Archimedes viewed the method of centroids as a valuable tool for intuitive discoveries. This article presents several uses of this technique and discusses how the method of centroids could be used in secondary schools. (Author/MK)

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)

Explores areas of polygons by comparing polygon area to the area of the associated midpoint polygon, formed by joining the midpoints of consecutive sides. Considers triangles, quadrilaterals, pentagons, and regular polygons using paper folding, drawings on graph paper, and plexiglass MIRA constructions. (Contains 12 references.) (MKR)

Mnemonic devices to aid in the teaching of perimeter and circumference are suggested. (MK)

Presents lesson plans for activities to introduce recursive sequences of polygons: golden triangles, regular pentagons, and pentagrams. The resulting number patterns involve Fibonacci sequences. Includes reproducible student worksheets. (MKR)

Suggests one possible way to combine the technological facility of the computer with students' natural abilities for concept formation. Describes the software the "Geometric preSupposer." (PK)

Geometry is a fundamental part of the mathematics foundation provided by elementary education. Children have an intuitive understanding of geometry that they draw on when dealing with geometric concepts in activities like drawing, playing hopscotch, defending their "half of the room," and playing sports. This book offers no instruction…

Presents activities which use graphing calculators to explore parametric equations of spirals, circles, and polygons. (MKR)

Previous work has identified four areas of difficulty that students seem to have with the topic of similarity: (1) understanding the definition of similarity; (2) proportional reasoning; (3) dimensional growth relationships; and (4) correspondences in right triangle similarity. This paper reports the results of an investigation into high school…

Presents practical, teacher-tested tools and techniques based on National Council of Teachers of Mathematics (NCTM) standards for teaching mathematics. Covers Cognitively Guided Instruction (CGI) technique; story problems across the curriculum; advantages of using calculators in instruction; and manipulatives for plane geometry. Includes a chart…