Quilts are an integral part of the North American culture. Most households in North America have quilts with intricate geometric patterns. These patterns symbolize different things to different groups of people in this part of the world. It is important for students to see how mathematics comes from what is done in day-to-day life, not from the…

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…

This study involving 29 students enrolled in an 8-week summer Algebra II class for minority students was undertaken to determine the relationship between the kinds of symbolic forms used in problem-solving instruction and students' problem-solving processes and performance. All subjects were Black or Hispanic and were about to enter grade 11. For…

This manual describes the Mathematics Assessment Questionnaire (MAQ) and its development, provides relevant background from the research literature, describes approaches to the reporting and uses of the MAQ (including its use in instructional planning), and presents sample responses from students and classes. The MAQ provides teachers and students…

The Texas Educational Assessment of Minimum Skills (TEAMS) was developed by the Texas Education Agency (TEA), in response to Texas House Bill 72 (1984), which mandated a new basic skills assessment program for mathematics, reading, and writing at grades 1, 3, 5, 7, 9 and 11. The test given to students in Grade 11 is an exit-level examination, and…

Since 1983, the Educational Technology Center at the Harvard Graduate School of Education has studied the uses of computers and other technologies to improve K-12 instruction in science, mathematics, and computing. Collaborative research groups--including scientists and mathematicians, practicing teachers, learning theorists, and software…

Drawing on the experience of two first-year classrooms in Melbourne, Australia, this article explores numeracy learning within an information and communication technology (ICT) environment. Included are examples of how mathematical skills can be promoted and learned in such a way that children can extend their use to practical, problem-solving…

Describes a technique using a color-coded holistic scoring system to achieve greater understanding of the assessment process on the part of students by having them score classmates' solutions to a problem. (MKR)

This paper focuses on the relation between two areas of research which owe a great debt to the work of Giyoo Hatano: the ways in which the use of the abacus mediates arithmetic problem solving and the way in which the use of the kanji writing system mediates the interpretation of unfamiliar words. These examples are related to L. S. Vygotsky's…

Emphasis on problem solving in mathematics has gained considerable attention in recent years. While statistics teaching has always been problem driven, the same cannot be said for the teaching of probability where discrete examples involving coins and playing cards are often the norm. This article describes an application of simple probability…

In this paper, we take a look at two electrostatics problems concerning hemispheres. The first problem concerns the direction of the electric field on the flat cap of a uniformly charged hemisphere. We show that the symmetry and principle of superposition coupled with Gauss's law gives a delightfully simple solution and then go on to examine how…

We investigate the use of external visual representations in probability problem solving. Twenty-six students enrolled in an introductory statistics course for social sciences graduate students (post-baccalaureate) solved eight probability problems in a structured interview format. Results show that students spontaneously use self-generated…

This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The…

This article presents a story of Robert Andrew's mental engagement with mathematics. It has been jointly written by Robert, who is a Y8 student, and his father, Paul Andrews, who is a mathematics educator. It starts with Robert who presents the context for the story and is followed by Paul's commentary which draws on what Robert has written.…