Defining and measuring quality in students’ mathematical writing: a systematic literature review

IF 1.4 Q3 EDUCATION, SCIENTIFIC DISCIPLINES
Anna Teledahl, Cecilia Kilhamn, Linda Marie Ahl, Ola Helenius
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Abstract

Mathematical communication, encompassing writing in, about, and for mathematics, is a critical competency. Defining excellent mathematical writing standards, however, remains challenging. To address this, we conducted a systematic review of 48 scholarly works on quality in mathematical writing. Our findings reveal mathematical writing for different purposes under scrutiny, including general mathematical writing, proof writing, reflective writing, expository writing, and descriptive writing during problem solving. To assess quality, researchers explore a variety of facets, such as syntax and semantics. Progression pathways vary, with both quantitative and qualitative evaluations—analysing text structure, writing style, and the use of different semiotic elements. It seems that in mathematics education, a consensus on quality measurement remains elusive. Proof writing is a notable exception. Among reviewed articles examining proof writing, a common set of standards emerges and provides valuable guidance. We propose that mathematical writing, perhaps especially in the context of reporting solutions in problem solving, can draw from proof writing standards. ‘Good’ mathematical writing would then require students to focus on (1) defining assumptions and assigning variables; (2) producing a coherent narrative, including relevant calculations (semantic issues); (3) using correct language, representations, and mathematical symbols (syntax issues); and (4) attending to what is appropriate in the context.

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定义和衡量学生数学写作的质量:系统文献综述
数学交流,包括数学写作、关于数学的写作和为数学而写作,是一项重要的能力。然而,定义优秀的数学写作标准仍然具有挑战性。为此,我们对 48 篇有关数学写作质量的学术著作进行了系统回顾。我们的研究结果表明,不同目的的数学写作都受到了严格的审查,包括一般数学写作、证明写作、反思写作、说明性写作和问题解决过程中的描述性写作。为了评估写作质量,研究人员探讨了语法和语义等多个方面。进阶途径各不相同,既有定量评价,也有定性评价--分析文本结构、写作风格和不同符号元素的使用。在数学教育中,似乎仍未就质量衡量达成共识。证明写作是一个明显的例外。在审查证明写作的文章中,出现了一套共同的标准,并提供了有价值的指导。我们建议,数学写作,尤其是在报告问题解决过程中的解决方案时,可以借鉴证明写作的标准。好的 "数学写作将要求学生专注于:(1)定义假设和分配变量;(2)进行连贯的叙述,包括相关的计算(语义问题);(3)使用正确的语言、表述和数学符号(语法问题);以及(4)关注语境中的适当内容。
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来源期刊
Mathematics Education Research Journal
Mathematics Education Research Journal EDUCATION, SCIENTIFIC DISCIPLINES-
CiteScore
4.80
自引率
11.10%
发文量
30
期刊介绍: The Mathematics Education Research Journal seeks to promote high quality research that is of interest to the international community.   The Mathematics Education Research Journal seeks to present research that promotes new knowledge, ideas, methodologies and epistemologies in the field of mathematics education.    The Mathematics Education Research Journal actively seeks to promote research from the Australasian region either as research conducted in the region; conducted by researchers from the region and/or draws on research from the region.  The Mathematics Education Research Journal accepts papers from authors from all regions internationally but authors must draw on the extensive research that has been produced in the Australasian region.   The Mathematics Education Research Journal normally does not encourage publication of teacher education programs or courses. These are more suited for theother MERGA journal, Mathematics Teacher Education and Development.
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