The Psychology of Advanced Mathematical Thinking

By David Tall. 2002

280 citations recorded by the source corpus.

Subfields: Education, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/49519754c2e72ece6bf18bcd5a9880f706b8c631

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Citations in the corpus

Ten Misconceptions from the History of Analysis and Their Debunking (2012, methodology): “The use of the B-continuum as an aid in teaching calculus has been examined by Tall [146], [147]; Ely [44]; Katz and Tall [81] (see also [74, 75]).”
Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus (2011, background): “Applications of the B-continuum range from aid in teaching calculus [41, 73, 74, 129, 130] to the Bolzmann equation (see L.”
Approaching functions: Cabri tools as instruments of semiotic mediation (2007, background): “Difficulties are also widely described; most of them are related to the interpretation of graphic representation in terms of function (Dreyfus and Eisenberg 1983; Tall 1991, 1996; Vinner and Dreyfus 1989; and, for a thorough review, see Leinhardt et al. 1990).”
Conceptual Change in Mathematics: Understanding the Real Numbers (2002, background): “This conceptual change seems also to be the kind of change which demands a radical change of the ontological category ( Chi, 1992 ), which seems to explain the difficulty in integrating the two different kinds of knowledge of numbers and continuity and also the change in the quality of argumentation”
What makes a counterexample exemplary? (2008, background): “This type of teaching and learning orientation generates misconceptions among students and may be explained by the generic extension principle proposed by Tall [1].”
Understanding secondary–tertiary transition in mathematics (2009, background): “Further major difficulties arise in dealing with proofs (see, for instance, 8 , 18 , 19 ).”