Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)

Shares detailed episodes of children's work in repeatedly partitioning geometric shapes to highlight the process of recursion, which can lead to a deeper understanding of imagination and beauty in children's mathematics. (MKR)

An approach to teaching geometry is promoted that allows students to decide for themselves what they could prove from given information. Such an approach allows pupil involvement in the personal process of discovering mathematical ideas and formulating problems. It is noted these methods will not work for all. (MP)

Discusses how students construct mental images that aid estimation skills in the measurement of angles. Reports research identifying four strategies that students use to estimate sizes of angles. Strategies include utilization of the mental images of (1) a protractor; (2) a right angle; (3) a half-turn; and (4) angles of a polygon. (MDH)

Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…

Presents an activity in which students develop their own theorem involving the relationship between the triangles determined by the squares constructed on the sides of any triangle. Provides a set of four reproducible worksheets, directions on their use, worksheet answers, and suggestions for follow-up activities. (MDH)

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…

This book is the result of the collaborative effort of nine AYA National Board Certified Teachers in Mathematics. It represents a compilation of teacher-tested activities that prompt high school students to explore, conjecture and reflect on their mathematical adventures-- thus "experience mathematics." This edition will educate the teacher…

Presents the hierarchical structure of quadrilaterals as an illustration of learning a geometric concept by moving from the levels of visualization and analysis to the level of formal deduction. The development discusses the classification of quadrilaterals, the inheritance of properties within the hierarchy, connections between algebra and…

Described is how using LOGO tools for manipulating embodiments of geometric objects helps students construct more abstract and coherent concepts. Discussions are included on developing verbal definitions versus constructing concepts, tasks for integrating turns and angles, group discussions, and maze tasks. (KR)

Described and evaluated are microcomputers as a tool for construction in geometry education and heuristic theorem finding through interactive continuous variation of geometric configurations. Numerous examples of theorem finding processes are provided using the prototype graphics system CABRI-Geometer. (MDH)

Discusses a variation on tiling that offers opportunities for the construction of the fundamental mathematical concept of constructing abstract units called "unitizing." Tiling integrates geometric and numerical settings to develop spatial sense and present mathematics as constructing patterns. (MDH)