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<p>Textbooks play a crucial role in shaping instructional practices, making it essential to examine the reasoning-and-proving (RP) opportunities that they offer. While previous research on RP opportunities in textbooks has focused primarily on the secondary mathematics level, this study applies an established analytical framework to explore RP opportunities in the “number and early algebra” domain across 12 volumes of elementary textbooks (grades 1–6) in China. Across the 12 textbook volumes analyzed, RP tasks accounted for an average of 17.18% of the content, with notable differences between narrative sets (26.08%) and exercise sets (12.93%). In narrative sets, RP tasks focus on articulating justifications (48.4%) and identifying patterns (22.3%), with 45.7% of pattern-identifying tasks serving as conjecture precursors. Additionally, 40.1% of RP tasks use arithmetic representation forms. With respect to exercise sets, most RP tasks focus on articulating justifications (67.4%), with 39.3% of pattern-identifying tasks also serving as conjecture precursors and 40.0% of conjecture-making tasks serving as justification precursors. These exercise sets also feature a wider range of representation forms. Together, these findings suggest several directions for strengthening RP integration in future textbook development, guiding educators and curriculum developers to better foster students’ analytical and problem-solving skills in mathematics.</p>

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Opportunities for learning reasoning-and-proving in number and early algebra in China: an analysis of elementary mathematics textbooks

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Da Zhou,
  • Jinqing Liu,
  • Yifei Liu,
  • Heyang Zhang

摘要

Textbooks play a crucial role in shaping instructional practices, making it essential to examine the reasoning-and-proving (RP) opportunities that they offer. While previous research on RP opportunities in textbooks has focused primarily on the secondary mathematics level, this study applies an established analytical framework to explore RP opportunities in the “number and early algebra” domain across 12 volumes of elementary textbooks (grades 1–6) in China. Across the 12 textbook volumes analyzed, RP tasks accounted for an average of 17.18% of the content, with notable differences between narrative sets (26.08%) and exercise sets (12.93%). In narrative sets, RP tasks focus on articulating justifications (48.4%) and identifying patterns (22.3%), with 45.7% of pattern-identifying tasks serving as conjecture precursors. Additionally, 40.1% of RP tasks use arithmetic representation forms. With respect to exercise sets, most RP tasks focus on articulating justifications (67.4%), with 39.3% of pattern-identifying tasks also serving as conjecture precursors and 40.0% of conjecture-making tasks serving as justification precursors. These exercise sets also feature a wider range of representation forms. Together, these findings suggest several directions for strengthening RP integration in future textbook development, guiding educators and curriculum developers to better foster students’ analytical and problem-solving skills in mathematics.