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Supporting Online Collaborative Learning in Mathematics

2009· book-chapter· en· W65450525 on OpenAlexaff
Rod Nason, Earl Woodruff

Bibliographic record

VenueIGI Global eBooks · 2009
Typebook-chapter
Languageen
FieldPsychology
TopicInnovative Teaching and Learning Methods
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematics educationMeaning (existential)Factor (programming language)Computer scienceMathematical problemMathematicsPsychologyProgramming language

Abstract

fetched live from OpenAlex

Most school math problems do not require multiple cycles of designing, testing and refining (Lesh & Doerr, 2003), and therefore, do not elicit the collaboration between people with different repertoires of knowledge that most authentic math problems elicit (Nason & Woodruff, 2004). Another factor that limits the potential of most school math problems for eliciting knowledgebuilding discourse is that the answers generated from school math problems do not provide students with much worth discussing (Bereiter, 2002a). Another factor that has prevented most students from engaging in ongoing discourse and other mathematical knowledge-building activity within CSCL environments is the limitations inherent in most computerbased mathematical representational tools (Nason et al., 1996). Most of these tools are unable to carry out the crucial knowledge-building functions of: 1) generating multiple representations of mathematical concepts, 2) linking the different representations, and 3) transmitting meaning, sense and understanding.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.002
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.033
Threshold uncertainty score0.110

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0010.001
Scholarly communication0.0030.005
Open science0.0020.004
Research integrity0.0020.001
Insufficient payload (model declined to judge)0.0330.011

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.

Opus teacher head0.042
GPT teacher head0.392
Teacher spread0.350 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designNot applicable
Domainnot available
GenreEmpirical

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".

Quick stats

Citations1
Published2009
Admission routes1
Has abstractyes

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