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Izsák, Andrew; Jacobson, Erik; Bradshaw, Laine – Journal for Research in Mathematics Education, 2019
We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with…
Descriptors: Teacher Surveys, Middle School Teachers, Middle School Mathematics, Mathematics Instruction
Van Dooren, Wim; De Bock, Dirk; Evers, Marleen; Verschaffel, Lieven – Journal for Research in Mathematics Education, 2009
Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…
Descriptors: Cues, Word Problems (Mathematics), Primary Education, Problem Solving
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
Ng, Swee Fong; Lee, Kerry – Journal for Research in Mathematics Education, 2009
Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…
Descriptors: Mathematics Curriculum, Foreign Countries, Word Problems (Mathematics), Problem Solving
Xin, Yan Ping – Journal for Research in Mathematics Education, 2008
The purpose of this study was to examine the effects of a schema-based instructional strategy that emphasizes prealgebraic conceptualization of multiplicative relations on solving arithmetic word problems with elementary students with learning disabilities or problems (LP). Introducing symbolic representation and algebraic thinking in earlier…
Descriptors: Mathematics Education, Word Problems (Mathematics), Arithmetic, Algebra

Steffe, Leslie P.; Johnson, David C. – Journal for Research in Mathematics Education, 1971
Examined were differential performances among categories of first graders when solving arithmetical workd problems of eight types under two distinct conditions. The categories were based on various types of quantitative comparisons which children are known to make. Several statistically significant results were obtained involving differences…
Descriptors: Academic Ability, Arithmetic, Elementary School Mathematics, Learning

Steffe, Leslie P. – Journal for Research in Mathematics Education, 1970
Four levels of quantitative comparisons based on Piagetian task analysis and three IQ levels were used to partition a population of 341 first grade children. Each child was then tested on a set of addition facts and a set of addition problems which varied according to the use of aids or transformation. (JG)
Descriptors: Addition, Arithmetic, Conservation (Concept), Elementary School Mathematics
van Putten, Cornelis M.; van den Brom-Snijders, Petra A.; Beishuizen, Meindert – Journal for Research in Mathematics Education, 2005
Students' strategies for solving long division problems under a realistic mathematics approach (RME) at Dutch primary schools were categorized in two ways: (a) according to the level of how students created multiples of the divisor (chunking) to be subtracted from the dividend; and (b) according to their use, or nonuse, of schematic notation.…
Descriptors: Foreign Countries, Mathematics Instruction, Problem Solving, Teaching Methods

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

Van Dooren, Wim; Verschaffel, Lieven; Onghena, Patrick – Journal for Research in Mathematics Education, 2002
Investigates the arithmetical and algebraic problem-solving strategies and skills of preservice primary and secondary school teachers in Flanders, Belgium. Compares aspects of preservice teachers' own problem-solving behavior with the way in which they evaluated students' arithmetical and algebraic solutions to problems. Discusses teachers' use of…
Descriptors: Algebra, Arithmetic, Elementary Secondary Education, Foreign Countries
Pape, Stephen J. – Journal for Research in Mathematics Education, 2004
Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem…
Descriptors: Arithmetic, Word Problems (Mathematics), Reading Comprehension, Mathematics Achievement

Carey, Deborah A. – Journal for Research in Mathematics Education, 1991
A study asked 24 first grade children from 3 different classes to write number sentences and select appropriate alternative number sentences for addition and subtraction word problems. Results indicated that children could be characterized into five clusters according to their flexibility in accepting alternative number sentences and that…
Descriptors: Addition, Arithmetic, Cognitive Development, Cognitive Processes

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

Sellke, Donald H.; And Others – Journal for Research in Mathematics Education, 1991
This study tested the effectiveness of an experimental instructional strategy for writing arithmetic sentences for simple multiplication and division story problems involving nonintegral factors. Significant effects in favor of the experimental group were found on an intermediate test and a posttest. (Author/CW)
Descriptors: Arithmetic, Division, Equations (Mathematics), Junior High Schools
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