NSF Award
2400686
One goal of mathematics curricular and instructional reforms in the United States is to help students build “mature number sense,” which involves making sense of numbers and operations, using reasoning to notice patterns, and flexibly selecting the most effective and efficient problem-solving strategies. In support of this goal, mathematics educators have developed a variety of instructional practices designed to move students beyond seeing mathematics as a set of disconnected procedures and facts to appreciating it as a coherent set of ideas and tools. These practices have been growing in popularity across mathematics classrooms, but it is unclear whether they are effective. Moreover, there is limited evidence on the typical progression of students’ mature number sense across elementary and middle school. How does students’ mature number sense change across a school year? Does that pattern of change differ by grade level? Lack of such knowledge is a critical problem because, without it, researchers cannot explain, predict, and study mature number sense, and teachers are left to rely on their own intuitions about whether and how to focus on it in their classrooms. In this project, researchers will advance fundamental knowledge of mathematical cognition through a yearlong study of the progression of 3rd-8th grade students’ mature number sense. They will determine how malleable mature number sense is and how any such changes in mature number sense relate to students’ grade-level mathematics content learning. This project is funded by the ECR program which supports fundamental research that generates foundational knowledge that advances the research literatures in STEM learning and learning environments, broadening participation in STEM, and STEM workforce development.<br/><br/>The central hypothesis of this project is that mature number sense is a distinct and malleable characteristic of mathematical cognition that predicts students’ learning of grade-level mathematics content. The research team will work with a diverse sample of students in grades 3-8 to determine the malleability of mature number sense and how changes in mature number sense relate to students’ grade-level mathematics learning. They will start by studying the progression of 3rd-8th grade students’ mature number sense both within a school year and cross-sectionally across grade levels. They will collect student scores on a measure of mature number sense at three timepoints over a year, analyzing how students grow within a grade level as well as comparing how students grow across grade levels. The research team will then interview a representative subsample of students, balanced across grade levels, at two timepoints in the year to gain an in-depth understanding of their mature number sense. The researchers will pair student scores from the assessments with their cognitive interview reports to examine what has changed when students grow in mature number sense. In addition, the research team will examine if growth in mature number sense predicts students’ grade-level achievement at the end of the year, controlling for initial achievement, multiplication fluency, and grade level. By the end of the project, there will be significant evidence on the typical progression of students’ mature number sense in grades 3-8. The project will advance the understanding of a foundational construct in mathematical cognition and a core proficiency with longstanding importance in mathematics education.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
