Multiple pathways for developing functional thinking in elementary mathematics textbooks: a case study in China

Ding, Rui; Huang, Rongjin; Deng, Xixi

doi:10.1007/s10649-023-10237-w

Cited by 2 publications

(5 citation statements)

References 52 publications

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“…Tasks GA3 and GA4 (adapted from Chimoni et al 2018) presented an equation that included numbers and symbols; students were expected to calculate the value of the symbols (GA3: $ + 12 = $ + $ + $, $ = ___; GA4: If for three primary reasons. Firstly, a textbook analysis reveals that content related to algebraic thinking starts in Grade 3, ensuring that students from this grade onward possess the foundational skills required for algebraic assessment, which has also been confirmed by the recent study conducted by Ding et al (2023). Secondly, abstract thinking and the capacity for generalization begin to manifest in students around the third grade.…”

Section: Instrumentsmentioning

confidence: 56%

“…These tasks are related to the ability to express numerical and figure + for three primary reasons. Firstly, a textbook analysis reveals that content related to alg braic thinking starts in Grade 3, ensuring that students from this grade onward posse the foundational skills required for algebraic assessment, which has also been confirme by the recent study conducted by Ding et al (2023). Secondly, abstract thinking and th capacity for generalization begin to manifest in students around the third grade.…”

Section: Instrumentsmentioning

confidence: 62%

“…Firstly, a textbook analysis reveals that content related to alge-Grade 3, ensuring that students from this grade onward possess required for algebraic assessment, which has also been confirmed nducted byDing et al (2023). Secondly, abstract thinking and the tion begin to manifest in students around the third grade.…”

mentioning

confidence: 76%

“…Functional thinking tasks involve the generalization of relationships betwee covarying quantities. These tasks are related to the ability to express numerical and figu = 16, then irstly, a textbook analysis reveals that content related to algede 3, ensuring that students from this grade onward possess ired for algebraic assessment, which has also been confirmed ted by Ding et al (2023). Secondly, abstract thinking and the begin to manifest in students around the third grade.…”

Section: Instrumentsmentioning

confidence: 91%

“…Additionally, the outstanding mathematics performance of Chinese students in large-scale international assessments like PISA has garnered attention from mathematics researchers (OECD 2020). Currently, research on early algebra in China primarily focuses on textbook analysis (Ding et al 2023) and curriculum comparisons (Cai et al 2011), with relatively less attention given to students' developmental levels of thinking. There is a shortage of research, especially regarding the exploration of developmental pathways and levels of algebraic thinking.…”

Section: Introductionmentioning

confidence: 99%

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The Developmental Progression of Early Algebraic Thinking of Elementary School Students

Sun,

2023

J. Intell.

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Developing algebraic thinking in elementary school has gained consensus among mathematics educators. The objective of this study is to understand the developmental trajectory of early algebraic thinking in elementary school students so as to assist teachers and curriculum developers in implementing instruction that aligns with students’ cognitive development. This study adopted a cross-sectional survey approach, involving 526 students from grades three to five in Shanghai, who were tested using a 12-item assessment that measured three aspects: “generalized arithmetic”, “functional thinking”, and “quantitative reasoning”. Latent class analysis was used to analyze students’ response strategies, and, in conjunction with individual interviews, this study identified potential developmental pathways in students’ early algebraic thinking, progressing from “arithmetic thinking” to “concrete algebraic thinking”, “generalized algebraic thinking”, and finally to “symbolic algebraic thinking”. As thinking levels advanced, significant differences in students’ response strategies emerged, with notable improvements in “generalization abilities” and “symbolization abilities”. This study suggests that educational practices should encompass content in elementary arithmetic curricula that fosters generalization abilities. Additionally, providing students with opportunities for diverse representations can effectively stimulate the development of early algebraic thinking.

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Section: Instrumentsmentioning

confidence: 56%

Section: Instrumentsmentioning

confidence: 62%

mentioning

confidence: 76%

Section: Instrumentsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

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The Developmental Progression of Early Algebraic Thinking of Elementary School Students

Sun,

2023

J. Intell.

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What is functional thinking? Using cosine similarity matrix in a semantic ontological analysis

Sumpter,

Blomqvist

2025

INT ELECT J MATH ED

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Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different aspects of the concept are used as a theoretical base. In this paper, we analyse different definitions used in empirical studies. First, we did a systematic research review resulting in 19 empirical studies focusing on functional thinking with an appropriate theoretical underpinning. The definitions were analysed using an AI tool. After that, we analysed the results using intrinsic mathematical properties of how functions can be defined in mathematics to identify core aspects of the definitions. According to the analysis, two definitions capture most of the key aspects of functional thinking, and most empirical studies use these key concepts. These two definitions treat functional thinking as products or products and processes. One definition used in one empirical study stands out by theoretically operationalizing functional thinking as a process. As such, different ontological assumptions are made in the studies; however, in some cases, having the same epistemological outcome. From a methodological point of view, the cosine similarity matrix was a useful tool for an ontological analysis, but a qualitative analysis is still needed to make meaning of it.

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Multiple pathways for developing functional thinking in elementary mathematics textbooks: a case study in China

Cited by 2 publications

References 52 publications

The Developmental Progression of Early Algebraic Thinking of Elementary School Students

The Developmental Progression of Early Algebraic Thinking of Elementary School Students

What is functional thinking? Using cosine similarity matrix in a semantic ontological analysis

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