Carnegie Mellon University.
Dev Psychol. 2013 Oct;49(10):1994-2004. doi: 10.1037/a0031200. Epub 2012 Dec 17.
We examined developmental and individual differences in 6th and 8th graders' fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross-sectional design. Results indicated that the difference between low achieving and higher achieving children's fraction arithmetic knowledge, already substantial in 6th grade, was much greater in 8th grade. The fraction arithmetic knowledge of low achieving children was similar in the 2 grades, whereas higher achieving children showed much greater knowledge in 8th than 6th grade, despite both groups having been in the same classrooms, using the same textbooks, and having the same teachers and classmates. Individual differences in both fraction arithmetic and mathematics achievement test scores were predicted by differences in fraction magnitude knowledge and whole number division, even after the contributions of reading achievement and executive functioning were statistically controlled. Instructional implications of the findings are discussed.
我们在一个横断面设计中研究了六年级和八年级学生分数算术和整体数学成绩的发展和个体差异，并将其与对分数大小、整数除法、执行功能和元认知判断的理解差异相关联。结果表明，在六年级已经相当显著的低成就儿童和高成就儿童之间的分数算术知识的差异，在八年级时更大。低成就儿童的分数算术知识在这两个年级是相似的，而高成就儿童在八年级的知识明显多于六年级，尽管两组都在同一个教室，使用相同的教科书，有相同的老师和同学。即使在统计控制了阅读成绩和执行功能的贡献之后，分数大小知识和整数除法的差异也可以预测分数算术和数学成绩测试分数的个体差异。讨论了这些发现的教学意义。
