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

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.