Impulsing the Development of Students' Competency Related to Mathematical Thinking and Reasoning through Teaching Straight-Line Equations
Bibliographic record
Abstract
The research was carried out to develop students' ability to think and reason mathematically by teaching straight-line equations in a plane. Accordingly, teaching activities were designed according to five learning stages, which were integrated with mathematical thinking levels according to Van Hiele's model. Simultaneously, the learners' mathematical thinking and reasoning competencies were assessed according to the competency requirements specified in the Mathematics General Education Program and the levels of Van Hiele's model, the above three aspects of knowledge, skills and attitudes. The experiment involved 84 students in class 10, 44 of whom were in the experimental group, and 40 were in the control group. The research results showed that students in the experimental group achieved higher mathematical thinking and reasoning skills. Specifically, the two groups had equivalent results for the level of visualization and analysis. However, at the informal deduction and formal deduction and rigor levels, the ranking results of the two groups had a clear difference. The study group observations and students' opinion surveys also revealed that learning stages were designed according to Van Hiele's model and thought-provoking measures and visual images and language contributed to students' interest in learning and positive thinking.
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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 | 0.005 |
| 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 | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".