The empirical data in this study are from a series of two lessons on measurement implemented in seven classes with 119 six-year-old students in Sweden. Both problem solving and problem posing were shown to be important in early mathematics when students in this study worked on one problem-solving task and one problem-posing task on measurement. As…

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…

After evaluating a proposal by Jon Star (2005) that mathematics educators reconceptualize the construct of procedural knowledge, we offer an alternative reconceptualization based on an extension and amalgamation of his and other conceptualizations of procedural knowledge and conceptual knowledge. We then propose some implications for research…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

In this paper we examine the roles that metonymy may play in student reasoning. To organize this discussion we use the lens of a structured derivative framework. The derivative framework consists of three layers of process-object pairs, one each for ratio, limit, and function. Each of the layers can then be illustrated in any appropriate context,…

The purpose of the study was to determine whether students had knowledge of the extension rule (the conjunction of two or more events cannot be greater than the probability of any one of those events) and understanding of conjunction by giving a test of multiplicative probabilities. Involved were 598 students enrolled in introductory psychology…

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)

Four experiments investigated college students' judgments of inter-event contingency. Subjects were asked to judge the effect of a discrete response (tapping a wire) on the occurrence of a brief outcome (a radio's buzzing). Pairings of the possible event-state combinations were presented in a summary table, an unbroken time line, or a broken time…

This paper proposes an hypothsis describing how some college students incorrectly view semantically laden letters and provides both clinical and written data that supports that hypothesis. Several word problems were given to nine college math students. These students were then interviewed as they attempted to solve these problems. In addition to…

To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of five to seven years, children were tested on nonnumerical function tasks, numerical tasks, and aspects of logical reasoning. (PCB)

The theme of the sixth annual meeting of the North American Chapter of Psychology of Mathematics Education was "The Importance of Psychological Models for Research in Mathematics Learning." The conference proceedings contain papers organized around five major topics. In the first section, eight papers on the learning of arithmetic are…

Proportion problems were given to pupils in grades 3-5. Success rates were high, with elementary strategies based on addition often used. Familiarity with the use of ratios in the context, the presence of a mixture, and the use of manipulatives were variables that influenced performance. (Author/MNS)

Describes a study to determine middle school children's representational strategies to form part-whole or part-part relationships for relational numbers such as proportions, ratios, or fractions. Quantitative and qualitative analysis revealed that children prefer a part-part representation to solve relational quantity problems. (15 references)…

Through individual interviews with remedial and precalculus university students, five characteristics of the student were identified that influence whether a diagram is used in solving a problem and whether its use is successful. The interviews also suggested a set of subskills that contribute to the overall ability to draw effective diagrams.…

Discussed are the roles played by anticipation, belief, and motivation in two young children's problem-solving activity. It is argued that a solver's beliefs and motivations are intimately related, and that the discussion of the two children's behaviors may have some generality. (Author/MNS)