Advanced Mathematical Thinking

By B. S. Edwards, Ed Dubinsky, Michael A. McDonald. 2005

402 citations recorded by the source corpus.

Subfields: Education, Mathematical Physics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/b12b8b8963d7794903c7c429dcdc9d31e3797184

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Citations in the corpus

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “…numerous influential mathematics educators and organizations in mathematics education have argued that justification and proof should also play a central role in all mathematics classrooms (e.g., Dreyfus, 1990; Hanna, 1995; National Council of Teachers of Mathematics, 2000; Schoenfeld, 1994).”
The transition to formal thinking in mathematics (2008, methodology): “This was done in the Solution Sketcher (Tall, 1991) and has been implemented in the currently available Graphic Calculus software (Blokland & Giessen, 2000, figure 6).”
Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students. (2012, background): “Tall (1991) asserts that during such a transition, unstable behaviour is possible, with the Volume 5 Number 2, 2012 experience of previous ideas conflicting with new elements.”
DEVELOPING PRE-SERVICE TEACHERS’ NOTICING OF STUDENTS’ UNDERSTANDING OF THE DERIVATIVE CONCEPT (2014, neutral): “Students encounter many difficulties understanding the derivative concept linked to the modes of representation, the relation between the derivative of a function at a point and the global view of the derived function, and the relation between the first and second derivative of a function (Artigue, ”
Investigating the secondary–tertiary transition (2008, background): “Edwards et al. (2005), define AMT by focusing “on the phenomenon that seems to first occur during a mathematics student’s experience in undergraduate mathematics when he or she first begins to deal with abstract concepts and deductive proof” (p.”
Mathematics Majors' Perceptions of Conviction, Validity, and Proof (2010, background): “Many mathematics educators argue that proof serves many roles in mathematics beyond providing conviction that a theorem is true (e.g., Bell, 1976; de Villiers, 1990; Hanna, 1991; Knuth, 2002).”
Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof (2015, methodology): “…L. Blanton maria_blanton@terc.edu 1 City College School of Education, The City University of New York, New York, USA 2 TERC, Cambridge, MA, USA 3 Educational Testing Service, Princeton, NJ, USA (Dreyfus 1990, p. 126), it also serves as a tool for learning mathematics (Hanna 1990, 1995; Hersh 1993).”
Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond (2012, background): “Applications of the B-continuum range from aid in teaching calculus [36, 62, 63, 147, 148] (see illustration in Figure 5) to the Bolzmann equation (see L.”