DOI of the published article https://doi.org/10.22219/mej.v9i2.43364
Hypothetical Learning Trajectory Using Straws to Teach Subtraction to Elementary School Students
Hypothetical Learning Trajectory Berkonteks Sedotan untuk Mengajarkan Operasi Pengurangan bagi Siswa Sekolah Dasar
DOI:
https://doi.org/10.21070/ups.10314Keywords:
Hypothetical Learning Trajectory, Subtraction Operations, Straws, Elementary School Mathematics LearningAbstract
Hypothetical Learning Trajectory (HLT), which is based on the straw context, was created as a manipulative medium to help elementary school students understand two-digit addition and subtraction procedures. This study involved an initial design stage, two cycles of experimental instruction, and retrospective analysis. HLT was designed to enable students to transition from concrete representations to symbolic understanding of place value, including addition with and without carrying, and subtraction with and without borrowing. The results showed that straws helped students develop the concept of regrouping gradually, improved the accuracy of calculation strategies, and enhanced conceptual understanding, especially of the borrowing and carrying processes. Activities A through D demonstrated the alignment between actual and hypothetical learning trajectories and provided significant manipulative support for low-ability students. The findings indicate that concrete bundling-based media such as straws are effective in improving understanding of number structure and can support mathematics learning in early elementary classrooms.
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