The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

A logical analysis of word problems provides an hypothesis about the kinds of knowledge that may be necessary for solving multi-step word problems. This hypothesis is that knowledge of the overall pattern of relations in a problem may function in problem-solving apart from knowledge of the particular entities and the local relations in which they…

The thinking processes of students of Logo were examined to identify programming problems and possible instructional remedies. Subjects were 11 students between the ages of 8 and 12 who had completed 5 weeks of Logo instruction. These students were given a series of five short programming problems highlighting such areas of difficulty as judging…

Explores third and sixth grade children's acquisition and analogical transfer of the base of a relatively complex problem. One group at each grade level received two analogs of a scheduling problem; other groups received only one analog or a transfer task. After criterial performance, all children were transferred to an isomorphic analog and…

Previous studies indicate that many early elementary school children have the misconception that whole number subtraction is a commutative operation. The degree and character of this subtraction error was investigated in this longitudinal study. Results obtained from three groups of students with different number abilities provided further…

Discusses the problems of using chronometric analysis, a common cognitive psychological method, for educational assessment. Suggests that cognitive assessment has not reached the precision needed to analyze individual differences. (FMW)

Explores the role of premature cognitive closure in the development of inferential reasoning among 62 children aged 7, 9, and 12 years through two studies. Results indicate that despite a strong tendency to close on single alternatives, most children correctly assigned nonzero probabilities to each of the possible alternatives. (RJC)

First-, third-, fifth-, and sixth-grade children were administered 20 relational reasoning problems in which they had to deduce the possible sizes of one item relative to two others on the basis of a visual comparison and a written clue. Dramatic differences were observed between fifth- and sixth-grade children. Corrective feedback improved…

Determined effects of two task types on 12- and 13-year-olds' understanding of applications of multiplying and dividing positive numbers. Results indicate the persuasive nature of certain misconceptions and specific effects of context attributable to such aspects as relative familiarity. Implications of these and other results are discussed.…

Provides framework for assessing the extent to which problem-solving skills learned through LOGO, a children's graphics-oriented-structured computer language, may be transferred to other contexts. Examines principles governing generalization of learning. Discusses learning transfer and components of the LOGO experience that may affect transfer.…

Reported are early results of a research program that aims to improve children's mathematics learning by developing attitudes and strategies that support processes of interpretation and meaning construction in mathematics. Considerable research shows that many children learn mathematics as symbol manipulation rules, without meaning. Collaborative…

Mathematics is generally regarded as a well-structured discipline by educators and cognitive scientists. This leads to the analysis of the suggestion that practitioners begin investigating possibilities for teaching mathematics as if it were an ill-structured discipline, with more than one interpretation for mathematical statements. The paper is…

This study involved 48 students ages 9 to 12. The 29 experimental group students, divided into small groups, performed learning exercises designed to improve skills in analyzing and processing expressions frequently included in addition and multiplication problems. The exercises helped significantly to improve problem-solving performance. (MNS)

Review of existing research on the general cognitive outcomes of Logo training concludes there is little data-based or empirical evidence on the effects of teaching Logo to children. It is suggested that current research on Logo should be more directly tied to outcomes related to learning a structured computer language. (MBR)