Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

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

doi:10.17478/jegys.665836

Cited by 10 publications

(10 citation statements)

References 46 publications

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“…This research is explorative research with a qualitative approach (Moleong, 2012;Ikram et al 2020;Muhtarom et al 2019). In explorative research with a qualitative approach, researchers explore and conduct in-depth analyzes of the process of pattern generalization process students based on APOS theory.…”

Section: Methods Research Designmentioning

confidence: 99%

Number pattern generalization process by provincial mathematics olympiad winner students

Firdaus¹

2020

Journal for the Education of Gifted Young Scientists

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This research aims to the Number Generalization process based on APOS Framework (action, process, object, and schema). Furthermore, the research is explorative research with a qualitative approach. The subjects of the study were one of the junior high school students who won the provincial mathematics Olympiad in South Sulawesi, Indonesia. Subjects were given instruments that had been developed, namely the number patterns generalization test. Data collection of this study is the number patterns generalization test and in-depth interviews. The data analysis process was reducing, describing, validating, and concluding. The results showed that the students who won the Olympics in the action stage determine the next term, if given a sequence by using a number pattern. At the stage of the process, action interiorizing by calculating the value of the next term repeatedly and explaining the process of determining the next term. At the object stage, encapsulating the process by showing that a number pattern has certain characteristics, de-encapsulating by assessing the observed pattern, and checking the number pattern found. At the schema stage, explaining the generalization properties of number sequence patterns by linking the actions, processes, objects of a concept with other concepts, doing thematization by linking the existing concept patterns to the general sequence.

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Section: Methods Research Designmentioning

confidence: 99%

Number pattern generalization process by provincial mathematics olympiad winner students

Firdaus¹

2020

Journal for the Education of Gifted Young Scientists

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“…Mathematics grows and develops for itself as a science, also to serve the needs of science in its development and operation. Meanwhile, mathematics according to (Ikram et al, 2020;Wilkie, 2019) is a pattern of thinking, pattern of organizing, and logical proof. The need for understanding and using mathematics in daily life as well as in the working world is getting increasing and growing.…”

Section: Introductionmentioning

confidence: 99%

“…Suggests "four steps of the problem-solving process, namely: understanding the problem, designing problem solving, carrying out problem-solving, and checking again" (Siswono, 2010). Describes mathematical problems in two types, namely problem to find and problem to prove (Ikram et al, 2020). The problem of finding is a problem that aims to find, determine, or get the value of certain objects that are not known in the problem and provide appropriate conditions.…”

Section: Introductionmentioning

confidence: 99%

Investigating Middle School Students Generalization of Number Pattern Based on Learning Style

Firdaus¹,

Juniati²,

Wijayanti³

2021

TURCOMAT

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Pattern generalization is an important aspect of mathematics contained in every topic in teaching. This study aims to investigate middle school students’ generalization of number patterns based on learning style. Descriptive qualitative, portraying or describing the events that are the center of attention (problem-solving abilities, student learning styles) qualitatively.This study explored 4 participants (12 to 13 years old) with their constructed number pattern they had generalized during individual task-based interviews. Questions that include indicators of the problem solving process in terms of student learning styles, and interviews. The data analysis used was namely data reduction, data presentation, drawing conclusions. We found that students who are converger, diverger, accommodator, and assimilator understands the problem by knowing what is known and asked and explains the problem with their own sentences. The converger and assimilator students look back without checking the counts involved, the diverger students do not see other alternative solutions and do not check the counts involved, accommodator students consider that the solutions obtained are logical, ask themselves whether the question has been answered, check the counts that are done, reread the question, and use other alternative solutions. The implication of this study indicated that students of the type of converger, diverger, accommodator, and assimilator are able to solve problems through the stages of implementing plans by interpreting problems in mathematical form, implementing strategies during the process and counting takes place. Based on several studies on pattern generalization, there have not been researchers who have revealed the number pattern generalization of high school students based on learning styles.

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“…The reasoning is a thought process that is influenced by students' competencies and environment which consists of two main types namely creative and imitative reasoning (Lithner, 2008). The reasoning can focus on a particular concept, for example, reversible reasoning in inverse function problems (Ikram et al 2020). Mathematical reasoning can also be seen when students solve mathematical tasks.…”

Section: Introductionmentioning

confidence: 99%

Mathematical understanding and reasoning of vocational school students in agriculture-based mathematical tasks

Fatimah

Prabawanto

2020

Journal for the Education of Gifted Young Scientists

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Mathematical understanding and reasoning are important in solving agriculture problems. This research aims to describe students' mathematical understanding and reasoning in agriculture-based mathematical tasks. This mathematical task corresponds to the competency of students' expertise to minimize the gap between mathematics learned at school and the workplace. This research used a descriptive case study method. Participants are students of the vocational crops and horticulture agribusiness of 11th graders students. Data collected through tasks, observations, and interviews. Data analysis through constant comparative techniques to find out students' understanding (coherence, correspondence, and connection) and reasoning (algorithmic or creative). The results show students' mathematical understanding and reasoning was influenced by the design of tasks and students' experiences. Both algorithmic and creative reasoning, should by the plausibility of the reality of workplace practice in agriculture to affects the ability of coherence and correspondence of students' mathematical representations. Mathematical knowledge and experience affect the whole process of solving the tasks. The results of this research have implications for the design of mathematical tasks in vocational schools in agriculture to support problem-solving in the workplace. The development of mathematical tasks can continue to be done given the many problems in agriculture involving mathematics in solving them.

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Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Cited by 10 publications

References 46 publications

Number pattern generalization process by provincial mathematics olympiad winner students

Number pattern generalization process by provincial mathematics olympiad winner students

Investigating Middle School Students Generalization of Number Pattern Based on Learning Style

Mathematical understanding and reasoning of vocational school students in agriculture-based mathematical tasks

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