Students’ mental model in solving the patterns of generalization problem

Prayekti, Novi; Nusantara, Toto; Sudirman, Sudirman; Susanto, Hery

doi:10.1088/1755-1315/243/1/012144

Cited by 5 publications

(8 citation statements)

References 7 publications

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“…The final form of generalization used by students in solving problems cannot be stated in formal symbolic form which can be applied in larger cases (Vosniadou & Brewer, 1992). Fourth, Indirect Formal Mental Switch Model occurs when students in the process of solving problems about number patterns use a combination of arithmetic generalization strategy and algebraic generalizations strategy alternately (Radford, 2006;Prayekti et al 2019). During the process of solving a problem, students make a problem solving strategy from an arithmetic generalization strategy to an algebra generalization strategy so that the resulting rules pay attention to the relationship between numbers and substitute variables that indicate the sequence of numbers in the sequence.…”

Section: Resultsmentioning

confidence: 99%

“…Yet, mental models play a significant role in students' problem solving skill. Based on the previous studies have been conducted by several scholars (Bofferding, 2014;Prayekti et al, 2019;Radford, 2006;Vosniadou, 1994;Vosniadou & Brewer, 1992) and the presence of preliminary research findings that students with the same mental model can have a different form of generalization. Thus, it is necessary to conduct more in-depth research to detect the characteristics of students' mental models based on various generalization forms.…”

Section: Problem Of Studymentioning

confidence: 99%

“…In his research, Bofferding (2014) showed that students' mental models about sequence and integer values can be classified into 5 types: initial mental model, transition mental model I, synthetic mental model, transition mental model II, and formal mental model. A research on the student's mental model in solving patterns generalization problems conducted by Prayekti et al (2019) suggested that there are two types of mental models when solving the problems of patterns generalization: direct and Indirect mental models. The students are said to have a direct mental model if they only use one type of generalization strategy in problem solving i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Generalization, according to Radford (2006), can be viewed as a mathematical representation of a person at the time of solving the problem of generalization of patterns (Prayekti et al 2019). NCTM (2000) said that "representing involves translating a problem or an idea into a new form.…”

Section: Introductionmentioning

confidence: 99%

“…A research on the student's mental model in solving patterns generalization problems conducted by Prayekti et al (2019) suggested that there are two types of mental models when solving the problems of patterns generalization: direct and Indirect mental models. The students are said to have a direct mental model if they only use one type of generalization strategy in problem solving i.e.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Eighth-grades students’ mental models in solving a number pattern problem

Prayekti

Nusantara

Sudirman

et al. 2020

Journal for the Education of Gifted Young Scientists

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This study aims to explore all the types of students' mental models of number patterns. The study used a qualitative approach with an explorative type. The subjects used to characterize the student's mental models in this study were 46 eighth grade students in Indonesia. To reveal the subjects' mental model, they were asked to solve the number pattern problem and were interviewed. For ensuring the validity and reliability of the research results, triangulation technique was used by comparing the results of video recording interviews and written test results. The study showed that in solving the problem of number patterns given, there were 4 types of mental models. They were formal direct mental model, formal indirect mental model, synthetic direct mental model, and synthetic indirect mental model. What we found in this study shows that some students have different mental models to solve the problem. Hence, in future teachers must introduce various strategies to solve the problem and conduct learning that can enrich students' mental models.

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Section: Resultsmentioning

confidence: 99%

Section: Problem Of Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Eighth-grades students’ mental models in solving a number pattern problem

Prayekti

Nusantara

Sudirman

et al. 2020

Journal for the Education of Gifted Young Scientists

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Analysis of students’ mental models through the level understanding on the concept of straight motion kinematics graphics

Khumaidi¹,

Kusairi²,

Wisodo³

et al. 2022

AIP Conference Proceedings

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Unpacking mental models, strategies, and schemas pre-service mathematics teacher in solving maximum rectangular areas

Rumite

Purwanto

Parta

et al. 2023

EURASIA J Math Sci Tech Ed

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A mental model is an essential element that influences the quality of problem-solving. This study explores mental models, strategies, and schemes that are active in solving the maximum rectangular area problem. The approach used in this study is a descriptive qualitative approach. A total of four pre-service mathematics teachers as subjects were selected from 108 prospective subjects involved in the study. Data collection was carried out by providing task sheets for solving the most significant rectangular area problem and semi-structured interviews. Data reduction, data presentation, and conclusion are three stages in analyzing the research data. This study indicates three mental models for pre-service mathematics teachers in solving maximum rectangular area problems: initial, adaptive, and formal. Each has different strategies and schemes that are active while solving problems. The results of this study imply that mental models influence the quality of the problem solving process until results are obtained.

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Students’ mental model in solving the patterns of generalization problem

Cited by 5 publications

References 7 publications

Eighth-grades students’ mental models in solving a number pattern problem

Eighth-grades students’ mental models in solving a number pattern problem

Analysis of students’ mental models through the level understanding on the concept of straight motion kinematics graphics

Unpacking mental models, strategies, and schemas pre-service mathematics teacher in solving maximum rectangular areas

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