THINKING THROUGH THREE WORLDS OF MATHEMATICS
By David Tall. 2004
208 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/fc9872f1a1b07e8407282cba5f6e3d12008b81ff
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- Tom J. Cooper
- Rosana Nogueira de Lima
- Johan Lithner
- E. Warren
- Wolff‐Michael Roth
- Jennifer S. Thom
- O. Yevdokimov
- David Tall
Citations in the corpus
- Bodily experience and mathematical conceptions: from classical views to a phenomenological reconceptualization (2009, background): “There are also continued efforts to come to grips with the nature of mathematical conceptions, which have been theorized, for example, in the form of a duality of mathematical processes and products (Sfard 1991), a three-world hypothesis including embodied, proceptual, and formals worlds ( Tall 2004”
- Student learning of basis, span and linear independence in linear algebra (2010, methodology): “First, an action-process-object-schema (APOS) framework, as proposed by Dubinsky and others 5–7 for studying and promoting the development of learning, and second, Tall's embodied, symbolic and formal worlds of mathematics 8–11 .”
- Procedural embodiment and magic in linear equations (2008, methodology): “Following Tall (2004b), we define a 'met-before' to be a mental construct that an individual uses at a given time based on experiences they have met before.”
- A research framework for creative and imitative reasoning (2008, background): “Skemp (1978) distinguishes between instrumental and relational understanding, Sfard (1991), Asiala et al. (1996) and Tall (2004) analyse how development of understanding of objects and processes interact, and Pirie and Kieren (1994) describe levels of understanding.”
- 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…”
- Years 2 to 6 Students’ Ability to Generalise: Models, Representations and Theory for Teaching and Learning (2011, background): “We saw expression and language as essential to this journey as they gave subtle shades of meaning that arise from the students’ thinking ( Tall 2004 ).”