Hypothetical learning trajectory on cylinder with Bloom's taxonomy perspective
DOI:
https://doi.org/10.30862/jhm.v8i1.848Keywords:
Bloom’s taxonomy, conceptual understanding , cylinder, hypothetical learning trajectoryAbstract
Students’ persistent difficulties in understanding three-dimensional geometric figures, particularly cylinders, due to limited spatial visualization and difficulty identifying relationships among their elements, such as cylinder nets. These difficulties are often rooted in traditional instructional practices that emphasize procedural tasks over conceptual development. Despite various interventions, there remains a lack of structured instructional models based on cognitive development frameworks to support students’ conceptual growth in geometry. Addressing this gap, the present study aims to develop and evaluate a Hypothetical Learning Trajectory (HLT) grounded in Bloom’s taxonomy to enhance students' understanding of cylinders. This study employed a design research methodology consisting of three phases: preliminary design, design experiments, and retrospective analysis. Two experimental cycles were conducted with 28 fifth-grade students, categorized into low, moderate, and high levels of understanding. Data were collected through classroom observations, student worksheets, tests, and interviews, and analyzed qualitatively. The HLT consisted of four key learning activities: modeling a cylinder, identifying its elements, constructing the net, and solving application problems, mapped to Bloom’s cognitive levels of remembering, understanding, and applying. Findings revealed that students showed significant improvement in the first three activities, with increased spatial reasoning and conceptual clarity. However, difficulties persisted in the final activity involving reasoning and problem-solving. The results indicate that the proposed Bloom’s taxonomy-based HLT offers a systematic framework for guiding geometry instruction. This study contributes a practical and theoretically grounded instructional model that can support teachers in designing adaptive learning experiences. Further research is recommended to explore its application across diverse topics and student groups.
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