# Mathematical reasoning required when students seek the original graph from a derivative graph

Ikram, Muhammad; Purwanto, Purwanto; Parta, I Nengah; Susanto, Hery (2020). Mathematical reasoning required when students seek the original graph from a derivative graph. Acta Scientiae. Revista de Ensino de Ciências e Matemática, 22(6), pp. 45-64 .

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## 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.

Tipo de Registro: Artículo 06. Aprendizaje > Procesos cognitivos > Razonamiento12. Investigación e innovación en Educación Matemática > Fuentes de información > Entrevistas10. Otras nociones de Educación Matemática > Sistemas de representación > Gráfico12. Investigación e innovación en Educación Matemática > Tipos de estudio > Estudio de casos Título de grado universitario 28651 Monitor Funes 2 13 Jun 2022 17:02 13 Jun 2022 17:02

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