This instructional unit uses an intuitive approach in introducing the concept of congruent transformations. Extensive use is made of worksheets and manipulative methods. In the latter stages, the SSS, ASA, and SAS theorems are presented. The unit concludes with geometric proofs requiring the use of the fact that corresponding parts of congruent…

Presents a method that connects the area formulas for triangles, rectangles, parallelograms, and trapezoids by focusing on the relationships between the bases and heights of each figure. Transformations allow figures to be reconceptualized to establish a general concept of area that can be applied to other figures. (MDH)

Presents a proof of Euler's Theorem on polyhedra by relating the theorem to the field of modern topology, specifically to the topology of relief maps. An analogous theorem involving the features of mountain summits, basins, and passes on a terrain is proved and related to the faces, vertices, and edges on a convex polyhedron. (MDH)

The transformation assigning to every point its inverse with respect to a circle with given radius and center is called an inversion. Discusses inversion with respect to points, circles, angles, distances, space, and the parallel postulate. Exercises related to these topics are included. (MDH)

This research explored students' views of geometric objects through the implementation of a curriculum module that allowed them to explore the relationships between transformational geometry and linear algebra. The majority of the students were middle and secondary mathematics education majors enrolled in a one-semester geometry course that is…

The study investigated whether (1) instruction providing for experimental manipulation by students was superior to instruction in which teachers perform the manipulations and children observe, and (2) spatial ability was related to mode of instruction. Participating in the 8-week study were 141 students aged 12-15 in seven intact eighth-grade…

Observation of patterns constructed on geoboards can lead to discussions of properties of primes, number sequences, and complex numbers. (SD)

The post mortem item-examinee sampling investigation described herein explored the feasibility of using item-examinee sampling to estimate scale values denoting degree of affect toward stimuli when measured by the method of paired-comparisons. Results indicate clearly that such scale values can be approximated satisfactorily through item-examinee…

Explores the rationale behind the importance of teaching young secondary school students how to look for correlation patterns. Describes two lessons that show how pupils can experience zero, positive, and negative correlation patterns between variables. Indicates the possible success of the Cognitive Acceleration through Science Education project.…

Tests seven- , 10- , and 13-year-olds for developmental differences in processes and strategies involved in geometric matrix solution and the relationship between strategy differences and item complexity. (AS)

Focuses on two types of symmetry, rotation and reflection, their underlying structure as a mathematical group, and their presence in the designs of diverse cultures. Illustrates patterns created by applying these symmetry operations that offer students a visual image which forms the axiomatic basis of algebra. (KHR)

The LOGO subroutine turtle geometry and Euclidean geometry are compared with respect to their treatment of similarity and difference of plane figures. The problem and its proposed solution of introducing a FLIP operation are viewed briefly from the perspectives of mathematics, computer science, and education. (MDH)

Effects of graphic representations of algebraic functions on performance of tasks involving expression transformations were studied for 28 teachers debugging transformed expressions through syntactic manipulations (SYMs) or semantic interpretation (SEI). Those using SEI improved performance using graphs. Some positive effects of graphic feedback…

Presents a lesson that connects basic transformational concepts with transformations on a Cartesian-coordinate system, culminating with the application of matrix operations to perform geometric transformations. Includes reproducible student worksheets and assessment activities. (MKR)

This article describes a technology-based approach for dealing with a misconception that some students hold concerning the equivalency of geometric transformations. Students can begin to conceptualize transformations in terms of the relationship between preimage and image figures rather than focus on the motion of a figure. (Contains 7 figures.)