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<p>Functional thinking has long been recognized as a crucial entry point into algebraic thinking in elementary school. This mixed-method study investigates the learning progression for elementary students’ functional thinking within the context of routine classroom instruction. Drawing on the existing research, a theoretical framework was constructed to assess the functional thinking of 649 students across grades 3 to 6. The framework includes three modes of functional thinking: recursive patterning, covariational thinking, and correspondence relations, each with particular and general layers of algebraic generality. Psychometric analysis was conducted to validate the assessment instrument. The study identifies a five-level learning progression of functional thinking: <i>Pre-Structure</i>, <i>Pre-Functional Thinking</i>, <i>Emergent Functional Thinking</i>, <i>Specific Functional Thinking</i>, and <i>Condensed Functional Thinking</i>. The distinctive characteristics of each level are identified and illustrated. Furthermore, the developmental sequence of different functional thinking modes within this learning progression is analyzed. Finally, the theoretical and practical implications of these findings are examined.</p>

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Investigating a learning progression of functional thinking for elementary students

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • Xixi Deng,
  • Rui Ding,
  • Rongjin Huang

摘要

Functional thinking has long been recognized as a crucial entry point into algebraic thinking in elementary school. This mixed-method study investigates the learning progression for elementary students’ functional thinking within the context of routine classroom instruction. Drawing on the existing research, a theoretical framework was constructed to assess the functional thinking of 649 students across grades 3 to 6. The framework includes three modes of functional thinking: recursive patterning, covariational thinking, and correspondence relations, each with particular and general layers of algebraic generality. Psychometric analysis was conducted to validate the assessment instrument. The study identifies a five-level learning progression of functional thinking: Pre-Structure, Pre-Functional Thinking, Emergent Functional Thinking, Specific Functional Thinking, and Condensed Functional Thinking. The distinctive characteristics of each level are identified and illustrated. Furthermore, the developmental sequence of different functional thinking modes within this learning progression is analyzed. Finally, the theoretical and practical implications of these findings are examined.