Children's perception and understanding of three-dimensional figures and of operations on them is discussed. Piaget's findings are reviewed and more current research is described. Classroom implications are explored. (SD)

The concept of trigonometric ratios in a right triangle can be clearly presented through the use of interactive-geometry software. Investigation in this manner allows students to see the crucial features of the concepts before they are formalized and to gain ownership of these ideas through discovery. Many examples of the mathematical…

Presents a method for determining the coordinates of the endpoint of a line segment given its slope, point of origin, and length. Applies the notion of similar triangles to quickly solve this type of problem. Includes a calculator program. (KHR)

Examines secondary school students' ability to interpret representations of three-dimensional objects including prototypes of component, perspective drawings, orthogonal views, descriptions by coordinates, verbal descriptions, and verbal quasi-descriptions. Students were given four identical wooden cubes and asked to construct the objects. Reports…

Relationships among the sides are developed for right triangles whose sides are in the ratios 1:3, 1:4, and 1:5. The golden ratio appears in the results which can be used in secondary mathematics. (DC)

Provides a proof that, if two angle bisectors of a triangle are equal in length, the triangle is isosceles (Steiner-Lehmus Theorem) using two corollaries related to a side-side-angle correspondence in a triangle. Introduces historical developments in the discussion of the proof. (MDH)

Presents activities involving multiple embedded figures beginning with the problem of counting the number of squares on a checkerboard. Offers several extensions and assessment suggestions. Includes student worksheets. (MKR)

When given opportunities to explore mathematics, make conjectures, and write about what they have discovered, students gain a deeper understanding of this fascinating subject. In this article, the author describes her successful Geometry Portfolio class. In addition to traditional student work, the author frequently added short essay questions or…

This article presents a case study in which researcher-practitioner collaboration took place to promote effective use of technology in an urban elementary school mathematics classroom. Data were primarily gathered through classroom observations and interviews. The aim of this study was twofold. First, to increase our understanding of the effects…

The purpose of this current study was to investigate the reasoning stages of in-service middle and high school mathematics teachers in geometry. There was a total of 148 in-service middle and high school mathematics teachers involved in the study. Participants' geometric reasoning stages were determined through a multiple-choice geometry test. The…

In a geometry content course for pre-service elementary teachers, technology was utilized to assist students in making sense of shapes. They learned to write simple procedures in Logo that would program a turtle to draw various quadrilaterals. In the context of writing these procedures, the pre-service teachers used variables to represent the…

The purpose of the project reported in this article was to evaluate how assessing teachers' mathematical knowledge within a professional development course impacted from the teachers' perspective their learning and their experience with the course. The professional development course consisted of a 2-week summer institute and the content focus was…

Students explore the Pythagorean theorem and an extension using jelly beans to measure areas. Deductive thinking and algebraic notation help establish connections. (Contains 8 figures.)

This article addresses the issues of coaching and assessing. A preservice middle school teacher's unique solution to the Pizza problem was not what the professor expected. The student's solution strategy, based on sequences and a reinvention of Pascal's triangle, is explained in detail. (Contains 8 figures.)

As any ordinary person knows, the shortest distance between two points is a straight line. What, then, is the shortest distance between three points? Four points? The study reported in this article deals with the observed actions of Turkish student mathematics teachers as they were working with minimal network problems. Having analysed the…