R & D: Nurturing Multiplicative Reasoning in Students with Learning Disabilities in a Computerized Conceptual-Modeling Environmenty (NMRSD-CCME)

在计算机化概念建模环境中培养学习障碍学生的乘法推理(NMRSD-CCME)是一个为期五年的研究和开发项目，将通过提供工具来分析学生的概念并根据学生的个人需求制定最佳实践来加强教学实践。这个项目的目的是：(A)建立一个关于学习困难学生如何通过以改革为导向的教学法发展乘法推理的研究模型；(B)将该模型转化为一个计算机系统，动态模拟每个学生不断发展的概念并推荐任务，以促进他们进入更高水平的、基于标准的乘法结构和操作；以及(C)研究这种计算机化的教学工具如何影响学生的成绩，包括缩小学习困难学生与成绩正常的同龄人之间的差距。绩效指标借鉴了通用设计和三个以研究为基础的框架：来自计算机科学的机器(或统计)学习，来自特殊教育的文字问题基本结构(故事语法)的概括，以及从数学教育中学习的建构主义观点。后者包括认知教学可以通过引导学生对活动-效果关系的反思的任务和基于已有研究的具体内容的结构来促进学生将现有的数学概念转化为预期的数学概念。开发工作分三个阶段进行。第一个是教学实验，用SLDs来确定乘法推理的学习轨迹。第二个是开发一个计算机化的建模系统，以支持学生构建乘法推理(包括阿尔法、贝塔和试点测试)。最后一个阶段是对该系统进行评估，通过比较15名SLD学生和15名非SLD学生的学习过程和结果来判断该系统在缩小成绩差距方面的效果。此外，该系统对二语习得成绩的影响将与传统的教师授课对二语习得的影响进行比较。这些产品包括灵活和适应学习者的软件和供教师使用的协议。该项目还测试了动态推荐算法的可行性，这可能在乘法推理以外的其他领域以及其他学习数学概念有困难的学生中很重要。

Nurturing Multiplicative Reasoning in Students with Learning Disabilities in a Computerized Conceptual-Modeling Environment (NMRSD-CCME) is a five-year research and development project that will augment teaching practice by providing the tools to analyze student conceptions and enact best-practice on an individual, student-needs basis. The purpose of this project is to: (a) create a research-based model of how students with learning disabilities (SLDs) develop multiplicative reasoning via reform-oriented pedagogy, (b) convert the model into a computer system that dynamically models every student's evolving conceptions and recommends tasks to promote her/his advancement to higher level, standard-based multiplicative structures and operations, and (c) study how this computerized teaching tool impacts student outcomes, including diminishing the gap between SLDs and their normal achieving peers (NAPs). The PIs draw upon universal design and three research-based frameworks: machine (or statistical) learning from computer sciences, generalization of word-problem underlying structures (story-grammar) from special education, and a constructivist view of learning from mathematics education. The latter consists of recognizing teaching can promote transformation of students' available mathematical conceptions into intended ones via tasks that orient student reflection on activity-effect relationship and content-specific constructs informed by established research. The development is done in three stages. The first is a teaching experiment to determine learning trajectories for multiplicative reasoning with SLDs. The second is the development of a computerized modeling system to support students' construction of multiplicative reasoning (includes alpha, beta and pilot testing). The final stage is the evaluation of the system by comparing the learning process and outcomes of 15 SLD students with 15 non-SLD to judge the effect of the system on closing the achievement gap. In addition, the effect of the system on SLDs' performance will be compared to the effect of traditional teacher-delivered instruction on SLD. The products include software that is flexible and adaptive to the learner and protocols for teachers. The project also tests the viability of dynamic recommendation algorithms, which is likely to be important in other domains beyond multiplicative reasoning and with other students who have difficulties learning mathematics concepts.