Enhancing Students’ Understanding of Functions and Graphs through GeoGebra-Based Instruction
Bibliographic record
Abstract
Proficiency in functions and graphs is fundamental in Senior High School mathematics, serving as a prerequisite for advanced courses in calculus, statistics, and real-world applications. This study employed a quasi-experimental two-group pretest–posttest design to compare the effectiveness of the Traditional Lecture Method (TLM) and GeoGebra-based instruction in teaching functions and graphs to Grade 11 GAS students at Dapa National High School, S.Y. 2022–2023. Fifty students were purposively selected and randomly assigned into two groups of 25 each. The TLM group was taught through lecture-discussion and chalkboard demonstrations, while the GeoGebra group used interactive software for dynamic visualization. Results showed that in the first trial run, the TLM group improved from 28.18% (Low Mastery) to 39.45% (Average Mastery), while the GeoGebra group increased from 30.27% (Low Mastery) to 68.71% (Moving Towards Mastery). In the second trial run, the TLM group advanced from 33.45% to 66.13%, whereas the GeoGebra group progressed from 35.76% to 80.21%. ANCOVA confirmed a statistically significant difference favoring GeoGebra (p < 0.05). Perception results revealed a grand mean of 3.17 (Moderately Perceived), with students strongly agreeing on GeoGebra’s user-friendliness, motivational value, and effectiveness in visualizing graphs. Findings suggest that integrating GeoGebra enhances mastery, motivation, and engagement, making it a valuable instructional tool for strengthening mathematics learning.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| 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 | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".