ECR Projects

Explore past and current fundamental STEM education research projects across the three research areas that NSF's EDU Core Research (ECR) program funds, as well as across ECR funding types. Other search filters draw from both NSF's data and the ECR Hub's hand coding of award abstracts.

Ninth-grade biology students create cell models using clay.

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Becoming Euclid: Characterizing the geometric intuitions that support formal learning in mathematics

Effective Years: 2019-2024

Only humans are capable of doing formal mathematics, like the geometry in Euclid's Elements. The arguments and proofs of this geometry require one to imagine points so small they have no dimension and lines that extend so far they never end. And yet the points and lines experienced in everyday life have dimension and are finite. Where do the uniquely human ideas of abstract points and lines come from? To what extent does human reasoning work with idealizations and abstractions and to what extent does it remain rooted in everyday, physical finitudes? This project will address such questions by exploring three interrelated cognitive aspects of human geometric aptitude: 1) the role of mental simulation and rule-based reasoning in children's and adults' basic judgments about triangles; 2) the conditions that allow infants, children, and adults to identify lines as the shortest distance between two points; and 3) the effects of couching geometry in a physical context (e.g., gravity) on children's and adults' judgments about the fastest path between two locations in space. This proposal will characterize how early emerging perceptual sensitivities to the properties of the scenes and objects of everyday life might form the foundation of human understanding of the imperceptible. This understanding lies at the heart of much human achievement and also constitutes one of the main aims of school learning. The promise of this project is that in uncovering the basic and universal spatial intuitions humans rely on when confronted with difficult and novel geometry problems, the field will better be able to develop pedagogies that build on the strengths and supplement the limitations of these intuitions. The project is supported by a CAREER award to New York University by the EHR Core Research (ECR) program, which supports work that advances the fundamental research literature on STEM learning.

In three series of experiments, the project will both conduct research in active educational settings and lay the foundation for future educational interventions that harness our basic and universal spatial intuitions. Series 1 will characterize how people reason intuitively about the properties of triangles. Are their properties evaluated through mental simulation and imagery or through abstract rules? Series 2 will explore how people think about lines. Under what conditions are lines recognized as the shortest path between two points? How does that recognition relate to everyday experiences, like navigating from one place to another, through development? Series 3 will probe geometric intuitions about efficient paths in physical contexts with gravity. The experiments will take place in the laboratory and in the National Museum of Mathematics (MoMath). MoMath will also be a site for general dissemination of the project's findings, including a talk series that will bring together cognitive scientists, educators, and the public. This project will thus reach thousands of individuals through basic science research and through outreach at the museum.

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.