Conceptual Calculator for Fractions

描述（由申请人提供）：概念计算（tm）提出了分数的概念计算器（tm），这是对小学高年级和初中学生分数教学的重大创新。我们的目标是帮助解决我国中小学分数教学面临的挑战。第一阶段的可行性研究将侧重于一个基于网络的软件程序，为教师、学生和家长架起概念和程序理解的桥梁。这个软件既可以作为课程的补充，也可以作为学生的教学辅助。教师将能够分配给学生特定的问题集。该软件还将具有分析学生正在研究的特定分数问题的能力。该软件将引导学生掌握必要的技能，并对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，并被分配到接下来的挑战中。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，以及为有特殊残疾的学生提供的便利。在第一期项目中，我们将进行两类研究。首先是形成性评估，为我们的产品设计提供有价值的专家和用户意见。第二个是短期的、小规模的随机对照试验（RCT），以测试在第二阶段进行大规模随机对照试验的可行性，并建立合理的期望，即软件在适当实施时可以提高困难学生的成绩。RCT还将比较程序中嵌入的基于软件的学生测量与基于标准纸张的测量，目的是建立等效性，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。我们将仔细关注分数概念计算器的实现。实施服务将包括与地区领导一起规划、培训教师、确保在学校现场使用适当的软件、在教室里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，概念性计算将朝着商业上可行的软件程序取得重大进展。我们还将制定实施方案和一整套研究知识，为全面开展第二阶段工作奠定坚实基础。公共健康相关性：我们国家的学生在数学表现上落后于世界许多国家，这影响了我们在不断变化的国际商业环境中努力竞争的民众的福祉。概念计算（tm）建议将重点放在分数上，这是数学失败的一个有充分记录的起点，研究和开发分数的概念计算器（tm），这是小学高年级和初中的一项重大创新。该软件将帮助教师，学生，甚至家长提供成功的数学学习成果，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.