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

这个SBIR第一阶段项目提出，以确定新的软件实现的形成性评估（FA）技术的数学教学的可行性。iPad等平板设备具有促进教育革命性变革的巨大潜力，但这种潜力在很大程度上取决于适当软件和服务的可用性。拟议的活动将研究在何种程度上课堂FA技术可以应用或增强时，教师的作用是增强了计算机辅助教学平台。他们将寻求创建自适应学习环境，超越当前最先进的系统，并将自适应性应用于作为教学视频片段和高度互动的问题提供的自由形式的内容，并在保持内容流的同时保持自然的感觉。拟议的活动也有可能为分析数学教育和干预措施中的有效技术提供新的工具。模拟学生理解和分析学习过程的能力将导致创建新的学习分析工具，并使更多的研究成为数学教学和学习的有效做法，拟议活动的潜在更广泛的影响包括改善学生获得数学;增加代表性不足的群体在科学技术工程和数学（STEM）中的参与;并通过知情的教师实践和教育工作者的发展来改善STEM教育。拟议的活动直接解决数学教育在课程的一个关键点：前代数准备，对数学的流利程度，出现了小学年级的广泛差异。如果没有坚实的设施与前代数数学，许多科目是必不可少的参与现代世界变得困难或不可能掌握和学术信心和承诺侵蚀。数学学习比任何其他学科都要累积，随着学生落后于同学，新材料变得越来越难以理解，通过这种反馈，他们与同龄人的差距不断扩大。形成性评估的做法已被公认为有效地缩小这些差距，并告知教师的决策。通过建立具有新颖的、基于软件的形成性评估的工具包，并帮助推动教育工作者采用新的形成性评估技术，拟议的研究可能会产生更广泛的影响。通过满足关键客户需求，该项目将在教育市场中创造重要的新商业价值。

This SBIR Phase I project proposes to determine the feasibility of new software implementations of formative assessment (FA) techniques for mathematics instruction. Tablet devices such as the iPad have an enormous potential to facilitate revolutionary change in education, but such potential is heavily dependent on the availability of appropriate software and services. The proposed activities will research the extent to which classroom FA techniques can be applied or enhanced when the teacher's role is augmented by a platform for computer aided instruction. They will seek to create adaptive learning environments that go beyond current state-of-the-art systems and that apply the adaptivity to free-form content delivered as instructional video segments and highly interactive problems, and to do so while maintaining a flow of content that feels natural. The proposed activities also have the potential to provide new tools for the analysis of effective techniques in mathematics education and interventions. 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 potential broader impacts of the proposed activities include improved student access to mathematics; the increased participation of underrepresented groups in Science Technology Engineering and Mathematics (STEM); and improved STEM education through informed teacher practice and educator development. The proposed activities directly address mathematics education at a critical point in the curriculum: pre-algebra readiness, as set against the widely differing levels of mathematical fluency that emerge out of the elementary grades. Without a solid facility with pre-algebra mathematics, many subjects that are essential to participation in the modern world become difficult or impossible to master and academic confidence and commitment erode. More than any other subject, mathematical learning is cumulative, and as students fall behind their classmates, new material becomes less and less comprehensible and through this feedback they face an ever-widening gap to their peers. Formative assessment practices have been well-established as effective in closing these gaps and informing teacher decision making. It is by establishing toolkits with novel, software-based, formative assessment and helping to drive educator adoption of new formative assessment techniques that the proposed research may deliver these broader impacts. By addressing key customer needs, the project will create significant new commercial value within the educational market.