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Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities
The Journal of Mathematical Behavior Pub Date : 2020-03-01 , DOI: 10.1016/j.jmathb.2019.100753
Soo-hyun Im , Asha K. Jitendra

Abstract We investigated not only the effects of schema-based instruction (SBI) on the mathematical outcomes of seventh-grade students with mathematical learning disabilities (MLD), but also extended prior work to analyze students’ written explanations on open-ended items involving ratio and proportion situations—ratio, proportion, and percent of change problems— to understand the ability to reason about proportions and identify misconceptions. The sample of 338 students with MLD [scored below the 25th percentile on a proportional problem solving (PPS) pretest] was taken from Jitendra, Harwell, Im, et al. (2019), which randomly assigned classrooms to either the SBI or control condition. Students with MLD in SBI classrooms outperformed their counterparts in control classrooms on proportional problem solving and general mathematics problem solving. Similar results, favoring the SBI condition, were found on the open-ended items; however, overall mean scores across pretest, posttest, and delayed posttest were low. Findings provide evidence for the limited understanding of fractional representations of ratios and highlight students’ persistent use of numerical and additive reasoning in explaining their low performance on the open-ended items.

中文翻译:

数学学习障碍学生比例推理与误解分析

摘要 我们不仅调查了基于模式的教学 (SBI) 对有数学学习障碍 (MLD) 七年级学生数学成绩的影响,而且还扩展了先前的工作,以分析学生对涉及比率的开放式项目的书面解释。和比例情况——比例、比例和变化问题的百分比——了解推理比例和识别误解的能力。338 名 MLD 学生的样本 [在比例问题解决 (PPS) 预测试中得分低于 25%] 来自 Jitendra、Harwell、Im 等人。(2019 年),将教室随机分配到 SBI 或控制条件。在 SBI 课堂中患有 MLD 的学生在比例问题解决和一般数学问题解决方面的表现优于控制课堂中的同龄人。在开放式项目中发现了类似的结果,有利于 SBI 条件;然而,前测、后测和延迟后测的总体平均分数较低。调查结果为对比率分数表示的有限理解提供了证据,并突出了学生在解释他们在开放式项目上的低表现时持续使用数值和加法推理的情况。
更新日期:2020-03-01
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