Conceptual Calculator for Fractions

描述(由申请人提供)：概念计算(Tm)提出了分数概念计算器(Tm)，这是对高年级小学和中学学生教授分数的一项重大创新。我们的目标是帮助解决我们在向中小学生教授分数方面的全国性挑战。第一阶段的可行性研究将重点放在一个基于网络的软件项目上，该项目将为教师、学生和家长在概念和程序上的理解架起桥梁。该软件既可以作为课程补充，也可以作为学生的教学辅助工具。教师将能够给学生布置特定的问题集。该软件还将具有分析学生正在学习的特定分数问题的能力。该软件将指导学生掌握必备技能，并就解决问题所需的基本概念和程序提供直接和明确的指导。然后，学生们将被评估他们的进步，并被分配到后续的挑战中。学生将得到大量的支持，包括操作软件的口头解释，错误回答的策略反馈，以及为特定残疾学生提供的便利。在这个一期工程中，我们将进行两种类型的研究。首先是形成性评价，为我们的产品设计提供有价值的专家和用户意见。第二个是短期、小规模的随机对照试验(RCT)，以测试第二阶段大规模随机对照试验的可行性，并建立合理的预期，即该软件如果实施得当，可以提高困难学生的成绩。RCT还将比较嵌入在计划中的基于软件的学生衡量标准与基于标准纸面的衡量标准，目的是建立等价性，并为在第二阶段和商业化期间依赖软件进度监测铺平道路。我们将认真关注分数概念计算器的实现。实施服务将包括与地区领导人一起规划、培训教师、确保学校现场适当使用软件、在教室中进行联合教学，以及提供定期的教师支持。在第一阶段工作结束时，概念计算将在商业上可行的软件程序方面取得重大进展。我们还将制定执行方案和大量研究知识，为第二阶段的全面工作奠定坚实的基础。与公共健康相关：我们国家的学生在数学成绩上落后于世界大部分地区，这影响了我们民众的福祉，因为我们正在努力在不断变化的国际商业环境中竞争。概念计算(Tm)建议关注分数，这是数学失败的一个有充分证据的起点，研究和开发分数概念计算器(Tm)，这是高中小学和中学的一项重大创新。该软件将帮助教师、学生甚至家长提供成功的数学学习结果，并提高学生的成绩。

DESCRIPTION (provided by applicant): Conceptual Calculations(tm) proposes The Conceptual Calculator(tm) for Fractions, a significant innovation for teaching fractions to students in upper elementary and middle school. The goal is to help solve our national challenge in teaching fractions to elementary and middle school students. The Phase I feasibility study will focus on a web-based software program that bridges conceptual and procedural understandings for teachers, students, and parents. The software will be useful both as a curriculum supplement and as an instructional aid to students. Teachers will be able to assign students specific problems sets. The software will also have the capacity to analyze a specific fractions problem on which a student is working. The software will guide students to master prerequisite skills, and provide direct and explicit instruction on the both the underlying concepts and the procedures required to solve the problem. Students will then be assessed on their progress and assigned to move on to subsequent challenges. Students will receive a great deal of support including verbal explanations for operating the software, strategic feedback for incorrect responses, and accommodations for students with specific disabilities. In this Phase I project, we will conduct two types of research. The first is formative evaluation, to inform our product design with valuable expert and user opinion. The second is a short-term, small-scale randomized controlled trial (RCT), to test the feasibility of a large scale RCT in Phase II and to establish reasonable expectations that the software can raise achievement for struggling students when properly implemented. The RCT will also compare software-based student measures embedded in the program with criterion paper-based measures, with the goal of establishing equivalency and paving the way for reliance on software progress monitoring during Phase II and commercialization. We will pay careful attention to the implementation of The Conceptual Calculator for Fractions. Implementation services will include planning with district leaders, training teachers, assuring proper software access at the school sites, co-teaching in classrooms, and offering regular teacher support. At the conclusion of the Phase I effort, Conceptual Calculations will have made major strides towards a commercially viable software program. We will have also developed implementation protocols and a body of research knowledge that will form a strong basis for a full Phase II effort. PUBLIC HEALTH RELEVANCE: Our nation's students trail much of the world in mathematical performance, and this is impacting the well-being of our populace as we struggle to compete in the evolving international business climate. Conceptual Calculations(tm) proposes to focus on fractions, a well-documented starting point in mathematical failure, with research and development of The Conceptual Calculator(tm) for Fractions, a significant innovation for upper elementary and middle school. This software will help teachers, students, and even parents to provide successful mathematical learning outcomes and raise student achievement.