This book is about playing with mathematics, teaching: (1) How to multiply and divide large numbers mentally; (2) Making addition and subtraction easy; (3) Tricks for understanding fractions and decimals; and (4) How to quickly check answers for each calculation. Described as a foolproof way to do multiplication, division, factoring estimating,…

Students' mathematical problem-solving experiences are fraught with failed attempts, wrong turns, and partial successes that move in fits and jerks, oscillating between periods of inactivity, stalled progress, rapid advancement, and epiphanies. Students' problem-solving journals, however, do not always reflect this rather organic process. Without…

Problem solving theory and practice suggest that thinking is more important to solving problems than knowledge and that it is possible to teach thinking in situations where little or no knowledge of the problem is needed. Such an assumption has led problem solving advocates to champion "content-less heuristics" as the primary element of problem…

Seeking more effective mathematics instruction, this author decided to incorporate Cognitively Guided Instruction (CGI) into first-grade classroom lessons. Students in CGI mathematics classrooms are prompted to use their prior knowledge to solve new problems, establish cognitive structures to which new learning can be connected, and be driven by…

In this article, the author reflects on her session at the 2006 conference, including the learning styles and strategies she observed. In her session, they explored some of the more unusual aspects of convex polyhedra (with regular faces), including the notions of "valence" and "species". Although the session was about shape and space, there was…

In recent years, teachers have noticed a drop in student effort on complex problems in math and science. The purpose of this study was to determine if incorporating cooperative learning and self-recording strategies had an impact upon student effort on complex problems. A total of 38 9th through 11th grade math and science students at two…

Twenty-one 4th- and 5th-grade students with learning disabilities and emotional disabilities were assigned at random to a control condition or to an experimental condition in which they were taught, over a 9-week period, a five-step self-determination strategy for solving school- or home-related problems. Maintenance was assessed 3 weeks after the…

This study aimed at investigating the relations between students' strategic behaviour during problem solving, task performance and domain-specific self-concept. A total of 167 first- and second-graders were individually examined in tasks involving cubes assembly and in academic self-concept in mathematics. Students' cognitive, metacognitive, and…

This paper reports on five related studies on upper elementary school students' beliefs about the role of real-world knowledge in solving mathematical word problems, and on possibilities of overcoming their unrealistic mathematical modeling. Findings from the first study of 75 Belgian fifth-grade students showed that as a consequence of current…

The Thinking Mathematics project, a joint effort of the American Federation of Teachers and the Learning Research and Development Center, had the primary objective of developing more efficient means of disseminating new knowledge about mathematics learning and instruction. The resulting practitioner-researcher collaboration developed an…

Imagery use in high school mathematics classrooms was studied. A visual image was defined as a mental scheme depicting visual or spatial information, but this definition was not spelled out to teachers or students, in order to learn what they meant by the concept. Subjects were 13 high school teachers and 54 of their students interviewed over 3…

The National Assessment of Educational Progress (NAEP) is the only nationally representative and continuing assessment of what students in the United States know and can do in various academic subjects. The 1996 NAEP in mathematics assessed the current level of mathematical achievement as a mechanism for informing education reform. In 1996, 44…

The National Assessment of Educational Progress (NAEP) is the only nationally representative and continuing assessment of what students in the United States know and can do in various academic subjects. The 1996 NAEP in mathematics assessed the current level of mathematical achievement as a mechanism for informing education reform. In 1996, 44…

The National Assessment of Educational Progress (NAEP) is the only nationally representative and continuing assessment of what students in the United States know and can do in various academic subjects. The 1996 NAEP in mathematics assessed the current level of mathematical achievement as a mechanism for informing education reform. In 1996, 44…

The National Assessment of Educational Progress (NAEP) is the only nationally representative and continuing assessment of what students in the United States know and can do in various academic subjects. The 1996 NAEP in mathematics assessed the current level of mathematical achievement as a mechanism for informing education reform. In 1996, 44…