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

这个项目的目标是研究和支持有学习障碍的学生对分数概念理解的发展。研究人员建议，与其关注学习困难学生是否能够发展对分数的概念理解，不如尝试揭示学习困难学生对分数的理解，并考察这些学生的概念知识是如何增长的。这一方法建议对数学研究和教学实践进行重新构思，将重点放在学习困难学生实际上可以发展的概念性知识上。通过一系列涉及理论、设计、实施和改进的教学实验，该项目为学习困难学生开发了分数领域的教学轨迹。研究问题是：有学习障碍的学生通过使用策略、语言和表征，对分数的初始和发展的关键发展理解是什么？学习困难学生如何通过他们的数学活动发展和巩固对分数的概念理解？以及，反映基于研究的教学轨迹的干预措施在多大程度上促进了学习障碍学生的策略发展和增加分数概念知识？该项目的主要成果包括：(A)针对学习困难学生的针对分数概念理解的研究性教学轨迹，(B)一组90个分数任务用于分数概念的教学和/或形成性评估，(C)用于作为形成性评估的关键任务的评分/编码框架和核对表，(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，该项目有可能为有学习障碍的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，以解决这个研究很少的领域。该中心将把研究结果纳入数学教育和特殊教育学生的方法课程。她还将开发一门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.