Nigerian Teachers’ Perceptions of using Multiple Representations to Solve Mathematics Problems
Bibliographic record
Abstract
The use of representations in the teaching and learning of mathematics has shown promise. Representation can mean both the actual materials and images used to illustrate a mathematical idea, such as a model created from plastic classroom manipulatives, and it can also mean the act of generating such forms. This study of 71 grade eight teachers in Nigeria used a survey to examine participants’ self-reported beliefs and knowledge about the use of representations in mathematics teaching. A subset of the teachers was also interviewed and asked to solve mathematics-related problems. The results suggest that, in most cases, while teachers were interested in learning more, their understanding of types of representations tended to be centered around the more mathematically traditional ones such as symbols and graphs, with the teachers themselves doing the representing. There was little evidence that teachers supported students in generating their own representations to solve problems. Teachers expressed interest in the potential of representations, but indicated they needed more professional training in order to do so. Recommendations for teacher education and professional development are included.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".