Gives a lesson plan for a mathematics activity using balloons which shows connections between the algebraic concepts of slope, linear functions, and power functions and the geometric concepts of circle, sphere, volume, and pi. Includes reproducible student worksheets. (MKR)

Presents an activity in which students draw a picture, analyze each line and curve, and write the symbolic equations represented by the graph. Includes reproducible student worksheets. (MKR)

Discusses flexible polyhedrons, called flexors, that can be bent so that the faces stay rigid while the angles between them seem to change. Presents models representing flexors and directions on how examples can be constructed. (MDH)

The LOGO programing of 30 ninth graders was analyzed from 3 theoretical perspectives: the van Hiele levels, the Structure of Observed Learning Outcomes taxonomy, and Skemp's model of mathematical understanding. Results indicate that success in LOGO programing appears necessary but insufficient for success with the geometric aspects of the analyzed…

Presented is an alternative method for analyzing the van Hiele level of students' geometrical reasoning. The accuracy of students' answers may afford a description of acquisition and/or expertise for each of the van Hiele levels simultaneously rather than the traditional assignment and evaluation of one level at a time. (JJK)

Argues that the derivation of the area of a circle using integral calculus is invalid. Describes the derivation of the area of a circle when the formula is not known by inscribing and circumscribing the circle with regular polygons whose areas converge to the same number. (MDH)

Shows a way in which algebra and geometry can be used together to find the lengths and areas of spirals. This method develops better understanding of shapes, similarity, and mathematical connections in students. Discusses spirals embedded in triangles and squares, the Pythagorean theorem, and the area of regular polygons. (MKR)

The experiences of elementary teachers who invited their students to verify geometric theorems prior to the introduction of protractors form the basis of a pedagogical strategy for a sequence of learning activities offered here. Discussion focuses on the students learning strategies about angle concepts utilizing the dynamic interpretation of a…

Discusses selected children's literature dealing with geometry and measurement concepts. Suggests activities for grades three through six to be used as part of a learning center or to be completed in cooperative learning groups. (MG)

Presented are activities concerning the method of graphing the equation y=kx in the Cartesian and other coordinate systems. Students progress from the graph of a straight line to the investigation of conceptually related geometric loci in non-Cartesian coordinate systems. (MDH)

Presents a problem in which the incorrect application of the Law of Sines leads to an erroneous solution. Demonstrates that the commission of this error by an ophthalmologist using laser trabeculoplasty could lead to patient injury. (MDH)

Describes the Geometer's Sketchpad, a geometric construction kit composed of three manipulatable, dynamic, linked, multiple representation environments: the coordinate system, formulas, and graphs. Examines the use of the environments for studying parameter effects of linear and quadratic functions and for solving linear equations. (MDH)

A way for students to refresh and use their knowledge in both mathematics and physics is presented. By the study of the properties of the "Runge-Lenz" vector the subjects of algebra, analytical geometry, calculus, classical mechanics, differential equations, matrices, quantum mechanics, trigonometry, and vector analysis can be reviewed. (KR)

Contributes to the emerging picture of children's development of understanding in geometry and the kinds of teaching that can support it. Describes how teachers can use episode writing to capture student thinking and make instructional decisions. (ASK)

Describes vortex tessellation in which an individual tile becomes smaller, and swirls or spirals inward to the center. Provides mathematical uses of this type of tessellation. (ASK)