SBIR Phase I: Mathemantics: Diagnostic Math Games for Kindergarten Children

这个小企业创新研究（SBIR）第一阶段研究项目建立在几十年的数学教育研究的基础上，其中大部分未能在普通课堂上产生太大影响。我们的直接目标是为年轻学生创造一个丰富的数学世界，让他们探索，在这个世界里提出适合发展的挑战，监测儿童，因为他们参与解决问题，分析他们的行动，使他们的学习明智的推论，并使用该分析的结果，通知教师，并提出相关的建议。该项目将观察学生在没有指导的情况下与数学家的互动，寻找这样的导师可能有用的干预机会。基于这些观察，该项目将为Mathematics添加一个友好的基于计算机的化身，他将对学生的行为模式做出反应，并提供上下文敏感的帮助和反馈。该项目将汇总学生成绩数据，并利用这些数据以诊断报告的形式向教师提供形成性评估。其基本目标是将从数学教育和认知科学研究中获得的知识以可用和可操作的形式包装给教师和学生，从而将其引入小学课堂。结果表明，儿童发现他们很有吸引力，他们从他们那里学到了重要的数学概念，尽管有一名研究生在场，指导他们并给他们反馈。现在，该项目建议证明，通过适当的脚手架，这些游戏可以“独立”，以便儿童能够理解它们，并发现它们具有激励作用，最重要的是，他们将从中学习。也希望数学家能够产生教师认为可访问和有用的形成性评估。这些评估将与mCLASS：Math保持一致，mCLASS：Math是一款手持计算机应用程序，可指导教师与个别学生进行“临床访谈”，并分析教师输入的数据以生成诊断报告。在这项可行性研究取得成功之前，将制作mCLASS：Math的增强版，为如何定制Mathematics提供建议，以满足学生的需求并匹配每个学生的能力。通过向已经配备mCLASS：Math的教室提供Mathematics，我们将立即进入市场的一个重要的“早期采用者”部分。

This Small Business Innovation Research (SBIR) Phase I research project builds on decades of math education research, most of which has failed to have much impact in ordinary classrooms. Our immediate objective is to create a rich mathematical world for young students to explore, within that world to pose developmentally appropriate challenges, to monitor children as they engage in problem solving, analyze their actions to make informed inferences regarding their learning, and use the results of that analysis to inform teachers and to make instructionally relevant suggestions. The project will observe students' interaction with Mathemantics in the absence of mentoring, looking for opportunities where such a mentor might usefully have intervened. Based on these observations, the project will add to Mathemantics a friendly computer-based avatar who will react to patterns of student actions and provide context-sensitive help and feedback. The project will aggregate student performance data and use it to generate formative assessments in the form of diagnostic reports to teachers. The underlying goal is to introduce knowledge gained from math education and cognitive science research into elementary classrooms by packaging it for teachers and students in a usable and actionable form.In prior work a sequence of prototype Mathemantics games was created. It was demonstrated that children found them engaging and that they learned important mathematical concepts from them, albeit in the presence of a graduate student who guided them and gave them feedback. Now the project proposes to demonstrate that with appropriate scaffolding these games can 'stand alone' so that children will understand them and find them motivating, and most of all that they will learn from them. It is also hopes that Mathemantics is capable of generating formative assessments that teachers find accessible and useful. These assessments will be aligned to mCLASS:Math, an application for handheld computers that guides teachers through 'clinical interviews' with individual students and analyzes data teacher-entered to produce diagnostic reports. Pending a successful outcome of this feasibility study, an enhanced version of mCLASS:Math will be produced which will offer suggestions for how to customize Mathemantics to meet the needs and match the abilities of individual students. By offering Mathemantics to classrooms already equipped with mCLASS:Math, we will have immediate access to an important 'early adopter' segment of the market.