Location of Repository

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to d o mathematical problems and to think about mathematical relationships.\ud In this presentation we consider the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and procedural thinking. Evidence will be given from several different contexts in the development of symbols through\ud arithmetic, algebra and calculus, then on to the formalism of axiomatic mathematics. This is taken from a number of research studies recently performed for doctoral dissertations at the University of Warwick by students from the USA, Malaysia, Cyprus and Brazil, with data collected\ud in the USA, Malaysia and the United Kingdom. All the studies form part of a broad investigation into why some students succeed yet others fail

Topics:
QA, L1

Publisher: Routledge

Year: 2001

OAI identifier:
oai:wrap.warwick.ac.uk:473

Provided by:
Warwick Research Archives Portal Repository

- (1998). Aspects and Layers of the Function Concept, PhD Thesis,
- (1998). Cognitive Units, Concept Images and Cognitive Collages, PhD Thesis,
- (1999). Concept Maps & Schematic Diagrams as Devices for Documenting the Growth of Mathematical Knowledge.
- (1996). Conceptual and Procedural Approaches to Problem Solving,
- (1994). Duality, ambiguity and flexibility: a proceptual view of simple arithmetic.
- (1991). Encouraging Versatile Thinking in Algebra using the Computer,
- (1999). Function: Organizing Principle or Cognitive Root?
- (1998). In the mind. Internal representations and elementary arithmetic, Unpublished Doctoral Thesis,
- (1997). In the Mind. What can imagery tell us about success and failure in arithmetic?’
- (1991). Limits. In
- (1991). On the Dual Nature of Mathematical Conceptions: Reflections on processes and objects as different sides of the same coin,
- (1997). Persistent errors in indices: a cognitive perspective,
- (1986). Procedural and Conceptual Knowledge. In
- (1991). Reflective abstraction in advanced mathematical thinking. In
- (1986). Structure and Insight.
- (1999). Student constructions of formal theory: giving and extracting meaning.
- (1998). Students’ Understanding of Mathematical Analysis,
- (1996). Symbolic Manipulation Related to Certain Aspects Such as Interpretations of Graphs, PhD Thesis,
- (1999). The Roles of Cognitive Units, Connections and Procedures in achieving Goals in College Algebra.
- The student’s construction of quantification,
- (1995). Thinking Mathematically: A Framework for Developing Positive Attitudes Amongst Undergraduates, PhD thesis,
- (1996). Understanding the limit concept: Beginning with a co-ordinated process schema,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.