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<p>Mathematics can be delineated as either arbitrary conventions—names, labels, symbols, notations, or usages which have been historically agreed upon by “mathematicians”—or necessary rules, relationships, and properties (Hewitt in Learn Math 19(3):2–9). To illustrate, the <i>x</i>–<i>y</i> naming of axes on a Cartesian graph stems from variables chosen in 1637 by French mathematician and philosopher René Descartes (as reported by Burton (The history of mathematics: An introduction, McGraw-Hill, 1998); by Katz (A history of mathematics: An introduction, HarperCollins, 1998)). This study was guided by the question, “How are conventions introduced and treated in elementary classrooms in the context of introducing coordinate graphing?” A common set of 12 early algebra lessons enacted in 78 classrooms across the grades 3–5 were coded using a modified analytic induction approach. Teachers rarely explicitly addressed conventions as such despite occasionally using language attributing conventions to external agents (e.g., “they”, “people”, “mathematicians”) during instruction. Mnemonics and analogies were often used to support the introduction of conventions. On occasion, teachers presented overly rigid boundaries as mathematical conventional truths—an idea introduced in this study as “(mis)conventions.” Findings pertaining to students’ questions about mathematical conventions and cases of delegated authority to students for exploration of alternatives to canonical conventions are also addressed.</p>

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Elementary teachers’ treatment of mathematical conventions in lessons introducing coordinate graphing

  • 期刊论文

  • 发表日期：

    2025年10月24日

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  • Ingrid Ristroph

摘要

Mathematics can be delineated as either arbitrary conventions—names, labels, symbols, notations, or usages which have been historically agreed upon by “mathematicians”—or necessary rules, relationships, and properties (Hewitt in Learn Math 19(3):2–9). To illustrate, the x–y naming of axes on a Cartesian graph stems from variables chosen in 1637 by French mathematician and philosopher René Descartes (as reported by Burton (The history of mathematics: An introduction, McGraw-Hill, 1998); by Katz (A history of mathematics: An introduction, HarperCollins, 1998)). This study was guided by the question, “How are conventions introduced and treated in elementary classrooms in the context of introducing coordinate graphing?” A common set of 12 early algebra lessons enacted in 78 classrooms across the grades 3–5 were coded using a modified analytic induction approach. Teachers rarely explicitly addressed conventions as such despite occasionally using language attributing conventions to external agents (e.g., “they”, “people”, “mathematicians”) during instruction. Mnemonics and analogies were often used to support the introduction of conventions. On occasion, teachers presented overly rigid boundaries as mathematical conventional truths—an idea introduced in this study as “(mis)conventions.” Findings pertaining to students’ questions about mathematical conventions and cases of delegated authority to students for exploration of alternatives to canonical conventions are also addressed.