Selected and Constructed Response Systems in Mathematics Classrooms
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.Request access from your librarian to read this chapter's full text.
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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 | 0.007 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.017 | 0.005 |
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".