Teaching Number: Advancing Children′s Skills and Strategies
Bibliographic record
Abstract
The book lets teachers identify where their students are in terms of number skills, and sets out a strategy for developing their knowledge. The authors show how to advance children's learning across five stages of early arithmetical learning - emergent, perceptual, figurative, initial number, and facile number. This provides for increasingly sophisticated number strategies across addition, subtraction, multiplication and division, as well as developing children's number word and numeral knowledge, and their ability to structure number and have grouping strategies. The approach used nine guiding principles for teaching. Each chapter has clearly defined teaching procedures which show how to take the children onto the next more sophisticated stage. The teaching procedures are organized into key teaching topics, and each includes: o a clearly defined purpose o detailed instructions, activities, learning tasks and reinforcing games o lists of responses which children may make o application in whole class, small group and individualised settings o a link to the Learning Framework in Number (see Early Numeracy- second edition, 2005) o how the guiding principles for teaching can be used to allow teachers to evaluate and reflect upon their practice Primary practitioners in Australia, the United States, the United Kingdom and Canada have tested the teaching procedures which can be used in conjunction with each country's numeracy strategy. Primary teachers, especially of the early years, mathematics co-ordinators, heads of school, mathematics advisers, special educationalists, learning support personnel, teacher assistants, lecturers in initial teacher training and educational psychologists will all find this book invaluable.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".