APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research

By Ed Dubinsky, Michael A. McDonald. 2001

496 citations recorded by the source corpus.

Subfields: Education, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6850b01648bf43e15cbdbcf871b215c3cf44825d

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Citations in the corpus

Cognitive Development of Proof (2011, background): “…are also theories of development of symbolism through the encapsulation of processes (such as counting) into concepts (such as number) that reveal a different kind of development in arithmetic and the generalized arithmetic of algebra (Dubinsky & McDonald, 2001; Gray & Tall, 1994; Sfard, 1991).”
Student learning of basis, span and linear independence in linear algebra (2010, background): “A GD [7] of basis requires a combination of a GD of span and a GD of linear independence of vectors, a link that the students in this study often did Table 3.”
Conceptions of function translation: obstacles, intuitions, and rerouting (2003, unknown): “Though the studies of Eisenberg and Dreyfus (1994) andBaker et al.”
Is the derivative a function? If so, how do we teach it? (2015, background): “Some researchers go further, defining the input–output pair at a point or on an interval (e.g., Dubinsky & McDonald, 2001; Monk, 1994; Sfard, 1992).”
Some Historical Issues and Paradoxes Regarding the Concept of Infinity: An Apos Analysis: Part 2 (2005, methodology): “For more information about APOS Theory and a summary of how it has been used in mathematics education research, see Dubinsky and McDonald (2001).”
What Does Research Suggest About the Teaching and Learning of Introductory Statistics at the College Level? A Review of the Literature (2008, methodology): “Student responses were classified using APOS (Action, Process, Object, Schema) theory (Dubinsky and McDonald, 2001).”
A Thirty-Year Reflection on Constructivism in Mathematics Education in Pme (2006, background): “It included Douady’s dialectique outil-object (Douady, 1986), Sfard’s dual nature of conceptions (Sfard, 1991), Gray and Tall’s procept (Gray & Tall, 1994), and Dubinsky’s APOS (action, process, object and schema) (Dubinsky & McDonald, 2001).”
Eigenvalues and eigenvectors: embodied, symbolic and formal thinking (2011, methodology): “In an exposition related to APOS theory Gray and Tall (1994) have presented the idea of a procept, in which a symbol represents either a mathematical process or its encapsulation as an object. Thus these symbolic, proceptual forms need to be perceivable by students (and experts) in a dual manner, as”
Students’ understanding of trigonometric functions (2005, background): “(2000) proposed a learning trajectory for how a student can successfully construct an understanding of a mathematical procept – see, also, Dubinsky and McDonald (2001). In Tall et al’s theory, a student can go through the following three stages to understand a procept: • Procedure.”
A DNR perspective on mathematics curriculum and instruction. Part II: with reference to teacher’s knowledge base (2008, methodology): “Examples of such models include: Fischebein’s (1985) intuitive models for the concepts of multiplication and division; Tournaire’s (1986) model for the concept of proportionality; Dubinsky’s action-process-object-schema model for the concept of function (E. D. Dubinsky & McDonald, 2001 ); Schoenfel”
THE IMPACT OF A FLIPPED CLASSROOM MODEL OF LEARNING ON A LARGE UNDERGRADUATE STATISTICS CLASS (2018, background): “Constructivist theory also predicts higher student performance in flipped classes (Bishop & Verleger, 2013; Dubinsky & McDonald, 2001; Huang, 2002).”