily print a colon to bring in a potential alternative – more positive, one should hope. This alternative mentions to be about going “towards” something. If we care enough to read the next parenthesis (yep, another set!), we realize that this something does not exist yet, since it lies in the future. This something we finally name with the title’s last breath: “doing|mathematics”. For those who haven’t read our recent articles (e.g., in French, Maheux & Proulx, 2014, or in English, Maheux & Proulx, 2015), what that is will remain obscure for some time. In a certain way, it is also still mysterious for us: it is the object of our research, so we haven’t “found” it yet. We haven’t really found out what “doing|mathematics” is, or what it does. As a piece of research, this article thus also aims to help us figure some of these things out. As a result, this communication piece is not merely for you. And after all, as Von Foerster used to say, in the end you’ll know more about us than about the topic of the paper.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.010 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".