SBIR Phase II: A Question of Numbers: Numeracy, Learning, and Learning about Learning

中小企业创新研究（SBIR）第2阶段项目是为了响应总统“创造与私人导师一样有效的数字导师”的号召。与其他学科相比，数学学习是一门积累性的学科，随着学生落后于同学，新材料变得越来越难以理解，他们与同龄人之间的差距也越来越大。形成性评估（FA）实践在缩小这些差距和为教师决策提供信息方面行之有效。虽然移动计算设备的涌入具有帮助促进教育变革的巨大潜力，但这种潜力在很大程度上取决于是否有经过验证的、有研究支持的软件和服务。该项目将为学生提供适应性、个性化的指导，并为教师提供有价值的FA技术、数据和建议，从而帮助缩小成绩差距。更广泛地说，这些数据将为研究和模拟学生的理解以及分析学习过程提供机会，从而为数学教学和学习的有效实践提供额外的研究。凭借其强大的客户价值主张和创新，将实现软件增强教学和学习的新形式，该项目还将在教育市场中创造重要的商业价值。该项目将创建数字学习环境，超越当前最先进的系统，提供自适应选择的教学视频片段和高度互动的问题，同时保持自然的内容流，就好像学习发生在真正的导师面前。该系统适应个别学生需求的能力是基于对学生理解程度的实时评估，并利用了形成性评估、机器学习、人工智能和大数据领域的前沿研究。模拟学生理解和分析学习过程的能力将导致新的学习分析工具的创造，并使对数学教学和学习的有效实践的进一步研究成为可能。拟议的研究将寻求在随机交叉试验中证明自适应在线系统优于对照治疗的有效性。研究的解决方案还将采用新颖的FA实现，如协作审查和白板（通过无线通信），教师作业的记录和回放，学生情感的使用，协作作业的同伴分组，以及包含教师输入的学生理解模型（教师加上FA循环中的软件）。

This Small Business Innovation Research (SBIR) Phase II project aims to answer the presidential call to "create digital tutors that are as effective as personal tutors." More than any other subject, mathematical learning is cumulative, and as students fall behind their classmates, new material becomes less comprehensible and they can face an ever-widening gap to their peers. Formative assessment (FA) practices have been well established as effective in closing these gaps and informing teacher decision-making. While the influx of mobile computing devices has enormous potential to help facilitate change in education, the potential is heavily dependent on the availability of proven, research-backed software and services. This project will help close achievement gaps by providing students with adaptive, personalized instruction and also providing teachers with valuable FA techniques, data, and suggestions. More broadly, the data will yield opportunities to research and model student understanding and to analyze the learning process, enabling additional research into effective practices for the teaching and learning of mathematics. With its strong customer value propositions and innovations that will enable new forms of software-enhanced teaching and learning, this project will also create significant commercial value within the educational market. This project will create digital learning environments that go beyond current state-of-the-art systems to deliver adaptively selected instructional video segments and highly interactive problems, and do so while maintaining a flow of content that feels natural - as if the learning was occurring in the presence of an actual tutor. The ability of the system to adapt to the needs of an individual student is based upon a real-time assessment of student understanding and leverages cutting edge research from the fields of formative assessment, machine learning, artificial intelligence and big data. The ability to model student understanding and analyze the learning process will lead to the creation of new learning analytics tools and enable additional research into effective practices for the teaching and learning of mathematics. The proposed research will seek to demonstrate, in a randomized crossover trial, the effectiveness of the adaptive, online system over a control treatment. The researched solutions will also employ novel FA implementations such as collaborative review and white-boarding (via wireless communication), record and playback of teacher work, use of student sentiment, groupings of peers for collaborative work, and models of student understanding that incorporate teacher input (teacher plus software in the FA loop).