Examining Students  Mathematical Understanding of Patterns by Pirie-Kieren Model

Güner, Pınar; Uygun, Tuğba

doi:10.16986/huje.2019056035

Cited by 4 publications

(8 citation statements)

References 21 publications

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“…However, S1 could solve the addition arithmagon problem with the understanding layer outside of the boundary (image having). Image having occurred just outside of the first "don't need" Boundaries in the Pirie-Kieren Model because of not relying on the more specific inner understanding (Guner & Uygun, 2019). S1 has crossed the first "don't need" boundaries since in order to deliver the idea, which is far off the limit, it does not require deeper understanding (image making) which gives rise to external knowledge (image having).…”

Section: Discussionmentioning

confidence: 99%

“…S2 passed the second "don't need" boundaries in solving the addition arithmagon because S2 had a formal mathematical idea (formalising) and did not require a picture of the property noticing. Based on Pirie-Kieren's theory, formalising occurs precisely outside the second "don't need" boundaries (Thom & Pirie, 2006;Guner & Uygun, 2019). S2 solved the problem of multiplication arithmagon correctly (image having) without calculating or writing down the numbers and symbols (image making).…”

Section: Discussionmentioning

confidence: 99%

“…Thus, S2 has crossed the first "don't need" boundaries because according to Pirie-Kieren's theory, the students who work outside the "don't need" boundaries do not need to understand certain inner layer in order to bring out the external knowledge (Thom & Pirie, 2006;George, 2017) S3 has crossed the second "don't need" boundaries in solving the addition arithmagon because the subject had formal mathematical ideas (formalising) and did not require an overview of the property noticing. Formalising occurs just outside of the second "don't need" boundaries according to the Pirie-Keiren Model (Guner & Uygun, 2019).…”

Section: Discussionmentioning

confidence: 99%

“…Formalizing occurs right outside the second "don't need" boundaries in Pirie-Kieren's model and there is no need to analyze the patterns which exist in the triangular multiplication arithmagon. According to Pirie-Kieren's theory, formalising occurs right outside the second "don't need" boundaries (Thom & Pirie, 2006;Guner & Uygun, 2019).…”

Section: Discussionmentioning

confidence: 99%

See 3 more Smart Citations

Exploration on Students’ Understanding Layers in Solving Arithmagon Problems

Sa’dijah

Rahayuningsih

Sukoriyanto

et al. 2022

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The research aims at exploring the characteristics of ‘don’t need’ boundaries of students in solving arithmagon problems using qualitative descriptive approach. The participants win this research are 23 eight-grader junior high school students. The research used the instruments including test questions and unstructured interviews. The data collection procedure began with giving test questions to 23 participants. All of them could make mathematical diagrams/drawings/model precisely according to the information presented from the problem. The student who used effective and clear sentences in solving problems though could not solve the problem in a structured manner is called as Subject 1 (S1). The student who did not use effective and clear structured sentences is called as Subject 2 (S2). The student who used effective and clear sentences as well as structured in solving problems is called Subject 3 (S3). This research used triangulation method by exploring data obtained from the test and interview results. According to the research result, it is concluded that S1 crossed the first ‘don’t need’ boundaries when solving the addition and multiplication arithmagon problems. S2 crossed the first and second “don’t need” boundaries when solving addition arithmagon problem and only crossed the first ‘don’t need’ boundaries in solving multiplication arithmagon problems. However, S3 crossed the second ‘don’t need’ boundaries in solving arithmagon problem of addition and multiplication. Through this research, it is hoped that further research will be able to find and explore the third ‘don’t need’ boundaries in solving mathematical problems.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Exploration on Students’ Understanding Layers in Solving Arithmagon Problems

Sa’dijah

Rahayuningsih

Sukoriyanto

et al. 2022

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“…The folding back activity by FS contrasts with Pirie & Kieren's theory of mathematical understanding (Pirie & Kieren, 1994;Martin, 2008). The activities carried out show that the FS abstracts a mathematical concept based on the properties that emerge with the ability to formalize prior understanding (Martin, Lacroix, & Fownes, 2005;Güner & Uygun, 2019).…”

mentioning

confidence: 94%

Students’ Growing Understanding in Solving Mathematics Problems Based on Gender: Elaborating Folding Back

2021

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Students’ previous knowledge at a superficial level is reviewed when they solve mathematical problems. This action is imperative to strengthen their knowledge and provide the right information needed to solve the problems. Furthermore, Pirie and Kieren's theory stated that the act of returning to a previous level of understanding is called folding back. Therefore, this descriptive-explorative study examines high school students' levels of knowledge in solving mathematics problems using the folding back method. The sample consists of 33 students classified into male and female groups, each interviewed to determine the results of solving arithmetic problems based on gender. The results showed differences in the level of students' understanding in solving problems. Male students carried out the folding back process at the level of image having, formalizing, and structuring. Their female counterparts conducted it at image-making, property noticing, formalizing, and observing. Subsequently, both participants were able to carry out understanding activities, including explaining information from a mathematical problem, defining the concept, having an overview of a particular topic, identifying similarities and differences, abstracting mathematical concepts, and understanding its ideas in accordance with a given problem. This study suggested that Pirie and Kieren's theory can help teachers detect the features of students’ understanding in solving mathematical problems.

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Folding back in students’ construction of mathematical generalizations within a dynamic geometry environment

Yao

Manouchehri

2020

Math Ed Res J

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Examining Students Mathematical Understanding of Patterns by Pirie-Kieren Model

Cited by 4 publications

References 21 publications

Exploration on Students’ Understanding Layers in Solving Arithmagon Problems

Exploration on Students’ Understanding Layers in Solving Arithmagon Problems

Students’ Growing Understanding in Solving Mathematics Problems Based on Gender: Elaborating Folding Back

Folding back in students’ construction of mathematical generalizations within a dynamic geometry environment

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