The Maine Learning Results (MLR) expects the state's students in prekindergarten through grade 2 to describe two-dimensional shapes as well as use positional language. Requiring translations of two-dimensional shapes supports this expectation. Students in grades 3-4 are expected to "use transformations," while students in grade 5-8 are…

Providing for original and creative thinking by geometry students is discussed. Techniques for discovering theorems are suggested, and examples of places in geometry where these methods can be used are given. (DT)

This textbook provides the foundation for a course in mathematics covering arithmetic, algebra, geometry, conic sections, and arithmetic of infinites. An appendix on practical gauging is included, as well as a supplement containing the history of logarithms. [This edition was corrected and improved by Samuel Clark.]

Describes levels of thinking in geometry defined by Pierre van Hiele and Dina van Hiele-Geldof and discusses recent research on geometry learning levels among sixth and ninth graders. (GC)

A good mathematics instructor is a proficient organizer of pupils for instruction in mathematics. There are many specifics involved in organizing for instruction. This paper discusses organizational structures in mathematics instruction such as learning stations. "A Geometry Center" is provided as an example of a learning station. The organization…

Discusses a number of Theo van Doesburg's paintings concerning arithmetic composition. (KHR)

Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.

Two technology-oriented activities are used successfully with entry-level geometry students during their study of symmetry. Reflection symmetry gives students opportunities to deepen their understanding of fundamental mathematical concepts like slope and symmetry, in a flexible and self-paced way.

Circumscribable quadrilateral is the one that contains a circle tangent to each of its side and it is assumed to be convex. The way teachers could use their own mathematical curiosity to engender the same in students, thereby showing a simple but relentless habit of questioning could lead is illustrated.

A dynamic program for geometry called Cabri Geometry II is used to examine properties of figures like triangles and make connections with other mathematical ideas like ellipse. The technology tip includes directions for creating such a problem with technology and suggestions for exploring it.

Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. The vignette offered in this article provides insight into ways to solve open-ended problems using multiple technologies.

This article describes two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections.