Students' reported inner speech during mathematics problem solving was studied. Subjects from grades three to six were assigned to low-task or high-task difficulty groups. Between problems, students reported their inner speech. Both groups maintained an adaptive task-oriented problem-solving stance, with positive affect toward self. (Author/GDC)

Examines principles which can be applied to determine how hints can be used effectively in problem-solving. Conscious and unconscious hints, timing of hints, expected functions, and teaching are discussed. Conscious hints are explained in detail with suggestions and references. Charts are included for types, timing, and expected functions. (DH)

The author arranges 26 current states of mathematical knowledge (in relation to solving a problem) in an informal taxonomy and comments on them. (MNS)

Using questions to help students think mathematically and solve problems is discussed. The teacher's role is described, with a classroom example involving questions about a specific problem. (MNS)

One view of mathematical thinking is described, followed by detailing of the characteristics of a problem-solving program necessary to develop this kind of thinking. (MNS)

A problem-solving strategy that appears to be highly successful is having children write their own word problems. The stages of prewriting, writing, rewriting and revising, and publication are each discussed. (MNS)

Replies to Steinberg's article on protocol analysis in this issue and argues that even if the writing process is a problem-solving process, it is too complex to analyze sufficiently using protocols. (SRT)

The neurochemistry and physiology of memory and learning should be relevant to classroom techniques and methods of study. Findings should be examined to discover where positive and negative cross-correlated effects might occur between basic science information and educational methods. (MLW)

Included are a general introduction to the topic of metacognition, a discussion of how metacognition is involved in mathematical performance, and a short section on metacognition and instruction. (MNS)

To evaluate prevalence of perseveration in early search, nine-month-olds were tested on both two- and three-location version of Piaget's AB task. Three principal findings emerged: (1) infants did not show systematic perservation on either location task; (2) they did demonstrate positive search skills; and (3) they searched using similiar methods…

Examines the relationship between development of logical processes required in deductive reasoning and their use by preschoolers, also considering possible explanations for children's deductive reasoning. The relationship of problem content to real-world knowledge and the sequence of presentation of problem types were found to affect the display…

When the words "problem" and "answers" are used in connection with computational exercises, students think they are solving problems. Distinguishing between computational forms and problems is illustrated with a variety of topics. (MNS)

Examines reading as a problem-solving process and suggests that those processes evident in reading successfully and in successful problem solving can be made conscious, thus enhancing children's success in both areas. (FL)

This chapter examines research on the cognitive processes involved in mathematical problem solving. The introduction includes definitions of key terms and a summary of four cognitive processes used in mathematical problem solving: (1) translating; (2) integrating; (3) planning; and (4) executing. Examples are then provided and exemplary research…

This study explored the mental components that are most important for successful problem solving. Four components were studied: cognition, metacognition, noncognitive variables, and justification skills. It was hypothesized that cognition and knowledge of cognition would predict success at solving well-structured problems, which have one correct…