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To See or Not to See: Analyzing Difficulties in Geometry from the Perspective of Visual Perception
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Gal, Hagar; Linchevski, Liora – Educational Studies in Mathematics, 2010
In this paper, we consider theories about processes of visual perception and perception-based knowledge representation (VPR) in order to explain difficulties encountered in figural processing in junior high school geometry tasks. In order to analyze such difficulties, we take advantage of the following perspectives of VPR: (1) Perceptual…
Descriptors: Knowledge Representation, Visual Perception, Cognitive Processes, Geometry
Crossing the Cognitive Gap between Arithmetic and Algebra: Operating on the Unknown in the Context of Equations.
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Linchevski, Liora; Herscovics, Nicolas – Educational Studies in Mathematics, 1996
Reports the results of a teaching experiment involving like terms and equations in algebra. Seventh-grade students (n=6) experienced difficulties in decomposing an additive term into a difference. (Author/MKR)
Descriptors: Algebra, Concept Formation, Equations (Mathematics), Grade 7
A Cognitive Gap between Arithmetic and Algebra.
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Herscovics, Nicolas; Linchevski, Liora – Educational Studies in Mathematics, 1994
Investigated the upper limits of (n=22) seventh-grade students' informal processes in solving first degree equations in one unknown prior to instruction. Results indicated the existence of a cognitive gap between arithmetic and algebra characterized as the students' inability to operate spontaneously with or on the unknown. (37 references)…
Descriptors: Algebra, Arithmetic, Cognitive Development, Cognitive Structures
Structure Sense: The Relationship between Algebraic and Numerical Contexts.
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Linchevski, Liora; Livneh, Drora – Educational Studies in Mathematics, 1999
Interviews 53 sixth grade students individually in an attempt to discover whether wrong interpretations of the algebraic structure found in an algebraic context occurs in a purely numerical context. Concludes that students' difficulties with the algebraic structure were also found in purely numerical contexts. (Contains 27 references.) (Author/ASK)
Descriptors: Algebra, Arithmetic, Computation, Foreign Countries
Using Intuition from Everyday Life in 'Filling' the Gap in Children's Extension of Their Number Concept To Include the Negative Numbers.
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Linchevski, Liora; Williams, Julian – Educational Studies in Mathematics, 1999
Reports on an instructional method designed to address the cognitive gaps in children's mathematical development where operational conceptions give rise to structural conceptions. Describes two experiments in teaching integers and conceptualizes modeling as the transformation of outside-school knowledge into school mathematics. (Contains 28…
Descriptors: Educational Games, Elementary Education, Intuition, Mathematical Models