This review guide, prepared as an aid to teachers of Course III, starts with a pre-test review of Course II topics found again in Course III. The five units of Course III, as outlined in the New York State Syllabus, are then separated into nine smaller units. These include: real numbers; complex numbers; functions; logarithms; trigonometry;…

While repairing a sleeping bag, the author observed that the quilt stitching was unicursal. This led to development of a classroom activity relating the stitching patterns of quilts to the highest common factor of the numbers of "bumps" in each direction. (SD)

Figurate numbers based on seven geometric figures are discussed. The place of these numbers in Pascal's triangle is indicated. (SD)

This paper presents a laboratory exercise in which an integration problem is applied to cinematography, without the need for apparatus. The problem situation is about the oscillation control of a camera platform to attain the contrast angular rate of objects. Wave equations for describing the oscillations are presented and an expression for…

Five sets of activities for students are included in this document. Each is designed for use in secondary school mathematics instruction. Topics include: (1) "5-Con Triangles"; (2) "Striking Sequences"; (3) "Invariants"; (4) "On the Ball," (a geometry lesson); and (5) "Coloring Maps." These topics focus on geometric and statistical concepts. Each…

This is a sample of the final test for students in mathematics at the sixth-grade level in Alberta (Canada) schools. The test contains multiple-choice items and is divided into two sections. Section 1 contains 55 items related to numeration, operations and properties, measurement, geometry graphing, and problem solving. Section 2 consists of five…

This document contains detailed directions for constructing a device that mechanically produces the three-dimensional shape resulting from the rotation of any algebraic line or curve around either axis on the coordinate plant. The device was developed in response to student difficulty in visualizing, and thus grasping the mathematical principles…

This is the final report of a year-long research project on the implementation of a guided inquiry approach using the Geometric Supposer, a microcomputer software series, to teach high school geometry in three Boston area suburbs during the 1985-1986 school year. The project assessed student learning and examined the many and varied issues…

The purpose of this project is to help teachers of mathematics get started using the computer to aid the teaching and learning of many mathematical concepts in a meaningful way. To this end, commercially available software packages are described which are versatile, cost effective, and easy to use. A review and several lessons, including homework…

This publication provides suggested learner outcomes for guiding instruction and evaluation of students in grades 9-12 in Oklahoma. The goals are intended to provide teachers, administrators, school boards, parents, and other concerned citizens with a clear understanding of expected minimum learner outcomes for each mathematics course. Teachers…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

The Van Hiele level theory offers an explanation and a remedy for student difficulty with higher-order cognitive processes required for success in secondary school geometry. This document reports results of a study which involved about 2700 students in 13 high schools, selected to provide broad representation of community socio-economics in the…

This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.

The following questions are addressed: (1) Are there sex differences in achievement, either in entering knowledge of geometry in the fall, or in achievement in acquiring standard geometry content by year's end? (2) Are there sex differences in the performance of students on the van Hiele test, either at the beginning or end of the year? and (3)…

This document focuses on a series of studies that viewed aspects of conditional reasoning. The investigations were concerned with the processes children use to acquire patterns of deductive inference and logical relationships pertaining to propositional reasoning. The first experiment, involving 96 children each in grades 2 and 5, investigated the…