Selected and Constructed Response Systems in Mathematics Classrooms
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
This chapter examines two types of response technologies (selected and constructed) available to support discussion and participation in the classroom, and describes our experiences using and observing them in a variety of mathematics, science, and computer science classes at various educational levels. Selected response systems (a.k.a., clickers) display multiple-choice questions, and then collect and analyze student responses, and present distribution summaries to the class. Constructed response systems allow students to use handheld computers to generate free-form graphical responses to teacher prompts using various software applications. Once completed, students submit their responses to the instructor’s computer wirelessly. The instructor may then select and anonymously project these authentic student work samples or representations to promote classroom discussion. We review the purpose, design, and features of these two types of response systems, highlight some of the issues underlying their application, discuss our experiences using them in the classroom, and make recommendations.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 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