کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
360750 | 1436021 | 2013 | 14 صفحه PDF | دانلود رایگان |
The purpose of this paper is to illustrate cognitive challenges introduced by Common Core State Standards for Mathematics (2010) with regard to conceptualizing fractions. We focus on a strand of standards that appear across grades three through five, which is best represented in grade four, by standard 4.NF.4a: “[Students should] understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).” We argue that supporting such conceptualizations is a critical challenge for teachers and researchers to address in US education, but one fraught with conceptual hurdles for students. We adopt a scheme theoretic perspective and share the case study of a sixth-grade student, to illustrate the ways of operating students need to develop for meaningful attainment of the new standards.
► We investigate a fractions learning progression stipulated by Common Core Standards.
► We highlight cognitive challenges associated with attaining the new standards.
► Findings suggest standards need to further account for learning trajectories.
► Units coordination plays a critical role in conceptualizing fractions.
Journal: The Journal of Mathematical Behavior - Volume 32, Issue 2, June 2013, Pages 266–279