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Krasa, Nancy; Shunkwiler, Sara – Brookes Publishing Company, 2009
How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…
Descriptors: Mathematics Instruction, Learning Problems, Numbers, Arithmetic
Halford, Graeme S.; Boulton-Lewis, Gillian M. – 1989
Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representations used to teach mathematics are essentially analogs of mathematical concepts, and it is argued that analogies enter into mathematical concept acquisition in numerous other ways as well. According to Gentner's theory, analogies entail a…
Descriptors: Abstract Reasoning, Analogy, Elementary Education, Elementary School Mathematics

Watson, Jane; Mulligan, Joanne – Mathematics Education Research Journal, 1990
A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)
Descriptors: Abstract Reasoning, Cognitive Development, Cognitive Structures, Cognitive Style
Wilson, Patricia S. – Focus on Learning Problems in Mathematics, 1990
Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…
Descriptors: Abstract Reasoning, Cognitive Development, Cognitive Dissonance, Cognitive Structures
Millroy, Wendy Lesley – Journal for Research in Mathematics, 1992
The researcher conducted a six-month ethnographic study as an apprentice carpenter in Cape Town, South Africa, to document the valid mathematical ideas that are embedded in the everyday woodworking activities of a group of carpenters. A secondary objective was to examine and to give a firsthand account of the teaching and learning of mathematical…
Descriptors: Abstract Reasoning, Adult Programs, Apprenticeships, Carpentry