【作者】 崔佳歆； 王利； 李大伟； 周新林；

【Author】 Jiaxin Cui;Li Wang;Dawei Li;Xinlin Zhou;State Key Laboratory of Cognitive Neuroscience,Learning & IDG/McGovem Institute for Brain Research,Advanced Innovation Center for Future Education,and Siegler Center for Innovative Learning,Beijing Normal University;Center for Cognitive Neuroscience,Duke University;

【机构】 北京师范大学脑与认知科学研究院； 杜克大学认知神经科学中心；

【摘要】 数学知识可以通过数学符号和字母表达,比如加法交换律"a+b=b+a";也可以通过自然语言表达,比如"在加法算式中,交换加数的位置,和不变"。以往教学研究报告提到了用自然语言表达的言语化数学知识对于数学学习起到正面作用,然而目前并不清楚言语化数学是否在数学成就中有不可替代的作用。在本研究中,我们假设言语化数学与学生的数学成就关系紧密,因为它有助于数学概念理解。241名大学生完成了言语化数学(数学术语语义关系判断和语言表达的数学计算规则正误判断)、符号化数学(符号表达的数学计算规则正误判断、数字序列推理和简单减法)和综合性数学成就测验,以及一般认知(反应速度、一般智力、视知觉图形匹配、心理旋转和三段论推理)和语言测验(句子填充)。结果表明,控制了一般认知和语言能力后,言语化数学能力与综合性数学成就密切相关,相关系数分别达到.30和.36;即使再控制了符号化数学成绩,言语化数学成绩依然与数学成就有显著相关关系,相关系数分别为.20(p=.003)和.25(p<.001)。路径分析结果表明,语言能力通过言语化数学知识对数学学习起作用。该结果说明与数学知识有关的语言支撑数学学习,且言语化数学练习有益于数学教育。更多还原

【Abstract】 Math knowledge can be expressed with math symbols(e.g.,a+b=b+a) and natural language(e.g.,"Exchanging the positions of addends in an addition does not change the result").Little research has evaluated the role of verbalized math on math performance.In this study,we hypothesized that verbalized math has a close relation with math performance due to the involvement of conceptual understanding.Undergraduates(N=241) were asked to perform two verbalized math tests(math term and verbalized math principle),math achievement tests,and tests on related general cognitive processes and symbolic math processes as covariates.Results showed that both verbalized math tests had substantial contributions to math achievement after all covariates(including language processing) were controlled for.Language processing contributed to math achievement through verbalized math.The results suggest that mathematical thinking could be supported by math-related language,and that math education might benefit from extensive practice of verbalized math.更多还原