Variation of student numerical and figural reasoning approaches by pattern generalization type, strategy use and grade level

Mouhayar, Rabih El; Jurdak, Murad

doi:10.1080/0020739x.2015.1068391

Cited by 27 publications

(15 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…7 th and 8 th graders use numerical reasoning to explore how many units there are in given pictures. This finding is consistent with one of the findings of El Mouhayar and Jurdak's (2016) study. Similar to their results, we found that the numerical reasoning was more dominant in students' generalizations while using recursive strategy .…”

Section: Discussionsupporting

confidence: 94%

Farklı Sınıf Seviyelerindeki Ortaokul Öğrencilerinde Cebirsel Düşünme: Örüntülerde Genelleme Hakkındaki Algıları

Girit¹,

Akyüz²

2016

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

View full text Add to dashboard Cite

-Algebra is generally considered as manipulating symbols, while algebraic thin king is about generalization. Patterns can be used for generalizat ion to develop early graders' algebraic thinking. In the generalization of pattern context, the purpose of this study is to investigate middle school students' reasoning and strategies at different grades when their algebraic thin king begin s to develop.First, 6 open-ended linear growth pattern problems as numeric, pictorial, and tabular representations were asked to 154 middle g rade students. Next, two students from each grade (6 th , 7 th , and 8 th grade) were interviewed to investigate how they interpret the relationship in different represented patterns, and which strategies they use. The findings of this study showed that students tended to use algebraic symbolis m as their grade level was increased. However, the students' conceptions about 'variable' we re troublesome.

show abstract

Section: Discussionsupporting

confidence: 94%

Farklı Sınıf Seviyelerindeki Ortaokul Öğrencilerinde Cebirsel Düşünme: Örüntülerde Genelleme Hakkındaki Algıları

Girit¹,

Akyüz²

2016

Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi

View full text Add to dashboard Cite

show abstract

“…We reported the instances of connections between empirical reasoning (i.e., naïve empiricism, crucial experiment, reasoning by generic example) and different types of structuring reasoning. The results revealed that naïve empiricism was the dominant type of empirical reasoning, which is consistent with the existing literature on pattern generalization (e.g., EI Mouhayar, 2018;El Mouhayar & Jurdak, 2016;Küchemann, 2010;Küchemann & Hoyles, 2009). Although the inductive nature of the dynamic geometry environment made it relatively easy for the participants to observe, conjecture, validate, and generalize mathematical relations on the basis of perception and numerical patterns, identifying mathematical structure underlying these relations and using them to generalize the relations to broader contexts proved to be challenging for them.…”

Section: Discussionsupporting

confidence: 89%

“…These different forms of generalization imply that individual learners can generalize either at an empirical level (empirical reasoning) or based on mathematical structure (structural reasoning). A considerable body of research on pattern generalization has shown that learners of different ages tend to generalize on the basis of spurious numerical pattern rather than the pattern's structure (El Mouhayar, 2018;El Mouhayar & Jurdak, 2016;Küchemann, 2010;Küchemann & Hoyles, 2009), which implies a dominance of empirical reasoning over structural reasoning in generalizing activities as well as the need for students to move from empirical to structural generalization. Although both empirical and structural reasoning occur in the process of constructing, representing, and justifying generalizations, it still remains unclear whether and if so, how the two types of reasoning interact with each other, and how learners' reasoning gradually evolves from empirical to structural.…”

Section: Introductionmentioning

confidence: 99%

Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities

Yao¹,

Elia²

2021

INT ELECT J MATH ED

View full text Add to dashboard Cite

Mathematical generalization can take on different forms and be built upon different types of reasoning. Having utilized data from a series of task-based interviews, this study examined connections between empirical and structural reasoning as preservice mathematics teachers solved problems designed to engage them in constructing and generalizing mathematical ideas aided by digital tools. The study revealed closer connections between naïve empiricism and result pattern generalization, between naïve empiricism and recognizing a structure in thought, between reasoning by generic example and process pattern generalization, and between reasoning by generic example and reasoning in terms of general structures. Results from this study imply that the ability to generalize based on perception and numerical pattern does not necessarily lead learners to generalize based on mathematical structure.

show abstract

“…Patterns is a fundamental stage in the formation of generalization. Pattern generalization is a core area in mathematics that is recognized by a community of researchers as an approach to develop student's algebraic reasoning [6]. Patterning is critical to the abstraction of mathematical ideas and relationships, and the development of mathematical reasoning in young children.…”

Section: Introductionmentioning

confidence: 99%

Students' Reasoning Behavior on Generalization of Figural Pattern

Triwardani¹,

Fuad²,

Masriyah³

2018

Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018)

View full text Add to dashboard Cite

Pattern generalization is a core area in mathematics that is recognized by a community of researchers as an approach to develop student's algebraic reasoning. Examining students' generalization strategies of patterns becomes very important in term of learning advanced algebra. This study applied qualitative descriptive methods and was to investigate of students' reasoning behavior to generalize some algebraic patterns. The sample were the 8 th grade students of SMPN 2 Jatirejo Mojokerto. Two volunteer students (first and second) were selected as research subjetcs and based on the existing of students reasoning behaviors. The semi-structured interview were individually conducted to reveal students reasoning behaviors in constructing generalize patterns while they solved the given problem. The obtained data was classified through the generalization strategies in the existing literatures. According to the results of the task performed by the first subject, she performed figural reasoning based on the figural pattern task. The second subject categorized numerical reasoning based on the figural pattern task. The result of this study emphasized that students mainly utilized a recursive strategy to achieve immediate and near generalization. Two of subjects used functional strategy to reach the far generalization but had not yet received the correct answer. The expected implications of this study are as consideration for designing the learning on the generalization of patterns in accordance with the students' reasoning behavior.

show abstract

Variation of student numerical and figural reasoning approaches by pattern generalization type, strategy use and grade level

Cited by 27 publications

References 18 publications

Farklı Sınıf Seviyelerindeki Ortaokul Öğrencilerinde Cebirsel Düşünme: Örüntülerde Genelleme Hakkındaki Algıları

Farklı Sınıf Seviyelerindeki Ortaokul Öğrencilerinde Cebirsel Düşünme: Örüntülerde Genelleme Hakkındaki Algıları

Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities

Students' Reasoning Behavior on Generalization of Figural Pattern

Contact Info

Product

Resources

About