Introduces a special triangle for which many different problems can be posed on the basis of one unusual property. Presents three problems and considers different approaches for the first problem. Explores other mathematical problems using the "What if not?" strategy that can be used as classroom activities. (KHR)

Using differentiated instruction in the classroom can be a challenge, especially when teaching mathematics. This book cuts through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Specific strategies and examples for grades Kindergarten - 8 are organized…

Geometry is required for many secondary school students, and is often learned, taught, and assessed more in a heuristic image-based manner, than as a formal axiomatic deductive system. Students are required to prove general theorems, but diagrams are usually used. It follows that understanding how students engage in perceiving and reasoning about…

This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated…

In the study Cabri was used for teaching geometry at 4th grade. To investigate students' geometry level, a semi-experimental method was used. In the test group, geometry subjects are taught using Cabri. A multiple choice test was used to collect data as pre and post test. Answers were assigned as 1 to correct, 0 to wrong answers. Data were…

The purpose of this paper is to present a summary of selected facets of geometry and measurement in elementary school programs and to describe curricula content options designed to demonstrate the feasibility of seeking high level outcomes and meanings for students with learning disabilities. While there are a multitude of published papers…

The objective of this study was to investigate and characterize the geometric thinking and understanding of four pre-service middle and secondary mathematics teachers while considering their spatial ability levels. To investigate the differences, if any, that existed among these pre-service middle and secondary teachers with different spatial…

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

An alternate geometric interpretation of the correlation coefficient to that given in most statistics texts for psychology and education is presented. This interpretation is considered to be more consistent with the statistical model for the data, and richer in geometric meaning. (Author)

Describes the development of numbers, discussing natural and rational numbers; geometry (inscribing numbers on the number line); smoothness of motion reflected in the geometrical line; square roots; and irrational numbers. Concludes that whatever the ultimate identity of irrational numbers, what is known about them is less important than what is…

A general cubic equation ax[cubed] + bx[squared] + cx + d = 0 where a , b , c , d [is a member of R], a [not equal to] 0 has three roots with two possibilities--either all three roots are real or one root is real and the remaining two roots are imaginary. Dealing with the second possibility this paper attempts to give the geometrical locations of…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

This is part two of a three-part School Mathematics Study Group (SMSG) textbook. This part includes the index and chapters 6 through 10: (6) Curve Sketching and Locus Problems, (7) Conic Sections, (8) The Line and the Plane in 3-Space, (9) Quadric Surfaces, and (10) Geometric Transformations. (MK)

This is unit twelve of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include rigid motions and coordinates, squares and rectangles, and square roots and real numbers.…

Outlined are the minimum requirements for a quinmester course of introduction to high school geometry. After a description of the course content and overall goals, further details are presented in nine sections. Each section gives performance objectives, textbook references, content (including lists of vocabulary and associated properties), and…