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Fonger, Nicole L.; Stephens, Ana; Blanton, Maria; Isler, Isil; Knuth, Eric; Gardiner, Angela Murphy – Cognition and Instruction, 2018
Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked…
Descriptors: Academic Achievement, Mathematics Education, Algebra, Research and Development
Kainulainen, Mikko; McMullen, Jake; Lehtinen, Erno – Cognition and Instruction, 2017
Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of…
Descriptors: Numbers, Foreign Countries, Grade 3, Grade 4
Ding, Meixia; Li, Xiaobao – Cognition and Instruction, 2010
This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to…
Descriptors: Comparative Analysis, Mathematics Education, Textbooks, Elementary School Mathematics
Li, Xiaobao; Ding, Meixia; Capraro, Mary Margaret; Capraro, Robert M. – Cognition and Instruction, 2008
This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level.…
Descriptors: Foreign Countries, Comparative Analysis, Symbols (Mathematics), Grade 6
Wagner, Joseph F. – Cognition and Instruction, 2006
The theoretical perspective outlined here offers an alternative to explanations of knowledge transfer that posit its source in the construction and application of abstract, context-independent knowledge structures. A case study analysis of an undergraduate student's attempt to solve a series of problems related to an elementary statistical…
Descriptors: Case Studies, Undergraduate Students, Problem Solving, Statistics
Van Dooren, Wim; De Bock, Dirk; Hessels, An; Janssens, Dirk; Verschaffel, Lieven – Cognition and Instruction, 2005
Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…
Descriptors: Age Differences, Mathematics Education, Arithmetic, Mathematical Concepts
Peer reviewed
Fan, Ning; And Others – Cognition and Instruction, 1994
Investigated the effect of problem wording on solving arithmetic word problems by first graders. Found that wording is a crucial component in solving difference problems. Results suggest that further research on word problem-solving processes focus on the interaction between linguistic comprehension and mathematical reasoning. (AA)
Descriptors: Abstract Reasoning, Elementary School Mathematics, Elementary School Students, Instructional Effectiveness
Peer reviewed
Meira, Luciano – Cognition and Instruction, 1995
Discusses children's design of mathematical representations on paper. Suggests that the design of displays during problem solving shapes one's mathematical activity and sense making in crucial ways, and that knowledge of mathematical representations is not simply recalled and applied to problem solving, but also emerges out of one's interactions…
Descriptors: Children, Cognitive Development, Cognitive Processes, Instructional Materials
Peer reviewed
Bowers, Janet; Cobb, Paul; McClain, Kay – Cognition and Instruction, 1999
Presents a case study of third graders' development of place value conceptions to illustrate an approach for documenting students' mathematical development in the social context of the elementary school classroom. Documents the evolution of communal mathematical practices in which students participate and the development of individual…
Descriptors: Case Studies, Classroom Environment, Classroom Research, Classroom Techniques