An Analysis of Algebraic Thinking by Third Graders

Jeongsuk, Pang; Choi, Inyoung

doi:10.7468/jksmec.2016.19.3.223

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…In fact, students found correspondence thinking in a multiplicative relationship as difficult as such thinking in a square relationship (CP4 and CG4). To be clear, previous studies claimed that students had difficulties identifying and representing a square relationship and a linear relationship (e.g., Choi & Pang, 2012;Pang & Choi, 2016;Pinto et al, 2022;Stephens et al, 2017). This study extended these previous studies by showing the possibility that students' difficulties can differ depending on the functional thinking modes.…”

Section: Jermsupporting

confidence: 72%

“…Nevertheless, when asked to identify a rule for a linear relationship, a little less than half of the third graders examined in a previous study could succeed (Pang & Choi, 2016). A previous study's survey results concerning students' understanding of various functional relationships (Choi & Pang, 2012) showed that the fourth and sixth graders demonstrated considerable high performance both for a square relationship (i.e., 44.1% and 77.8%, respectively) and for a linear relationship (i.e., 55.0% and 81.9%).…”

Section: Literature Review 1 Types Of Functional Relationshipsmentioning

confidence: 98%

“…Specifically, we chose third-grade students mainly because they were expected to demonstrate various modes of functional thinking (Pang & Choi, 2016). Note that the third graders in this study did not learn covariation or correspondence relationships through their regular mathematics curriculum.…”

Section: Research Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

Task Development to Measure Functional Thinking: Focusing on Third Graders’ Understanding

Jeongsuk

Kim

Sunwoo³

2022

Kor Soc Edu Stu Mathematics -J Edu Re Mathematics

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The purpose of this study was to develop the tasks to measure functional thinking and to verify their suitability by applying them to third-grade students. For this purpose, various tasks related to functional thinking were analyzed and developed according to the different modes of functional thinking and functional relationships. To verify the tasks, the Cronbach's α value for each task type was calculated with the results of how the third graders solved the tasks. Exploratory factor analysis (EFA) was performed as needed. As a result, tasks were developed to measure four types of thinking: recursive, covariation, correspondence-particular, and correspondence-general. In particular, recursive patterning tasks were divided into repeated geometric patterns, growing geometric patterns, repeated numeric patterns, and growing numeric patterns through EFA. Only growing geometric patterning and growing numeric patterning tasks were found to be suitable for measuring third-grade students' recursive thinking. Growing numeric patterning tasks were divided by arithmetic sequences and other sequences through EFA. The covariation, correspondence-particular, and correspondence-general tasks developed in this study were also verified. Contrary to the consistently high performance regarding the additive relationships, students' functional thinking varied depending on the different types of functional relationships. This study is expected to inspire researchers to pay more attention to task development and verification to measure students' functional thinking.

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Section: Jermsupporting

confidence: 72%

Section: Literature Review 1 Types Of Functional Relationshipsmentioning

confidence: 98%

See 1 more Smart Citation

Task Development to Measure Functional Thinking: Focusing on Third Graders’ Understanding

Jeongsuk

Kim

Sunwoo³

2022

Kor Soc Edu Stu Mathematics -J Edu Re Mathematics

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Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective

Jeongsuk

Kim²

2017

Teaching and Learning Algebraic Thinking With 5- To 12-Year-Olds

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A Case Study on the Changes in the Levels of Arithmetical Thinking and Transition to Algebraic Thinking of a 7th Grader who was an Underachiever in Number and Operation

Lim¹,

Chang²

2018

Kor Soc Edu Stu Mathematics -J Edu Re Mathematics

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Arithmetic and algebra are considered to be the most basic and core contents in school mathematics. However, many students in elementary and middle school have difficulties in arithmetic and algebra learning, and immense studies have been carried out in the field of mathematics education to solve these problems. The present study is a follow-up study which was conducted following the previous study conducted on a student who had difficulties in number and operation domain. This study investigated the manner in which the level of arithmetical thinking changed and how the transition from arithmetical thinking to algebraic thinking occurred after that student spent a year studying mathematics in middle school. Based on the results of the analysis, we suggest several implications for teaching and learning of number and operation domain at elementary and middle school in terms of the development of arithmetical thinking.

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An Analysis of Algebraic Thinking by Third Graders

Cited by 4 publications

References 6 publications

Task Development to Measure Functional Thinking: Focusing on Third Graders’ Understanding

Task Development to Measure Functional Thinking: Focusing on Third Graders’ Understanding

Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective

A Case Study on the Changes in the Levels of Arithmetical Thinking and Transition to Algebraic Thinking of a 7th Grader who was an Underachiever in Number and Operation

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