Mathematical Beliefs and Conceptual Understanding of the Limit of a Function

By J. E. Szydlik. 2000

134 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d15cf9e326c2a9b7ccdc6a8a4341d2674c816bc6

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Citations in the corpus

Collapsing dimensions, physical limitation, and other student metaphors for limit concepts : an instrumentalist investigation into calculus students' spontaneous reasoning (2009, background): “…1983), nonmathematical concepts such as speed limits, physical barriers, and motion (Davis & Vinner, 1986; Frid, 1994, Tall, 1992; Tall & Vinner, 1981; Thompson, 1994; Williams, 1991), and epistemological beliefs about mathematics in general (Sierpinska, 1987; Szydlick, 2000; Williams, 1991, 2001).”
Transformation and contextualisation: conceptualising students’ conceptual understandings of threshold concepts in calculus (2010, background): “Tall and Vinner (1981) suggest that if students' concept images are dominated by a dynamic process they often have the misconception that the limit cannot be reached.”
Nonstandard Student Conceptions About Infinitesimals (2010, background): “…have with the ideas of infinite processes and the real numbers (e.g., Cornu, 1991; Cottrill et al., 1996; Davis & Vinner, 1986; Przenioslo, 2004; Schwarzenberger & Tall, 1978; Sierpinska, 1987; Szydlik, 2000; Tall & Vinner, 1981; Weller, Brown, Dubinsky, McDonald, & Stenger, 2004; Williams, 1991).”
Letting the Intuitive bear on the Formal; A Didactical Approach for the Understanding of the Limit of a Sequence (2001, background): “The belief that infinitesimals exist would seem very influential in how limits are thought of, but one recent paper (Szydlik, 2000) claims to have some evidence against this.”
Predications of the Limit Concept: An Application of Repertory Grids (2001, background): “Contrasted with this are various static views, ranging from informal and intuitive (e.g., “The limit of a function is L if whenever x is close to the limiting value s, the function is close to L.” [Szydlik, 2000, p. 268]) to the formal ε − δ definition.”