MétaCan
Menu
Back to cohort
Record W3102201288 · doi:10.5951/mt.96.4.0249

Penny Packing for Your Thoughts

2003· article· en· W3102201288 on OpenAlex
Stanley J. Bezuszka, Margaret J. Kenney

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.

aboutThe title or abstract carries a Canadian signal from the geographic lexicon.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueMathematics Teacher Learning and Teaching PK-12 · 2003
Typearticle
Languageen
FieldComputer Science
TopicTeaching and Learning Programming
Canadian institutionsnot available
Fundersnot available
KeywordsCover (algebra)Quarter (Canadian coin)PennySet (abstract data type)MathematicsTask (project management)Mathematical economicsCombinatoricsComputer scienceEconomicsManagementEngineeringHistory

Abstract

fetched live from OpenAlex

Packing pennies onto a piece of paper provides perplexing problems for students to ponder. To set the stage for students to gain insight into penny-packing problems, we suggest that you provide groups of students with small sheets of paper and an ample supply of pennies. At the start of the investigation, a quarter of a standard-size 8.5 in.- by-11 in. sheet of paper is sufficient for each group. Ask the groups to cover their paper completely with pennies. Students typically choose one of the covering patterns shown in figure 1 and figure 2 . As part of the task, students should determine the number of pennies needed to completely cover the paper using each pattern. The penny-packing problem is, Which pattern guarantees the most pennies on the page?

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.005
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.933
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0050.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0020.000
Scholarly communication0.0010.000
Open science0.0010.000
Research integrity0.0000.002
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.037
GPT teacher head0.298
Teacher spread0.261 · 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