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Lamb, Lisa A.; Bishop, Jessica Pierson; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P. – Journal for Research in Mathematics Education, 2018
In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…
Descriptors: Problem Solving, Grade 2, Grade 4, Grade 7
Whitacre, Ian; Nickerson, Susan D. – Journal for Research in Mathematics Education, 2016
This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…
Descriptors: Preservice Teachers, Multiplication, Elementary School Teachers, Elementary School Mathematics
Thanheiser, Eva – Journal for Research in Mathematics Education, 2009
Although preservice elementary school teachers (PSTs) lack the understanding of multidigit whole numbers necessary to teach in ways that empower students mathematically, little is known about their conceptions of multidigit whole numbers. The extensive research on children's understanding of multidigit whole numbers is used to explicate PSTs'…
Descriptors: Grounded Theory, Preservice Teachers, Numbers, Elementary School Teachers
Chandler, Cynthia C.; Kamii, Constance – Journal for Research in Mathematics Education, 2009
The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…
Descriptors: Problem Solving, Arithmetic, Number Concepts, Children
Van Dooren, Wim; De Bock, Dirk; Janssens, Dirk; Verschaffel, Lieven – Journal for Research in Mathematics Education, 2008
The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…
Descriptors: Mathematics Instruction, Mathematical Logic, Problem Solving, Mathematical Concepts

Fuson, Karen C.; Kwon, Youngshim – Journal for Research in Mathematics Education, 1992
Thirty-six Korean first graders were interviewed to study their ability solving addition problems with sums of 10, single-digit sums between 10 and 18, and subtraction problems with minuends between 10 and 18. Finger methods to show sums over 10 and the regular named-10 Korean number words supported their learning of 3 efficient recomposition…
Descriptors: Addition, Concept Formation, Cultural Context, Cultural Influences

English, Lyn D. – Journal for Research in Mathematics Education, 1998
Investigates the problem-posing abilities of third-grade children who displayed different profiles of achievement in number sense and novel problem solving. Concludes that children had difficulties in posing a range of problems in formal contexts in contrast to informal contexts, and children of different achievement profiles displayed different…
Descriptors: Grade 3, Mathematics Achievement, Mathematics Education, Mathematics Instruction

Christou, Constantinos; Philippou, George – Journal for Research in Mathematics Education, 1998
Investigates the effect of mental schemes corresponding to additive and multiplicative situations in the process of interpreting and solving problems. Classifies relative difficulties of problems according to their situations which are considered through a written test administered to pupils in grades 2, 3, and 4. Supports the assumption that…
Descriptors: Addition, Arithmetic, Cognitive Development, Concept Formation

Cobb, Paul – Journal for Research in Mathematics Education, 1987
Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)
Descriptors: Cognitive Processes, Educational Research, Elementary Education, Elementary School Mathematics

Brenner, Mary E.; Herman, Sally; Ho, Hsiu-Zu; Zimmer, Jules M. – Journal for Research in Mathematics Education, 1999
Compares sixth-grade American students to three samples of (Chinese, Japanese, and Taiwanese) sixth-grade Asian students to determine if the well-documented mathematical achievement of students from these Asian nations might be due in part to a greater understanding of mathematical representations. Indicates that all Asian samples scored…
Descriptors: Comparative Education, Cross Cultural Studies, Foreign Countries, Grade 6

Nesher, Pearla; Katriel, Tamar – Journal for Research in Mathematics Education, 1986
Different uses of numbers in natural language and mathematics is argued to have consequences for children's learning of numbers and for primary-grade textbooks. A study using particular properties of Hebrew indicates a crossing of the two language systems in children's reading of an arithmetic textbook. (MNS)
Descriptors: Educational Research, Elementary Education, Elementary School Mathematics, Hebrew

Carpenter, Thomas P.; And Others – Journal for Research in Mathematics Education, 1988
The study investigated children's ability to write number sentences for simple addition and subtraction word problems. The results suggest that open number sentences may provide mathematical symbolism that allows young children to build on informal strategies for presenting and solving simple word problems. (Author/PK)
Descriptors: Addition, Basic Skills, Educational Research, Elementary Education

Klein, Anton S.; Beishuizen, Meindert; Treffers, Adri – Journal for Research in Mathematics Education, 1998
Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)
Descriptors: Addition, Arithmetic, Cognitive Development, Concept Formation

Fuson, Karen C.; And Others – Journal for Research in Mathematics Education, 1997
Researchers from four projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe a common framework of conceptual structures children construct for multidigit numbers, and categories of methods children devise for multidigit addition and subtraction. Conceptions include unitary, decade and…
Descriptors: Classroom Techniques, Cognitive Development, Comprehension, Concept Formation

Journal for Research in Mathematics Education, 1987
Reports on the progress of a project designed to establish both a research agenda for mathematics education and a conceptual framework for such an undertaking. Describes four conferences which have been organized to consider teaching problem solving, effective teaching, teaching and learning algebra, and middle school number concepts. (TW)
Descriptors: Algebra, Elementary School Mathematics, Elementary Secondary Education, Mathematics Curriculum
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