Preservice Teachers' Understandings of Relational and Instrumental Understanding
Bibliographic record
Abstract
This paper reports on the responses of a cohort of preservice primary teachers to a statement about the extent to which helping children achieve relational understanding is a realistic expectation. Although the preservice teachers ’ course had included teaching about understanding a number of misconceptions about the meanings of relational and instrumental understanding were evident in the responses of a sizeable minority, along with evidence that many held beliefs that were likely to result in them teaching instrumentally. The findings highlight the idiosyncratic nature of preservice teachers ’ knowledge construction and draw attention to a range of disparate meanings that may be attached to the term ‘understanding ’ even when it is qualified with other words such as ‘instrumental ’ or ‘relational’. BACKGROUND AND THEORETICAL FRAMEWORK Ongoing calls for reform in education generally and mathematics education in particular have stressed the importance of teaching for understanding (e.g. NCTM, 2000). In several Australian states, including Tasmania where this study was conducted, significant shifts to values-based curricula that place a heavy emphasis on
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 | 0.006 | 0.020 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.003 | 0.007 |
| Scholarly communication | 0.005 | 0.003 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.001 | 0.004 |
| 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".