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Download full textZwanch, Karen – North American Chapter of the International Group for the Psychology of Mathematics Education, 2019
The number sequences describe a hierarchy of students' concepts of number. This research uses two defining cognitive structures of the number sequences--units coordination and the splitting operation--to model middle-grades students' abilities to write linear equations representing the multiplicative relationship between two unknowns. Results…
Descriptors: Middle School Students, Mathematics Instruction, Algebra, Thinking Skills
Kaput, James J. – Focus on Learning Problems in Mathematics, 1989
Describes environments for concretely enacting multiplication and division. Discusses difficulties occurring when students use one of the concrete environments to model situations involving modified environments. (YP)
Descriptors: Cognitive Structures, Computer Assisted Instruction, Division, Elementary School Mathematics
Peer reviewedWatson, 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
