Algebraic Generalization Strategies Used by Kuwaiti Pre-service Teachers

Alajmi, Amal Hussain

doi:10.1007/s10763-015-9657-y

Cited by 9 publications

(17 citation statements)

References 25 publications

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“…Ayrıca, bu teori birçok farklı alanda bir araç olarak kullanılmıştır. Örneğin, öğretmen eğitimi (Borgen, 2006;Nillas, 2010), öğretim modeli geliştirme (Higgins ve Parsons, 2009;Wright, 2014), matematiksel anlamanın doğası (Martin, Towers ve Pirie, 2006;Towers ve Martin, 2006), öğretmen uygulamaları (Warner, 2008), öğretmenlerin matematiksel anlamalarının gelişimi (Borgen, 2006;Cavey ve Berenson, 2005), ortak matematiksel anlama (Martin ve Towers, 2015, 2016Towers ve Martin, 2014). Bunların yanı sıra, matematiksel anlamanın kesirler (Arslan, 2013;George, 2017;Gökalp, 2012), rasyonel sayılar (Lawan, 2011), permütasyon ve faktöriyel (Argat, 2012), oranlar (Wright, 2014), sayısal seriler (Valcarce et al 2012) ve geometri (Gülkılık, Uğurlu ve Yürük, 2015; Mabotja, 2017) gibi bazı konular için araştırıldığı görülmüştür.…”

Section: Results Discussion and Recommendationsunclassified

Examining Students Mathematical Understanding of Patterns by Pirie-Kieren Model

Güner¹,

Uygun²

2019

HUJE

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Bu çalışmanın amacı öğrencilerin örüntülere ilişkin matematiksel anlamalarını araştırmaktır. Bir devlet okulunda öğrenim gören üç yedinci sınıf öğrencisi çalışmaya katılmış ve örüntülerle ilgili soruları çözmüştür. Bu öğrencilerle çözümlerine yönelik yarı yapılandırılmış görüşmeler gerçekleştirilmiştir. Veriler Pirie-Kieren teorisi kullanılarak analiz edilmiştir. Elde edilen bulgular, öğrencilerin matematiksel anlamalarının ön bilgiden gözlem yapmaya kadar ilk altı düzey arasında çeşitlilik gösterdiğini ve genellikle imaj oluşturma ile formülleştirme aşamalarında gerçekleştiğini ortaya koymaktadır. Teoriye göre, öğrencilerin ilk ve ikinci ihtiyaç duyulmayan sınırların ilerisine gidebildikleri fakat üçüncü sınırı geçemedikleri görülmüştür. Sonuçlar öğrencilerin örüntülere ilişkin bilgilerinin olduğunu ve örüntünün genel formülünü bulmak için çoğunlukla bir kural belirlemeye ve bunun doğrulunu ilk üç terim için kontrol etmeye çalıştıklarını göstermektedir.

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Section: Results Discussion and Recommendationsunclassified

Examining Students Mathematical Understanding of Patterns by Pirie-Kieren Model

Güner¹,

Uygun²

2019

HUJE

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“…For example: [1] Researcher: How you get to step 7? [2] Andi: Look at this. I found the number of squares in step 7 by repeatedly adding 2 from step 4 until step 7.…”

Section: How the Student Generalize A Linear Growing Figural Patternmentioning

confidence: 99%

“…The students' generalization strategies using various activities such as numerical, geometric, and repeating patterns help students use symbols to express generalizations and develop meaning for symbolic generalizations (Alajmi, 2016;Lannin et al, 2006). Understanding mathematical symbols and concepts are an essential component of mathematical knowledge (Skemp, 1987).…”

Section: Introductionmentioning

confidence: 99%

Strategies of Pattern Generalization for Enhancing Students’ Algebraic Thinking

Nurwidiyanto¹,

Zhang²

2020

PTQ

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Mathematics is seen as a science of pattern. Identifying and using patterns is the essence of mathematical thinking for children to improve algebraic thinking from their early schooling. The pattern is an arrangement of objects that have regularities or properties that can be generalized. Therefore, it is essential to know the strategies used by students in generalizing patterns and how students think in these processes. This study is descriptive research with a mixed quantitative-qualitative approach that aimed to investigate student’s algebraic thinking using various strategies to generalize the visual pattern. An instrument about the linear geometric growing pattern was administrated to 75 upper primary school students (grades 5-6) and 81 lower secondary students (grades 7-8) in two private schools in Semarang, Indonesia. The results showed that students used different pattern generalization strategies. The student generally preferred recursive, chunking, and functional approaches in each generalization task, whereas few used counting from drawing strategies to generalize patterns. The use of the recursive strategy decreased, whereas the chunking strategy and the functional strategy increased across grades 5-8 for the problems. The results also showed the student who used the recursive and chunking strategy preferred to change visual patterns into rows of numbers. Hence, they adopt a numeric approach by finding the common difference of visible pattern in each step.

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“…On the other hand, several investigations highlighted that pre-service elementary and middle school teachers face difficulties in generalizing from a finite class of particular cases; the greater difficulties are found in the non-linear patterns such as quadratic ones (e.g. Alajmi, 2016;Hallagan, Rule & Carlson, 2009;Rivera & Becker, 2003). Research on inductive reasoning reports that these difficulties are linked to their different skills and ways of generalizing quadratic patterns.…”

Section: Research On Teachers' Inductive Reasoningmentioning

confidence: 99%

“…They tend to focus on invariant attributes in numbers over relationships (Rivera y Becker, 2003). The most frequently used strategy to generalize quadratic patterns is the recursive one, but this strategy makes it more difficult to recognize the structure of the quadratic pattern and reach the generalization (Alajmi, 2016;Manfreda et al, 2012;Yeşildere & Akkoç, 2010).…”

Section: Research On Teachers' Inductive Reasoningmentioning

confidence: 99%

Characterization of Inductive Reasoning in Middle School Mathematics Teachers in a Generalization Task

Moguel

Landa

Cabañas-Sánchez

2019

Int Elect J Math Ed

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This paper reports on the characterization of the inductive reasoning used by middle school mathematics teachers to solve a task of generalization of a quadratic pattern. The data was collected from individual interviews and the written answers to the generalization task. The analysis was based on the representations and justifications used to move from particular cases to the formulation of the general rule. Three processes characterize the inductive reasoning of the mathematics teachers to obtain a general rule: observation of regularities, establishment of a pattern and formulation of a generalization; while some teachers revealed problems in moving from the observation of regularities to the formulation of a generalization. Therefore, some difficulties in generalizing associated with these processes are also mentioned.

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Algebraic Generalization Strategies Used by Kuwaiti Pre-service Teachers

Cited by 9 publications

References 25 publications

Examining Students Mathematical Understanding of Patterns by Pirie-Kieren Model

Examining Students Mathematical Understanding of Patterns by Pirie-Kieren Model

Strategies of Pattern Generalization for Enhancing Students’ Algebraic Thinking

Characterization of Inductive Reasoning in Middle School Mathematics Teachers in a Generalization Task

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