Examined is the relationship between junior high school students' directional reasoning about rates and numerical reasoning on proportion-related word problems. The relationship between the ability to solve context-free fraction exercises and the ability to solve mathematically similar word problems is discussed. (KR)

Describes PRECEPTOR, an intelligent tutoring system that provides multiple explanations for algebraic word problems involving two variables. Modeling the cognitive processes of an effective teacher is discussed, the capacity for individualized tutoring is examined, and differential tutoring based on varying difficulty levels is explained. (17…

This issue contains articles on mathematical modeling of school arithmetic word problems; cognitive load theory; cognitive effects of practical experience for high and low achievers; perspectives of college-bound students on learning mathematics; and training-based assessment of school achievement. (SLD)

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…

This study is to explore the potential of Fauconnier's mental space theory in understanding the teaching and learning processes of mathematics. Notions from cognitive linguistics have been introduced to research in mathematics education recently, but there have been little studies about what potential the framework of mental space has in…

A growing body of empirical and theoretical work indicates that young children (grades K-3) have difficulties solving word problems because of deficient language and text comprehension strategies. Describes a computer simulation designed to model working memory demands in "bottom-up" comprehension of arithmetic word problems, offering a…

A study involving 66 sixth-graders with learning disabilities, average achievers, and gifted students found gifted students used significantly more visual-spatial representations than the other two groups in solving mathematical problems. Students with learning disabilities used significantly more pictorial representation than their peers, a…

Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…

This study examined the arithmetic calculation abilities of kindergarten and first-grade children (n=108) with different patterns of cognitive functioning: low language, low spatial ability, general delays, and nonimpaired. Nonverbal, story, and number fact problems were differentially sensitive to variation in cognitive ability. (Author/JDD)

The construct validity of algebra word problems for measuring quantitative reasoning was examined, focusing on an analysis of problem attributes and on the analysis of constructed-response solutions. Constructed-response solutions to 20 problems from the Graduate Record Examinations (GRE) General Test were collected from 51 undergraduates.…

This paper reports the latest in a series of studies investigating children's performance in solving division story problems involving remainders. One aspect of the work involved examining the way in which "sense-making" is involved in the interpretation of the numerical solution obtained. Subjects were 195 sixth, seventh, and eighth…

This study examines the construct of problem representation and the processes used by learners to construct or modify problem representations in problem-solving situations. Students (n=14) from freshman calculus courses at the University of California at San Diego participated in videotaped interviews in which they were asked to think aloud as…

Most studies of children's solution processes on simple addition and subtraction word problems have used individual interviews or the analysis of error patterns on paper-and-pencil tests as the primary data-gathering techniques. The present paper reports an investigation in which the contribution of eye-movement data was explored for studying…

Six students (ages 12-14) with learning disabilities received either cognitive or metacognitive strategy instruction for mathematical problem solving, followed by instruction in the complementary component. Results indicated that cognitive and metacognitive strategies were more effective than either cognitive or metacognitive strategy instruction…

This study examined ways in which two independent variables, peer collaboration and the use of a specific tool (the TAPS interface), work together and individually to shape students' problem-solving processes. More specifically, the researchers were interested in determining how collaboration and TAPS use cause metacognitive processes to differ…