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

本项目的目标是研究和支持发展的概念理解分数的学习障碍（LD）的学生。研究者建议，而不是专注于LD学生是否可以或不能发展分数的概念理解，研究应试图揭示LD学生的理解，并检查概念知识的增长发生在这些学生。 本研究通过一系列的教学实验，包括理论、设计、实施和改进的循环，为学习困难的学生发展分数领域的教学轨迹。解决的研究问题是：什么样的初始和发展中的关键发展的分数理解学习障碍的学生的证据，通过采用的策略，语言和表示？学习障碍学生如何通过数学活动发展和巩固分数的概念理解？ 以及，在何种程度上反映了一个基于研究的教学轨迹的干预促进战略发展和增加分数概念知识的学习障碍的学生？该项目的主要成果包括：（a）为学习困难学生提供一个以研究为基础的教学轨迹，专门针对分数作为数字量的概念理解;（B）一套90个分数任务，用于分数概念的教学和/或形成性评估;（c）评分/编码框架和检查表，用于关键任务的形成性评估;（d）决策框架，任务排序指南和建议，以帮助教师设计个性化的，以学生为中心的教学，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的数学教学提供一种变革性的方法，汇集了学习障碍和数学教育方面的专业知识，以解决一个研究很少的领域。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。她还将开发一个名为诊断和补救的研究生课程。

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.