This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

Visualization of mathematical relationships enables students to formulate conjectures as well as to search for mathematical arguments to support these conjectures. In this project students are asked to discover the sufficient and necessary condition so that two circles form the circumscribed and inscribed circle of a triangle and investigate how…

"It's All Connected" provides teachers of mathematics the support they need to improve their instruction. This in-demand collection of lessons for grades 6-8 explores proportionality, proportional relationships, and proportional reasoning, acknowledging that the ability to reason proportionally is crucial in the middle school mathematics…

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

This textbook is a course in Euclidian geometry conic sections. It was translated by the original Latin, and was revised, corrected and enlarged.

This textbook commences with a brief sketch of the history of Elementary Geometry. The definitions throughout have been somewhat amplified, and several notes have been added which it is hoped may be found useful and suggestive. The subject of Ratio has been expanded; a few new propositions have been added; and there is a considerable collection of…

This textbook covers the first six books of the elements of Euclid, the 11th and 12th books, and the book of Euclid's data. Elements of plane and spherical trigonometry are included.

This textbook covers geometry and trigonometry and presents problems for student consideration. Geometry principles are applied to surface and solid measurement. Tables of logarithms and logarithmic sines are included. [This book was translated from the French of A. M. Legendre. It was revised and abridged by Charles Davies.]

This textbook presents readings in geometry and the theory of infinitesimals.

This textbook covers geometry and trigonometry and presents problems for student consideration. Contents include geometry, plane trigonometry, analytical trigonometry, spherical trigonometry, and mensuration. [This book was adapted by Charles Davies.]

Since all manner of quantities require to be compared together, in mathematical computations, and their various relations searched out and determined and as most of our knowledge in mathematical subjects depends on the proportions of several things to one another: so it is requisite that the nature of proportion, and the methods of reasoning…

his is the second volume of a series of textbooks on junior high-school mathematics. Like the first volume, it is organized on the principles that were stated in the preface of Book One. Geometry is the basis of the first part of this course. By actual measurement formulas are developed for finding the areas of triangles, quadrilaterals, and the…