Arguing for Access: Teachers’ Perspectives on the Use of Argumentation in Elementary Mathematics
Bibliographic record
Abstract
This study investigates teachers’ perspectives on the use of a mathematical argumentation teaching strategy in elementary mathematics in which students disprove mathematical statements they already know to be false. Mathematical argumentation is a process through which students develop an argument about a mathematical concept and rationalize its truth or untruth through mathematical reasoning but is if often underused in mathematics. In this study we focused on a argumentation tasks which involved providing students with number statements which they already knew to be false, and inviting them to argue, using visuals, numeric notation, and/or written explanations, why it was false. Through practical action research, seven teachers from two different schools implemented this approach in their mathematics programs to one hundred and thirty-one students over the course of five months. Findings indicate this approach was easy to implement, improved student engagement, supported learners who struggled and deepened students’ mathematical knowledge. We believe that this approach can be used as a precursor to more formal proofs and provide more access for teachers and students in exploring mathematical proofs in elementary classrooms.
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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 | 0.029 | 0.067 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.007 | 0.019 |
| Scholarly communication | 0.013 | 0.010 |
| Open science | 0.002 | 0.009 |
| Research integrity | 0.005 | 0.008 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".