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Recently, I have begun what I expect will be a broad-ranging and long-term program of research in mathematical cognition (watch this video or rea d this paper for a description of the approach). The work grows out of my long-standing interest in developmental transitions and in readiness to learn from new experiences as well as from the hope that a Parallel-Distributed Processing approach may shed light on some of the most awe-inspiring achievements of human thought --- the insights and structured reasoning systems that have been created by mathematicians. In this effort, we are combining experimental studies and computational modeling studies. The lab is seeking to recruit experimentally and/or computationally oriented students interested in contributing to this effort.
The goal is to understand the development of human abilities in mathematics at all levels, from numerosity and the initial stages of counting to arithmetic, algebra, geometry, and even multivariate mathematics and calculus. At the heart of the effort is the belief that mathematics is best viewed as a matter of learning a set of models that characterize the objects of mathematical thought and their properties, and to carry out operations on expressions that have meaning in terms of objects represented with such models. On this view, mathematics can be thought of as providing a way of seeing properties of (real or imagined, often idealized) objects or sets of objects that bring out useful relationships that are captured in symbolic expressions but that are often understood in terms of intuitively grasped relationships that gives these expressions their meaning. There is also an emphasis on understanding how gradual learning processes can eventually lead to insight and qualitatively different levels of understanding and mathematical ability, and on determining how best to support learners as they attempt to acquire such models.
The goal is to understand the development of human abilities in mathematics at all levels, from numerosity and the initial stages of counting to arithmetic, algebra, geometry, and even multivariate mathematics and calculus. At the heart of the effort is the belief that mathematics is best viewed as a matter of learning a set of models that characterize the objects of mathematical thought and their properties, and to carry out operations on expressions that have meaning in terms of objects represented with such models. On this view, mathematics can be thought of as providing a way of seeing properties of (real or imagined, often idealized) objects or sets of objects that bring out useful relationships that are captured in symbolic expressions but that are often understood in terms of intuitively grasped relationships that gives these expressions their meaning. There is also an emphasis on understanding how gradual learning processes can eventually lead to insight and qualitatively different levels of understanding and mathematical ability, and on determining how best to support learners as they attempt to acquire such models.
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Open mind : discoveries in cognitive science (2024): 148-176
CVPR 2024 (2023)
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bioRxiv (Cold Spring Harbor Laboratory) (2023)
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Siu‐Wai Chan, A. Santoro,Andrew K. Lampinen,Jane X. Wang, Ashutosh Singh,Pierre H. Richemond,James L. McClelland,Felix Hill
arXiv (Cornell University) (2022)
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arxiv(2022)
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