Concrete Models in Improving Students Performance on Operations of Integers
DOI:
https://doi.org/10.5281/zenodo.22803928Keywords:
concrete models, color counters, number lines, integer operations, Grade 7 mathematics, quasi-experimental designAbstract
This quasi-experimental study examined the effectiveness of two concrete models - color counters and number lines - in improving Grade 7 students' performance in integer addition and subtraction. The study was conducted at Batasan National High School during School Year 2025-2026 and involved 35 learners from two intact Grade 7 classes: 17 in the experimental group and 18 in the control group. Both groups completed a validated 25-item researcher-made achievement test before and after a one-week instructional period. The instrument received an overall expert-validation mean of 4.00 (Highly Valid) and demonstrated good internal consistency in pilot testing (KR-20 = .868 for the pretest and .873 for the posttest). The experimental group was taught using color counters and number lines, whereas the control group received traditional lecture-based instruction. Baseline performance was statistically comparable, with mean pretest scores of 11.06 and 10.56 for the experimental and control groups, respectively, t(33) = -0.483, p = .632. At posttest, the experimental group achieved a higher mean score (M = 19.18) than the control group (M = 15.44), t(33) = -3.190, p = .003. Both groups improved significantly, but the experimental group obtained a substantially greater mean gain (M = 8.12, SD = 1.36) than the control group (M = 4.89, SD = 1.68), t(33) = 6.23, p < .001. Within the study context, color counters and number lines were associated with stronger learning gains than lecture-based instruction, supporting the purposeful use of concrete representations before or alongside symbolic procedures in integer instruction.
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