Bridging Gaps: Pre-Service Mathematics Teachers’ Handling the Difficulties in Posing Real-World Mathematical Problems
Bibliographic record
Abstract
Real-world mathematical problem (RWMP) solving and posing are important aspects of teaching and learning mathematical modelling, as well as developing a mathematization disposition for both teachers and students. Several researchers have explored blockages or difficulties in such modelling processes and in problem posing. However, prior research has identified difficulties that the pre-service mathematics teachers (PSMTs) encountered when they tried to pose a modelling problem by choosing the general topic themselves, as there is little known about possible obstacles that PSMTs can encounter when trying to pose a real-world problem relevant to a given mathematical topic. The current study explored the difficulties encountered by PSMTs in a RWMP-posing activity. The target group was 23 PSMTs with prior experience in mathematical modelling and mathematical problem posing. The findings showed that the PSMTs struggled with: (a) task organization, which involved selecting and understanding mathematical knowledge; (b) specialized content knowledge, which included a lack of real-world knowledge and difficulty in connecting mathematical concepts to real-world contexts; and (c) individual considerations of aptness, which encompassed authenticity, interest, complexity, language, and relevance to task organization. The PSMTs applied various strategies to complete the posing task, such as using problem-posing and solving heuristics, adapting existing problems, sharing and discussing with friends, and considering the perspective of a typical student. The implications of these findings should help in developing preparatory instructional practices for mathematics teachers.
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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 | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".