Construction of High School Students’ Abstraction Levels in Understanding the Concept of Quadrilaterals
Bibliographic record
Abstract
The purpose of this study was to examine the abstraction thinking or the vertical reorganization activity of mathematical concepts of high school students while taking account of the abstraction that was constructed earlier, and the socio-cultural background. This study was qualitative in nature with task-based interviews as the method of collecting the data. It involved 62 high school students, and conducted for one year. The study focused on activities related to how the subjects grouped plane figures, recognized the attributes of each two plane figure, recognized the relation among them based on their attributes, defined plane figures, connected their attributes, as well as constructed the relations among plane figures. The results indicates that the abstraction level of high school students in constructing the relations among quadrilaterals consists of concrete visual level, semi-concrete visual level, semi-abstract visual level, and abstract visual level, together with indicators of each level. Therefore, the researchers suggest that it is necessary to design a learning activity that facilitates the four levels of abstraction, so that a student might increase his/her level of abstraction.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 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".