How Students Understand the Area under a Curve: A Hypothetical Learning Trajectory
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Resumo
The area under the curve is a fundamental concept for students to build their understanding of the Definite Integral. This research reveals how students comprehend the area under the curve in given contextual problems and how the Hypothetical Learning Trajectory (HLT) can help students find the concept. This research follows the development research model of Gravemeijer and Cobb, which consists of three stages: preparing for the experiment, experimenting, and retrospective analysis. This research involved three students with varying abilities: low, medium, and high. Data were collected through the analysis of student work documents and in-depth interviews. The research findings indicate that students often struggle with determining the area under the curve. Students approach the area by using various polygons. With the guidance of their lecturers, students discovered that the area under the curve can be approached by partitioning the area into polygons. The more polygons used, the closer the approximation becomes. In other words, the HLT designed in this study facilitates students in understanding the concept of the area under the curve, formulated as [equation omitted].
Dados da obra
- Tipo
- Artigo
- Periódico
- Mathematics Teaching Research Journal
- Ano
- 2024
- Idioma
- en
- Palavras-chave
- Geometric Concepts; Student Attitudes; Knowledge Level; Academic Ability; Mathematics Instruction; Calculus; College Mathematics
- Temas
- Cálculo, Geometria
- Acesso
- Download disponível
- Fontes
- ERIC — Education Resources Information Center
- Na Biblioteca desde
- 01/10/2026 · verificada em 03/10/2026
Como citar
ABNT
ANISWITA; FAUZAN, Ahmad; ARMIATI. How Students Understand the Area under a Curve: A Hypothetical Learning Trajectory. Mathematics Teaching Research Journal, 2024. Disponível em: https://eric.ed.gov/?id=EJ1442340. Acesso em: 5 nov. 2026.
APA
Aniswita,, Fauzan, A., & Armiati, (2024). How Students Understand the Area under a Curve: A Hypothetical Learning Trajectory. Mathematics Teaching Research Journal. https://eric.ed.gov/?id=EJ1442340
BibTeX
@article{aniswita2024,
author = {Aniswita and Fauzan, Ahmad and Armiati},
title = {How Students Understand the Area under a Curve: A Hypothetical Learning Trajectory},
year = {2024},
journal = {Mathematics Teaching Research Journal},
url = {https://eric.ed.gov/?id=EJ1442340},
language = {en}
}RIS
TY - JOUR AU - Aniswita AU - Fauzan, Ahmad AU - Armiati TI - How Students Understand the Area under a Curve: A Hypothetical Learning Trajectory PY - 2024 JO - Mathematics Teaching Research Journal UR - https://eric.ed.gov/?id=EJ1442340 LA - en ER -
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