Presents two teaching ideas. The first helps students identify and correct their own mistakes. A checklist of common mistakes is filled out by students after quizzes and tests and examined for error patterns. The second develops the formula to determine the payments necessary to pay off a loan over a required period of time. (MDH)

Proposes a novel method of introducing and promoting the topic of geometric sequences through the problem of calculating the number of games necessary to determine the winner of a single elimination tournament in which two, three, or more teams compete at a time. (MDH)

Uses conic sections, trigonometric functions, and polar coordinates to solve the problem of determining the shape of a baseball outfield fence, given the distances along the foul lines and to straightaway center field. Graphing programs and calculators are utilized to plot different solutions. (MDH)

Responses of students in grades K-10 (42 interviewed; 98 written) to 4 common fractions problems were analyzed for iconic mode processes in relationship to concrete symbolic mode development. Concludes that progress in the latter, without development of complementary iconic support, limits both understanding and flexibility in solving problems.…

Describes a mathematics course for prospective elementary teachers that has teaching and learning mathematics via problem solving at its core. Presents a problem-solving activity involving number theory and reactions by the students and teacher to the activity. (MDH)

As part of Alberta's provincial initiative, teacher-researchers in two Calgary school districts developed and field-tested quality indicators for assessment of student artwork and mathematical problem solving. The resulting qualitative materials depend on informed professional judgment and student involvement in self-assessment; celebrate…

Suggests that using the iconic and computing features of a spreadsheet enhances the transition from natural language sentences to pictorial and numerical representations of algebraic word problems. Presents work performed in a lab setting with preservice and inservice teachers enrolled in contemporary general mathematics and problem-solving…

Investigates the effects of computer-assisted video-based anchored instruction on promoting students' attitudes toward mathematical instruction and problem-solving skills. Examines the effects of different media attributes on students' mathematical achievement and attitudes in a situated learning environment. Findings suggest that anchored…

In a cooperative research program, classroom teachers and university researchers developed and implemented a contextualized performance-based assessment in mathematics. The assessments were intended to model what students may do in the course of daily activity and designed to assess problem solving, and conceptual and procedural understanding.…

Excerpts a student-teacher discourse from a 4th-grade mathematics classroom to illustrate how discourse helps students construct algebraic thinking. Discusses the implications of the discourse method of collaborative inquiry for teaching. (JPB)

The purpose of the study reported in this article was to explore the mathematical discourse in which four dyads engaged while sharing the storybook "One Snowy Night" (Butterworth, 1989) while at home or in other locations (e.g., day care centers). Each dyad consisted of a mother and her four-year-old child. Various discourse patterns were evident,…

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

T-algebra is a project for creating an interactive learning environment for expression manipulation tasks of elementary algebra. Our main didactical principle has been that all the necessary decisions and calculations at each solution step should be made by the student, and the program should be able to understand the mistakes. This paper…

Using symbolic algebra to represent and solve linear equations is one of the expectations within the "Algebra" content standard for the 6-8-grade band in the National Council of Teachers of Mathematics (NCTM) "Principles and Standards for School Mathematics" (2000). Students' understanding of these concepts, even before a formal algebra course,…

Our research is concerned with teacher's knowledge, and especially with teacher's processes of learning, in the classroom, from observing and interacting with students' work. In the first part of the paper, we outline the theoretical framework of our study and distinguish it from some other perspectives. We argue for the importance of…