The Emergence of 3D Geometry From Children's (Teacher-Guided) Classification Tasks
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Geometry, classification, and the classification of geometrical objects are integral aspects of recent curriculum documents in mathematics education. Such curriculum documents, however, leave open how the work of classifying objects according to geometrical properties can be accomplished given that the knowledge of these properties is the planned outcome of the curriculum or lesson. The fundamental question of the present study therefore is this: How can a lesson in which children are asked to participate in a task of classifying regular 3-dimensional objects be a geometry lesson, given that the participating 2nd-grade children do not yet classify according to geometrical properties (predicates)? In our analyses, which are inspired by ethnomethodological studies of work, we focus on the embodied and collective work that leads to the emergence of the geometrical nature of this lesson. Thus, we report both the collective and the individual work by means of which the lesson outcomes—the complete classification of a set of “mystery” objects according to geometrical (shape) rather than other (color, size, “pointy-ness”) properties—are achieved. In the process, our study shows how geometrical work is reproduced by 2nd-grade children who, in a division of labor with their teachers, produce a particular set of geometrical practices (sorting three-dimensional objects according to their geometrical properties) for the 1st time.
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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 | 0.007 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it