Uncovering the foundation of mathematical and probabilistic thought across cultures

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Learning mathematical concepts is an essential STEM skill. Although the capability to learn mathematics is found across human cultures, how mathematical skills depend on universal, underlying cognitive processes is still not understood. This project seeks to uncover the core cognitive underpinnings of children’s ability to learn and reason about arithmetic and probability by examining mathematics acquisition across cultures with differential exposure to pedagogical practices targeting early numeracy. By examining these abilities in a culture with relatively fewer supports for learning mathematics, the indigenous Tsimane’ peoples of South America, this project will be able to disentangle culture and human nature as factors in learners’ success, and correspondingly uncover likely targets for future educational innovations. In addition to arithmetic, this project tackles early understanding of probability in these groups in order to provide a strong test of developmental hypotheses that thinking probabilistically is at the core of how children form an understanding of the world. This study will first characterize indigenous methods for arithmetic, beginning with addition, then expanding to multiplication, division, and fractions using field experimental methods as well as structured interviews. Both of these components will quantify the algorithms and techniques that individual learners develop for solving mathematical problems using state of the art machine learning tools. This will formalize the systems of knowledge that learners acquire and allow us to create a rigorous theory of how this knowledge changes with schooling, culture, and development. Building on work with fractions and division, we will then test Tsimane’ children on their understanding of probability in order to explore whether probabilistic inferences are a shared human ability, even in the absence of formal schooling or strong cultural support for number. The final aim of these studies tests children’s ability to update probabilities in the face of evidence, as in Bayesian inference, which is hypothesized to be a core mechanism of cognitive change. This theory makes a strong prediction that learners in any culture should succeed on tasks requiring probabilistic thinking. By testing a particularly remote population with few cultural supports for these abilities, this project will be able to determine whether such abilities are a shared part of human nature that supports cognitive development more broadly, and in turn whether these cognitive skills would be a promising target for educational interventions. This project is supported by NSF's EDU Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development. 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.