—Examining the Impact of a Mental Computation Classroom Intervention on the Relational Thinking of Seventh-Grade Students
Bibliographic record
Abstract
The present study examined the impact of a mental computation intervention on the relational thinking and equivalence knowledge of seventh-grade students.The instructional intervention focused on classroom discussions, the sharing of mental computation strategies, and conceptual scaffolding from the teacher.A multiple baseline design was used with 66 students in three classes.In each class, students were assessed at five time points on (a) mental computation, (b) mathematical equivalence problem solving, and (c) relational thinking, which was assessed by asking students to make judgments about true-false number sentences.Students in one class improved on equivalence problem solving after the intervention, although ceiling effects mitigated the observation of potential instructional benefits.All students improved their relational thinking skills, and performance paralleled observed gains in mental computation in two of the three classes.Relational thinking performance levels were maintained for up to 12 weeks.The link between mental mathematics and relational thinking implies that mental computation should play a more prominent role in the seventh-grade mathematics classroom.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".