Systematic Error Analysis in Technology-Enhanced Calculus: Comparing Maple and GeoGebra Approaches in Pre-Service Teacher Education in Ghana
Keywords:
GeoGebra, Maple, Pólya, Technology-Enhanced, CalculusAbstract
The study focused on errors committed by 120 Ghanaian Pre-service teachers learning the volumes of solids of revolution (VOSR) through the lecture method or technology-enhanced instruction (TEI) using Maple and GeoGebra. A quasi-experimental pretest–posttest nonequivalent groups design was used. The errors were categorised according to Pólya's four problem-solving stages: understanding, planning, carrying out, and verification. The errors at pretest were dominated by those in verification (77.5%) and carrying out (70.0%), with no difference between the groups. Errors at pretest were dominated by those of verification (77.5%) and carrying out (70.0%), with no differences between groups. Technology group error reduction was significantly higher than that of the lecture instruction group after 8 weeks. Mean errors decreased by 78.3% for Maple (M pretest = 115, M posttest = 25) and 76.9% for GeoGebra (M pretest = 104, M posttest = 24), compared to 41.2% for lecture (M pretest = 114, M posttest = 67). Concept errors were reduced the most by Maple (88.0%), and procedural errors by GeoGebra (84.0%). For both, the number of calculation errors decreased (GeoGebra: 8.3%; Maple: 5.0%). The highest percentage of spatial reasoning errors was found in the group using GeoGebra (25.0%), and the verification errors were high across all groups, with significant differences between the lecture and the technology groups according to χ² analysis (χ²(3, N = 116) = 15.23, p = .002, V = .58) but not between Maple and GeoGebra.
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