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

SBIR第一阶段项目建议确定数学教学中形成性评估(FA)技术的新软件实施的可行性。IPad等平板设备在促进教育革命性变革方面有着巨大的潜力，但这种潜力在很大程度上依赖于合适的软件和服务的可用性。拟议的活动将研究当教师的作用被计算机辅助教学平台扩大时，课堂教学技术可以在多大程度上得到应用或加强。他们将寻求创造适应性学习环境，超越当前最先进的系统，将适应性应用于作为教学视频片段提供的自由形式内容和高度互动的问题，并在这样做的同时保持感觉自然的内容流。拟议的活动还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，并使更多关于数学教与学的有效做法的研究成为可能。拟议活动的潜在更广泛影响包括改善学生获得数学的机会；增加未被充分代表的群体参与科学、技术、工程和数学(STEM)；以及通过知情的教师实践和教育者发展改善STEM教育。拟议的活动直接针对课程中关键时刻的数学教育：预代数准备，与小学年级数学流利程度差异很大的水平形成对比。如果没有扎实的预代数数学能力，许多对参与现代世界至关重要的学科就很难或不可能掌握，学术信心和承诺也会受到侵蚀。与其他任何学科相比，数学学习是积累的，随着学生落后于同学，新材料变得越来越不容易理解，通过这种反馈，他们面临着与同龄人越来越大的差距。形成性评估做法在缩小这些差距和为教师决策提供信息方面是行之有效的。正是通过建立具有新颖的、基于软件的形成性评估的工具包，并帮助推动教育者采用新的形成性评估技术，拟议的研究可能会产生这些更广泛的影响。通过满足主要客户需求，该项目将在教育市场内创造显著的新商业价值。

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.