The transition to formal thinking in mathematics

By David Tall. 2008

318 citations recorded by the source corpus.

Subfields: Cognitive Neuroscience, Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8a892ea0fb48d75950998b4318864f8309c5359f

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Citations in the corpus

Student learning of basis, span and linear independence in linear algebra (2010, background): “The embodied world builds on an iconic and enactive approach to produce embodied notions [10].”
Eigenvalues and eigenvectors: embodied, symbolic and formal thinking (2011, background): “Since students arrive at university with many met-befores (Tall 2008) constructed from their school experiences with algebra, the new ways of working with algebraic representations of matrices and constructing meanings in context are unfamiliar, and so teaching needs to address these explicitly.”
Shortcomings of Mathematics Education Reform in The Netherlands: A Paradigm Case? (2016, background): “Or as Tall (2008, p. 13) put it: “ Procedural learning (. . .) needs the additional compression into thinkable concepts to enable the long-term development of increasingly sophisticated mathematical thinking.”
Cognitive Development of Proof (2011, background): “…proof from initial perceptions of objects and actions to axiomatic mathematics can be formulated in terms of three distinct forms of development (Tall, 2004, 2008): • a development of the conceptual embodiment of objects and their properties, with increasing verbal underpinning appropriate for…”
Metaphor or Met-Before? The effects of previouos experience on practice and theory of learning mathematics (2010, background): “As Tall (2008) observes, these structure theorems, proved logically and verbally, lead to structures that again enable the mathematician to think in embodied terms that are now no longer naïve embodied constructions, but are now formally linked together in a logical manner.”
A framework for mathematical thinking: the case of linear algebra (2009, background): “In Tall's view ‘formal mathematics does not arise in isolation’ [ 12 , p.”
The learning effects of computer simulations in science education (2012, background): “Embodiment of abstract concepts could provide such a function (Tall, 2008) and deserves attention in future research.”
Professional development through lesson study: teaching the derivative using GeoGebra (2015, background): “The Japanese approach aims at making sense of mathematics in a way that not only improves students’ understanding, but maintains longer-term success (Tall 2008).”