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…

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics…

Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the…

Critical thinking is an essential skill for learners and teachers alike. Therefore, it is essential that educators be given practical strategies for improving their critical thinking skills as well as methods to effectively provide critical thinking skills to their students. The "Handbook of Research on Critical Thinking and Teacher Education…

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…

The authors examined the effectiveness of strategy instruction taught by general educators in mixed-ability classrooms. Specifically, the authors compared the mathematical word problem-solving performance and computational skills of students who received schema-based instruction (SBI) with students who received general strategy instruction (GSI).…

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…

Over the past decade, research on the use of technology in the mathematics classroom has focused primarily on issues of student learning and engagement. In this article, we focus on middle grades mathematics teachers' use of The Geometer's Sketchpad, and study both the decisions they make about when to use technology, and their motivations for…

This paper is an attempt at clarifying the concept of "problem," in order to improve the teaching of problem solving. Four categories are employed in the analysis: formulation, context, solutions, and methods of approach. Examples are included. (MNS)

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…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

This article presents a graduated word problem sequence in mathematics, beginning with simple words; progressing to phrases, sentences, and paragraphs; advancing to paragraph word problems with extraneous information; and finally having students create their own word problems. Results from 67 elementary students with learning disabilities support…

Experimental studies conducted since 1980 were reviewed. Each of the 34 studies concerning problem solving is briefly summarized, followed by comments, criticisms, and/or concerns. A summary indicates that experimental research of the 1980s seems to focus on: (1) children's processes, understanding, functioning, difficulties, and representations;…

An alternative explanation is presented for the pattern of relative difficulty of arithmetical word problems to that suggested in a 1983 article. It is argued, that for many problems, much of the symbolic manipulation is accomplished externally, not internally. (MNS)