The Effect of Concrete and Virtual Manipulative Blended Instruction on Mathematical Achievement for Elementary School Students
Bibliographic record
Abstract
Abstract Mathematics has been crucial to learning and extending the frontiers of knowledge in all academic areas. At the elementary level, several teaching approaches have been implemented to improve students’ mathematical achievement. However, compared to traditional teaching exposition techniques, the teaching with the use of math manipulatives has been found useful to enhance mathematical achievement. The current quasi-experimental study was carried out with Pakistani students, and aimed to explore the blended effect of concrete and virtual manipulatives on fifth-graders’ mathematical achievement. Different mathematical concepts such as whole number, decimals and percentages, fraction, unitary method, perimeter, area, and geometry from a grade 5 textbook were targeted for the intervention period. Following randomization, one section from a public school was chosen as a control group and the other section classified as an experimental group. The mathematical achievement of fifth graders was measured through mathematics achievement test (MAT), developed, and piloted for this particular study, in a pre–posttest design. The data were analysed using one-way ANCOVA and mixed between-within ANOVA test to examine the significant differences, if any exist, in pretest/posttest scores between and within the groups over the period of intervention. The results revealed blended use of concrete and virtual manipulatives significantly enhances students’ mathematical achievement as compared to the results achieved from traditional instruction. This study offers information for teachers and students to incorporate concrete and virtual manipulatives simultaneously in mathematics lessons.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".