CAREER: Fraction Activities and Assessments for Conceptual Teaching (FAACT) for Students with Learning Disabilities

本计划的目标是研究和支持学习障碍学生对分数概念理解的发展。研究人员建议，与其关注LD学生是否能够或不能发展对分数的概念理解，不如尝试揭示LD学生的理解，并研究这些学生的概念知识是如何增长的。这种方法建议对数学研究和教学实践进行重新概念化，将重点放在LD学生实际上可以发展的概念性知识上。通过一系列的教学实验，包括理论、设计、实施和改进的循环，该项目为LD学生在分数领域发展了教学轨迹。研究的问题是：学习障碍的学生通过使用策略、语言和表征来证明对分数的初始和发展中的关键发展理解是什么？有学习障碍的学生如何通过数学活动来发展和巩固对分数的概念理解？并且，在多大程度上，反映基于研究的教学轨迹的干预有助于学习障碍学生的策略发展和增加概念知识的比例？该项目的主要成果包括：(a)为有学习障碍的学生提供一个以研究为基础的教学轨迹，特别是对分数作为数字量的概念理解，(b)一套90个分数任务，用于分数概念的指导和/或形成性评估，(c)用于形成性评估的关键任务的评分/编码框架和清单，(d)决策框架，任务排序指南，以及帮助教师设计个性化、以学生为中心的教学的建议，所有这些都可以通过互联网获得。最重要的是，该项目有可能为学习障碍学生提供一种变革性的数学教学方法，将学习障碍和数学教育方面的专业知识结合起来，解决这一研究很少的领域。PI将把研究结果纳入数学教育和特殊教育学生的方法课程。她还将开设一门名为“诊断与补救”的研究生课程。

The goal of this project is to study and support the development of conceptual understanding of fractions by students with learning disabilities (LD). The researcher proposes that rather than focusing on whether LD students can or cannot develop conceptual understanding of fractions, research should attempt to uncover the understanding LD students have and examine how growth of conceptual knowledge occurs in these students. This approach suggests a reconceptualization of research and instructional practice in mathematics that focus on the conceptual knowledge students with LD can in fact develop.Through a series of teaching experiments that involve cycles of theorizing, design, implementation, and refinement, the project develops instructional trajectories for LD students in the area of fractions. The research question addressed are: What initial and developing key developmental understandings of fractions do students with learning disabilities evidence through employed strategies, language, and representations? How do students with learning disabilities progress in developing and solidifying conceptual understandings of fractions through their mathematical activity? And, to what extent does an intervention reflective of a research based instructional trajectory facilitate strategic development and increased fraction conceptual knowledge in students with learning disabilities?The main outcomes of the project include (a) a research-based instructional trajectory for students with LD specific to conceptual understandings of fractions as numeric quantities, (b) a set of 90 fraction tasks to be used for instruction and/or formative assessment in fraction concepts, (c) scoring/coding frameworks and checklists for use with key tasks as formative assessments, (d) decision-making frameworks, task sequencing guides, and suggestions to aid teachers in designing individualized, student-centered instruction, all available via the Internet. Most important, the project has the potential to offer a transformative approach to mathematics instruction for students with LD, bringing together expertise on learning disabilities and mathematics education to address a area in which there is very little research. The PI will incorporate finding from the study into methods courses for both mathematics education and special education students. She will also develop a graduate course entitled Diagnosis and Remediation.