Mathematical reasoning required when students seek the original graph from a derivative graph
Tipo de documento
Autores
Ikram, Muhammad | Parta, I Nengah | Purwanto, Purwanto | Susanto, Hery
Lista de autores
Ikram, Muhammad, Purwanto, Purwanto, Parta, I Nengah y Susanto, Hery
Resumen
Background: Finding the original graph when given the derivative graph is not a trivial task for students, even though they can find the derivative graph when given the original graph. Objective: In the context of qualitative research, this paper presents and analyses the mathematical reasoning that comes to light when the students seek the original graph from a derivative graph. Design: The research is assigned as a qualitative study, where the analyses of cases aim to extend understanding with respect to some phenomena or theory. Setting and participants: The study was conducted with 86 students from a State University in East Java. We conducted clinical interviews, and present data highlighting the reasoning participants used when solving tasks. Data collection and analysis: Task-based interviews were used to collect data, and data analysis was used to analyse interpretations of the graphs that emerged as mathematical reasoning models. Results: From our data analysis, we found that three mathematical reasonings were rooted in students’ awareness of problem-situations on graphs we provided, consisting of direct reasoning, reversible reasoning, and combined direct-reversible reasoning. Conclusions: We suggest that there are different mathematical reasonings in the construction of the original graph, due to the mental activity in which students use the relation between a function and its derivative. We suggest that future projects continue this inquiry with rigorous single-subject experiments with students.
Fecha
2020
Tipo de fecha
Estado publicación
Términos clave
Enfoque
Idioma
Revisado por pares
Formato del archivo
Volumen
22
Número
6
Rango páginas (artículo)
45-64
ISSN
21787727
Referencias
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