A Meta-Analysis: Improvement of Students’ Algebraic Reasoning through Metacognitive Training
Bibliographic record
Abstract
Although algebraic reasoning has been considered as an important factor influencing students’ mathematical performance, many students struggle to build concrete algebraic reasoning. Metacognitive training has been regarded as one effective method to develop students’ algebraic reasoning; however, there are no published meta-analyses that include an examination of the effects of metacognitive training on students’ algebraic reasoning. Therefore, the purpose of this meta-analysis was to examine the impact of metacognitive training on students’ algebraic reasoning. Eighteen studies with 22 effect sizes were selected for inclusion in the present meta-analysis. In the process of the analysis, one study was determined as an outlier; therefore, another meta-analysis was reconstructed without the outlier to calculate more robust results. The findings indicated that the overall effect size without an outlier equaled d=0.973 with SE=0.196. Q=20.201 (p<.05) and I2=0.997, which indicated heterogeneity of the studies. These results showed that the metacognitive training had a statistically significant positive impact on students’ algebraic reasoning.
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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 | 0.017 | 0.041 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.011 | 0.045 |
| Bibliometrics | 0.007 | 0.006 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".