Introducing angles in grade four : a realistic approach based on the van Hiele Model
Bibliographic record
Abstract
This thesis is a study of teaching and learning Geometry, and, in particular, angles. The theoretical framework used in the research is a combination of a teaching theory called Realistic Mathematics Education (RME) and a learning theory called the can Hiele Model of Geometric Thinking. These frameworks, backed up by a historical study of geometry, were used in the design, experimentation and evaluation of a lesson where fourth grade students were introduced, for the first time, to the idea of angle and relations between angles of different sizes. The in-class experiment was conducted in two different fourth grade classrooms. The lessons were taught by teachers of the respective classrooms, based on a detailed script and materials prepared by the researcher. At the end of the lesson the students answered, in writing, questions on what they had learned during the lesson. These answers, combined with the classroom observations, provided a basis for the evaluation of the experiment. The written answers were categorized into analytical and narrative statements. The analytical statements were divided into the different levels of the van Hiele Model. The narrative statements were divided into whether or not they mentioned angles. The research findings suggest the usefulness of using lesson plans based on the two theoretical frameworks in helping students develop an analytical conceptualization of mathematics.
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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 | 0.002 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".