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Direct linkWhite, Paul; Mitchelmore, Mike; Wilson, Sue; Faragher, Rhonda – Australian Primary Mathematics Classroom, 2009
Being numerate involves using mathematical ideas efficiently to make sense of the world, which is much more than just being able to calculate. What is needed is the accurate interpretation of mathematical information and the ability to draw sound conclusions based on mathematical reasoning. This skill may be called "critical numeracy",…
Descriptors: Numeracy, Mathematics Instruction, Teaching Methods, Mathematical Concepts
Peer reviewedMitchelmore, Michael C.; White, Paul – Mathematics Education Research Journal, 1995
Discusses two meanings of abstract: abstract-apart, ideas removed from reality; and abstract-general, ideas general to a wide variety of contexts. Suggests that greater interest in abstraction as a process, instead of just a product, would be beneficial to mathematics education theory and practice. (48 references) (MKR)
Descriptors: Abstract Reasoning, Elementary Secondary Education, Mathematics Instruction, Semantics
Download full textMitchelmore, Michael; White, Paul – International Group for the Psychology of Mathematics Education, 2004
It is claimed that, since mathematics is essentially a self-contained system, mathematical objects may best be described as "abstract-apart." On the other hand, fundamental mathematical ideas are closely related to the real world and their learning involves empirical concepts. These concepts may be called "abstract-general" because they embody…
Descriptors: Cognitive Processes, Mathematics Education, Abstract Reasoning, Mathematical Concepts
White, Paul; Mitchelmore, Michael – 1999
This paper presents a cognitive theoretical framework for the learning of mathematics which has generic implications for other disciplines. The framework has been developed using a combination of established theories about learning and the authors' research into the understanding of some specific types of learning. It is based on the integration…
Descriptors: Abstract Reasoning, Cognitive Development, Elementary Secondary Education, Learning Strategies
Peer reviewedMitchelmore, Michael C.; White, Paul – Educational Studies in Mathematics, 2000
Proposes that children progressively recognize deeper and deeper similarities between their physical angle experiences, and classify them firstly into specific situations, then into more general contexts, and finally into abstract domains. Indicates that the standard angle concept first develops in situations where both arms of the angle are…
Descriptors: Abstract Reasoning, Cognitive Processes, Concept Formation, Elementary Education
Mitchelmore, Michael C.; White, Paul – 1995
This paper explores a framework for research on the development of the angle concept based on theories of abstraction. The framework suggests that children initially acquire a body of disconnected angle knowledge situated in everyday experiences, group the situations to form angle contexts, and then form an abstract angle concept. The framework is…
Descriptors: Abstract Reasoning, Concept Formation, Context Effect, Foreign Countries
