Mathematical Reasoning Required when Students Seek the Original Graph from a Derivative Graph

Ikram, Muhammad; Purwanto, Purwanto; Parta, I Nengah; Susanto, Hery

doi:10.17648/acta.scientiae.5933

Cited by 6 publications

(4 citation statements)

References 35 publications

(56 reference statements)

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“…Observing particular cases is one of the activities of the inductive reasoning process in solving problems. This is supported by Cañadas et al (2007), Ikram et al (2020), Canadas and Castro (2007), Pinto and Cañadas (2005), Polya (1973), Reid (2002), Yuniati (2018), andYuniati (2020), who states that observing cases is an activity of an inductive reasoning process that is carried out on certain cases of the proposed problem. Thus, the functional thinking process is an inductive reasoning process.…”

Section: Functional Thinking Process At the Action Stagementioning

confidence: 89%

Investigating Functional Thinking Processes that Impact on Function Composition Problems in Indonesia

Yuniati¹,

Nusantara

Sulandra

et al. 2022

Acta Sci.

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Background: Every student has the ability to think, especially the ability to think when solving mathematical problems. The teacher must explore this ability to determine student understanding of the material being taught. Functions are essential because they are the basis for understanding algebra. The way of thinking about function is called functional thinking. Objective: This study aims to investigate the functional thinking process of students in solving mathematical problems based on the APOS theory. Design: This type of research is qualitative through an exploratory, descriptive approach. Setting and participants: Two out of 44 university students that can communicate fluently when working on questions using the think-aloud and interview methods. Data analysis: Analysis of students' functional thinking processes using the triangulation method, namely comparing think-aloud data, student answer sheets, and interview results. Results: This study found two ways of student functional thinking processes, namely semi-compositional functional thinking processes and compositional functional thinking processes, where students can generalise the relationship between quantity variations in the form of a composition function. Conclusion:This study investigates the functional thinking process of students in exploring the understanding of the concept of function so that students are expected to be able to represent and generalise function forms.

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Section: Functional Thinking Process At the Action Stagementioning

confidence: 89%

Investigating Functional Thinking Processes that Impact on Function Composition Problems in Indonesia

Yuniati¹,

Nusantara

Sulandra

et al. 2022

Acta Sci.

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“…Despite feeling under pressure during the imagination process, P1 and P3 were actually entering the productive-imaginative thinking stage. According to Ladd & Troop-Gordon (2003), Sirajuddin, et al (2020, Ikram et al, (2020) ideas emerge through imagination and anticipation. There are two types of imagination, passive imagination such as daydreaming or dreaming and reproductive imagination such as imagination in science.…”

Section: Discussionmentioning

confidence: 99%

Using Open-ended Problem-solving Tests to Identify Students’ Mathematical Creative Thinking Ability

Rahayuningsih

Sirajuddin

Ikram

2021

Participatory Educational Research

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This study aimed to examine an open-ended problem-solving assessment tool that can be used to measure the profile of students' mathematical creativity based on the type of mathematical creativity. The open-ended problem-solving assessment consists of open-ended problem-solving sheets and interview guidelines to measure the profile of students' mathematical creativity. One hundred and five students were asked to solve open-ended problems. From each group, one student was selected to be interviewed with the aim of obtaining a more detailed explanation of each of these types. The two types can be explained as follows. The "very creative" students were those who could perform cognitive flexibility and cognitive fluency in solving open-ended problems. The other type of students was creative students who were able to think flexibly (cognitive flexibility) when solving open-ended problems. Cognitive flexibility includes the ability to describe various solutions and provide more than one answer to a problem. Cognitive fluency includes the ability to interpret the answer smoothly and accurately without any constraints. It may also refer to the ability to correct a wrong answer even though there was a mistake during the operating process. The analysis results showed that the open-ended problem-solving assessment was an effective tool to measure students' mathematical creativity in terms of results (products) and processes. In terms of results (products), it was able to determine the type of students' mathematical creative ability, namely very creative and creative, while in terms of processes, it was able to describe the differences in the cognitive profile of the two types.

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“…The interpretation, dominated by the assimilation process, causes students to involve direct thinking processes to solve problems (Ikram, Purwanto, Nengah Parta, et al, 2020;Ikram, et al, 2020cIkram, et al, , 2020aIkram, et al, , 2020bMa'rufi et al, 2020;Rahayuningsih et al, 2021). In that sense, students involve an integration process to obtain a graph 𝑓.…”

Section: Ongoing Reversiblementioning

confidence: 99%

Exploring Students Reversible Reasoning when Sketching an Original Graph Involving Derivatives Concept

Ma’rufi

Ikram²,

Muzaini

et al. 2022

Acta Sci.

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Background: Reversible reasoning, a key aspect of mental activity, is important for students at all levels of mathematics. Objective: The purpose of this study was to characterise students' reversible reasoning when sketching graphs involving derivatives. Setting and participants: The data for this research was generated from a qualitative approach. We conducted clinical interviews with four students aged 18-19 who had completed and graduated in advanced calculus courses. They were selected for their high scores in the course. Data collection and analysis: Think aloud methods and task-based interviews were used to collect data. The analysis covered two original graph sketch assignments involving the graph of the derivative and its properties. Results: Through data analysis, we discovered two characteristics of reversible reasoning: Initial Reversible and Ongoing Reversible, which provide the initial framework for future research. These two characteristics are rooted in the student's perspective of the problem at hand, where the Initial Reversible student is dominated by the accommodation process, while the Ongoing Reversible student tends to experience cognitive conflicts that cause him to change his direction of thinking. Conclusions: We discuss the implications of our findings for future teaching and curriculum development in calculus.

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Mathematical Reasoning Required when Students Seek the Original Graph from a Derivative Graph

Cited by 6 publications

References 35 publications

Investigating Functional Thinking Processes that Impact on Function Composition Problems in Indonesia

Investigating Functional Thinking Processes that Impact on Function Composition Problems in Indonesia

Using Open-ended Problem-solving Tests to Identify Students’ Mathematical Creative Thinking Ability

Exploring Students Reversible Reasoning when Sketching an Original Graph Involving Derivatives Concept

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