The purpose of this study is to investigate the metacognitive strategies that middle school students used in the process of solving problems individually. The study group consisted of 37 middle school students in the eighth grade. The students were asked one non-routine word problem, and their written answers were collected. After solving the…

Background: The ability to translate concrete manipulatives into abstract mathematical formulas can aid in the solving of mathematical word problems among students, and metacognitive prompts play a significant role in enhancing this process. Aims: Based on the concept of semantic congruence, we explored the effects of metacognitive prompts and…

Research on the multimedia effect in testing indicates that static representational pictures (RPs) and, potentially, dynamic RPs that further subdivide the picture into segments may support students' mental processing. This might be especially relevant for mathematical word problems that pose high mental demands in a multistage solution process.…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

Awareness of one's own strengths and weaknesses during visualisation is often initiated by the imagination -- the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West…

Students with mathematics learning disabilities (MLD) have a weak understanding of fraction concepts and skills, which are foundations of algebra. Such students might benefit from computer-assisted instruction that utilizes evidence-based instructional components (cognitive strategies, feedback, virtual manipulatives). As a pilot study using a…

We developed an intervention based on the learning by teaching paradigm to foster self-regulatory processes and better learning outcomes during complex mathematics problem solving in a technology-rich learning environment. Seventy-eight elementary students were randomly assigned to 1 of 2 conditions: learning by preparing to teach, or learning for…

There is a reciprocal relationship between mathematics and reading cognition. Metacognitive training within reading-enhanced problem solving should facilitate students developing an awareness of what good readers do when reading for meaning in solving mathematical problems enabling them to apply these strategies. The constructs for each cognitive…

Although the characteristics of PBL (problem focused, student centered, self-directed, etc.) are well known, the components of a problem-based learning environment (PBLE) and the cognitive scaffolds necessary to support learning to solve different kinds of problems with different learners is less clear. This paper identifies the different…

This study measured the amounts of different types of metacognitive statements made by students enrolled in Elementary Algebra courses at a community college in California. A total of 17 students were interviewed three times during the course of a semester. All interviews were coded for types of metacognitive statements that fell into one of three…

This article discusses outcomes of a study that indicated gifted children as young as 6 years old can use metacognitive processes for solving math problems, are aware of knowing certain operations and are able to use them automatically, and know which strategy they usually use for solving problems. (Contains references.) (CR)

Examined relationships between kindergarten children's acquisition of metacognitive knowledge related to mathematics, subjects' general ability, and the role of metacognition and ability in facilitating word problem solutions. Found that subjects acquired a substantial metacognitive knowledge about mathematical word problems, which correlated…

A study investigated the repertoire of cognitive schemes used by 15 adolescents with mental retardation in the process of solving additive word problems. Findings provide evidence of at least a partial part-part-whole scheme for about half of the students and more use of metacognitive knowledge than is usually expected. (Contains references.)…

This article reviews current knowledge about using computers to teach problem-solving skills to students with learning disabilities (LD). It presents the case for use of hypermedia to improve students' mathematics problem-solving abilities. Specific suggestions are given for applying hypermedia to cognitive strategy instruction and the graduated…

Junior high school students (n=72) with learning disabilities received direct instruction in cognitive strategies, instruction in metacognitive activities, or both. Students improved in mathematical word problem performance and compared well with normally achieving peers. Discussion focuses on the treatment effects and maintenance and the issue of…