Autores - Editores Purwanto, Purwanto
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Mathematical reasoning required when students seek the original graph from a derivative graph
Descripción
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.
Lista de autores
Ikram, Muhammad, Purwanto, Purwanto, Parta, I Nengah y Susanto, Hery
Fecha
2020
Autores
Ikram, Muhammad | Parta, I Nengah | Purwanto, Purwanto | Susanto, Hery
Términos clave
Nivel educativo
Educación superior, formación de pregrado, formación de grado
Enfoque
Tipo de documento
Students’ thinking process when using abductive reasoning in problem solving
Descripción
Background: abductive reasoning is the process of making conjectures to explain surprising observations. Although this conjecture is not certain to be true, in solving a problem, this reasoning is very helpful to determine the best solution strategy. Objectives: the study aims to investigate whether all types of abductive reasoning lead to the formation of new schemes. Design: this research used a qualitative approach with a descriptive exploratory design. Setting and participants: a total of 41 students of the research degree in mathematics education programme were involved in solving a task. Then, eight of them were chosen for an in-depth interview, representing the undercoded and overcoded abductive reasoning types. Data collection and analysis: the data collected were the results of the students’ works and task-based interviews. Piaget’s schema theory was used to analyse students' thinking processes using abductive reasoning. The analysis was carried out at all steps of problem solving, namely understanding the problem, devising a plan, carrying out the plan, and looking back. Results: those who carried out overcoded abductive reasoning used this reasoning to determine problem solving strategies. Meanwhile, those who carried out undercoded abductive reasoning used it to determine problem solving strategies as well as to form new schemes. Conclusions: the results showed that students who did abductive reasoning did not always produce new schemes. This study also notes that the truth value of answers from the application of abductive reasoning in problem solving was open and the importance of the look back step to perform accommodation.
Lista de autores
Shodikin, Ali, Purwanto, Purwanto, Subanji, Subanji y Sudirman, Sudirman
Fecha
2021
Autores
Purwanto, Purwanto | Shodikin, Ali | Subanji, Subanji | Sudirman, Sudirman
Términos clave
Estrategias de solución | Otro (procesos cognitivos) | Razonamiento | Tareas