Hypothetical Learning Trajectory Using Straws to Teach Subtraction to Elementary School Students

Artigo2026

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Resumo

This study developed a context-based Hypothetical Learning Trajectory (HLT) using straws as concrete manipulatives to support elementary students’ understanding of two-digit addition and subtraction. Employing a Design Research approach, the study consisted of an initial design, two cycles of teaching experiments, and a retrospective analysis. The HLT was constructed through sequential activities that guided students from concrete representations to symbolic reasoning related to place value, addition with and without carrying, and subtraction with and without borrowing. The findings indicate that straw-based manipulatives effectively supported students in developing the concept of regrouping, enhancing calculation accuracy, and strengthening conceptual understanding, particularly during carrying and borrowing processes. Across Activities A–D, the actual learning trajectory aligned with the hypothetical pathway, with notable benefits for students with lower initial abilities. Overall, the results confirm that bundling-based concrete media such as straws offer a meaningful and feasible instructional alternative for early-grade mathematics learning.

Dados da obra

Tipo: Artigo
Periódico: MEJ (Mathematics Education Journal), v. 9, n. 2, p. 177-190
Editora: Universitas Muhammadiyah Malang
Ano: 2026 (2026-02)
Idioma: en
DOI: 10.22219/mej.v9i2.43364
ISSN: 2579-5260, 2579-5724
Acesso: Acesso aberto
Fontes: DOAJ — Directory of Open Access Journals
Na Biblioteca desde: 01/10/2026 · verificada em 03/10/2026

Como citar

ABNT
PINASTHI, Titah; AMIR, Mohammad Faizal. Hypothetical Learning Trajectory Using Straws to Teach Subtraction to Elementary School Students. MEJ (Mathematics Education Journal), v. 9, n. 2, p. 177-190, 2026. DOI: https://doi.org/10.22219/mej.v9i2.43364.

APA

Pinasthi, T., & Amir, M. F. (2026). Hypothetical Learning Trajectory Using Straws to Teach Subtraction to Elementary School Students. MEJ (Mathematics Education Journal), 9(2), 177-190. https://doi.org/10.22219/mej.v9i2.43364

BibTeX

@article{pinasthi2026,
  author = {Pinasthi, Titah and Amir, Mohammad Faizal},
  title = {Hypothetical Learning Trajectory Using Straws to Teach Subtraction to Elementary School Students},
  year = {2026},
  journal = {MEJ (Mathematics Education Journal)},
  volume = {9},
  number = {2},
  pages = {177-190},
  publisher = {Universitas Muhammadiyah Malang},
  doi = {10.22219/mej.v9i2.43364},
  language = {en}
}

RIS

TY  - JOUR
AU  - Pinasthi, Titah
AU  - Amir, Mohammad Faizal
TI  - Hypothetical Learning Trajectory Using Straws to Teach Subtraction to Elementary School Students
PY  - 2026
JO  - MEJ (Mathematics Education Journal)
VL  - 9
IS  - 2
SP  - 177
EP  - 190
DO  - 10.22219/mej.v9i2.43364
LA  - en
ER  -

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