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有学习障碍学生的乘法推理能力（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，并根据个人和学生的需求制定最佳实践，从而增加教学实践。本项目的目的是：(a)创建一个基于研究的学习障碍学生如何通过改革导向的教学法发展乘法推理的模型，(b)将该模型转换为一个计算机系统，该系统动态地模拟每个学生不断发展的概念，并建议任务，以促进他们向更高水平、基于标准的乘法结构和操作的发展，以及(c)研究这种计算机教学工具如何影响学生的成绩。包括缩小特殊学习障碍儿童和他们的正常同龄人之间的差距。pi借鉴了通用设计和三个基于研究的框架：来自计算机科学的机器（或统计）学习，来自特殊教育的词问题底层结构（故事语法）的泛化，以及来自数学教育的建构主义学习观。后者包括认识到教学可以促进学生现有数学概念向预期概念的转变，通过任务引导学生反思活动-效果关系和根据既定研究提供的特定内容结构。开发分为三个阶段。第一个是一个教学实验，以确定用SLDs进行乘法推理的学习轨迹。二是开发计算机建模系统，以支持学生构建乘法推理（包括alpha、beta和先导测试）。最后一个阶段是对系统的评价，通过比较15名特殊学习障碍学生和15名非特殊学习障碍学生的学习过程和结果，来判断系统在缩小成绩差距方面的效果。此外，还将比较该系统对特殊学生表现的影响与传统教师授课对特殊学生表现的影响。这些产品包括灵活适应学习者的软件和针对教师的协议。该项目还测试了动态推荐算法的可行性，这在乘法推理以外的其他领域以及对其他学习数学概念有困难的学生来说可能很重要。

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.