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Herman, Jan; Ilucova, Lucia; Kremsova, Veronika; Pribyl, Jiri; Ruppeldtova, Janka; Simpson, Adrian; Stehlikova, Nada; Sulista, Marek; Ulrychova, Michaela – International Group for the Psychology of Mathematics Education, 2004
Within the large range of potential theoretical perspectives on fractions, this paper considers one particular interpretation: fractions' duality as process and object. By considering the number-fractionbar-number composite symbol as simultaneously representing division and rational, some process-object theories imply that fraction-as-process and…
Descriptors: Mathematics, Mathematics Instruction, Cognitive Processes, Foreign Countries
Simpson, Adrian; Zakaria, Nora – International Group for the Psychology of Mathematics Education, 2004
The Malaysian educational system tends to take a clear instructionally-focused approach to the teaching of mathematics. This means that many students gain a good procedural command of areas of mathematics. This paper explores one outcome of a teaching experiment in which one area of mathematics (differentiation) was taught in a radically different…
Descriptors: Mathematics Instruction, Mathematics Education, Foreign Countries, Teaching Methods
Simpson, Adrian; Stehlikova, Nada – International Group for the Psychology of Mathematics Education, 2004
This paper explores one student's attempt to apprehend an abstract mathematical structure (similar to Z[99]). We discuss Karmiloff-Smith's theory of representational redescription as a model for the development of structural understanding and contrast this with existing process-object theories. We use two cycles in Molly's movement from an action…
Descriptors: Case Studies, Teacher Education, Abstract Reasoning, Learning Theories
Inglis, Matthew; Simpson, Adrian – International Group for the Psychology of Mathematics Education, 2005
In this paper we briefly describe the dual process account of reasoning, and explain the role of heuristic biases in human thought. Concentrating on the so-called matching bias effect, we describe a piece of research that indicates a correlation between success at advanced level mathematics and an ability to override innate and misleading…
Descriptors: Heuristics, Mathematics Instruction, Mathematics Education, Cognitive Processes
Inglis, Matthew; Simpson, Adrian – International Group for the Psychology of Mathematics Education, 2004
Learning to think logically and present ideas in a logical fashion has always been considered a central part of becoming a mathematician. In this paper we compare the performance of three groups: mathematics undergraduates, mathematics staff and history undergraduates (representative of a "general population"). These groups were asked to solve…
Descriptors: Logical Thinking, Mathematics Education, Undergraduate Students, College Mathematics
de Hoyos, Maria; Gray, Eddie; Simpson, Adrian – International Group for the Psychology of Mathematics Education, 2004
This paper discusses the role of uncertainty during the early stages of problem solving. It is argued that students start the problem solving activity with some degree of uncertainty that may vary from high to low. This degree of uncertainty may affect students' decisions at early stages of the problem solving process. It may be suggested that an…
Descriptors: Problem Solving, Undergraduate Students, Mathematics Instruction, Models