The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…

Two studies investigated the effects of a storytelling-context for teaching geometry skills to kindergarten girls and boys. In Study 1, the story+geometry intervention consisted of an adventure story teaching geometry through part-whole-relations puzzles. Learning was assessed through transfer of skills, using a pre-/post design comparing…

This document presents a summary of changes made to the 2008 Mathematics Standard for grade 8. The table presented in this document offers a summary of the: (1) Removed Performance Objectives (POs); (2) POs Moved to a Different Grade Level; (3) POs Moved within the Grade Level or from another Grade Level; and (4) New POs.

Despite widespread agreement that the activity of "reasoning-and-proving" should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that…

By translating inequalities into equations (e.g., x greater than 0 can be written x- absolute value of x = 0) and forming equations for unions and intersections of solution sets, students can develop equations for polygons. The method can be generalized to yield equations in three dimensions. (SD)

A Reuleaux triangle is an example of a curve of constant width; the distance between parallel tangents is the same no matter which direction is used. A consideration of a particular set of Reuleaux triangles is offered which leads to a good example of problem-solving in geometry. (JN)

The investigation of how a circle and square lying in the same plane could intersect each other is an excellent example of geometric problem-solving. This paper explores three facets of the investigation: (1) finding out how many points of intersection are possible, (2) classifying the different ways of intersection, and (3) determining which ways…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated…

Introduces a special triangle for which many different problems can be posed on the basis of one unusual property. Presents three problems and considers different approaches for the first problem. Explores other mathematical problems using the "What if not?" strategy that can be used as classroom activities. (KHR)

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

I report on the findings from research and literature on (a) use of symbols in mathematics, (b) algebraic/trigonometric expressions, (c) solving equations, and (d) functions and calculus. From these, some insights and implications for teaching and learning are derived.

This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…

A question posed by Euler is considered: How can polyhedra be classified so that the results is in some way analogous to the simple classification of polygons according to the number of their sides? (MK)

On a triangular grid of equilateral triangles an analytical procedure is presented for solving puzzles that require one to measure out a specified amount of liquid from containers of various volumes. (JP)