Math teachers who spend most of their time lecturing at a chalkboard or assigning textbook problems are not reaching many students. To achieve math literacy goals, the National Council of Teachers of Mathematics encourages teachers to help students learn to value mathematics, gain confidence in their math abilities, and become good mathematical…

Reports on an intensive study of problem-solving activity of female students at the senior secondary level. Focuses on both the mathematical processing and the underlying cognitive and metacognitive activities that led to that processing. Concludes that all successful groups displayed a high number of key points where metacognitive decisions could…

Introduces a technique for developing tasks suitable for group investigation where students work from sets of numerical examples toward making generalizations. (ASK)

Investigated gender differences in problem-solving and computational strategies used by 44 boys and 38 girls as they progressed from grades 1 to 3. Found no gender differences in solving number fact, addition/subtraction, or nonroutine problems but strong gender differences in strategies used to solve problems. Discusses the use of invented…

Presents suggestions for teaching chess to young children as part of the problem-solving component of a kindergarten mathematics curriculum. Discusses the introduction of pairs of chess characters, playing challenge games with teachers to enhance skill development, and writing down the rules of the game. Notes that children's problem-solving and…

This article offers guidelines and suggestions for adapting mathematics instruction when teaching students with learning disabilities in the general classroom. Techniques for teaching computational skills, solving algorithms, and problem solving are offered. General techniques include increasing instructional time, varying group size, and using…

Presents science investigations that involve some challenging mathematics related to proportional reasoning. Can be embedded in thematic, interdisciplinary units to reinforce understanding of specific proportions, provide practice in proportional thinking, or assess abilities in solving problems that involve proportions. (JRH)

Four human judges agreed highly among themselves about the presence of errors committed by 60 adults solving algebra word problems, but were in less agreement about categorizing faults. An expert system agreed with judges about correctness of answers, but was in even less agreement about categorizing the faults. (SLD)

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…

This article discusses the structuring of mathematics to challenge the mathematically gifted elementary student. Theoretical background examines the nature of the learning task and the role of the teacher. An example is given of three related tasks that scaffold the learning experience and help the student extend his/her mathematical thinking…

This article describes a video- and computer-based program used to motivate and develop mathematics skills in middle school students with disabilities. The program emphasizes real-life problems such as building a cage for a pet, a skate boarding ramp, and a "hovercraft" frame. Case studies illustrate the program's effectiveness with individual…

This paper describes the global feedback in ActiveMath, a Web-based adaptive learning environment for mathematics and beyond. It addresses some of the cognitive foundations and the architecture of the suggestion mechanism with its components. This architecture separates components for diagnosis from components for suggestions and different types…

This paper briefly outlines the evolution of ICT-based learning environments discussing some of the main aspects that have characterised such evolution (eg, technological evolution, changed cognitive and pedagogical frameworks, changed role assigned to ICT-based systems in education). The objective is to point out how the implementation of…

This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring…

The purpose of this study was to investigate students' use of visual imagery and its relationship to spatial visualization ability while solving mathematical word problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N = 66) participated in this study. Students were assessed on measures of…