Relationships between embodied objects and symbolic procepts: an explanatory theory of success and failure in mathematics

By Eddie M. Gray, David Tall. 2004

79 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6bba5720db8d83334ab58bdbff0ba14cadb756be

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Sepideh Stewart
2. Eddie M. Gray
3. Jack Pegg
4. Michael O. J. Thomas
5. David Tall
6. Joanne Mulligan

Citations in the corpus

• The fundamental cycle of concept construction underlying various theoretical frameworks (2005, background): “Table 3 shows three theoretical frameworks for local cycles of construction (Davis, 1984; Dubinsky (Czarnocha et al, 1999); Gray & Tall, 1994, 2001) laid alongside the SOLO UMR sequence for assessing responses at successive levels.”
• A framework for mathematical thinking: the case of linear algebra (2009, background): “The embodied world, containing embodied objects 10 , is where we think about the things around us in the physical world, and it ‘includes not only our mental perceptions of real-world objects, but also our internal conceptions that involve visuo-spatial imagery’ [ 8 , p.”
• Abstraction as a natural process of mental compression (2007, background): “ Gray and Tall (2001) hypothesised that these three forms of abstraction lead to the construction of three distinct forms of mathematical object which were later formulated as occurring in distinct worlds of mathematics:”