Students learn to use linear algebra covered in their first algebra course to design mobiles like those created by artist Alexander Calder. (Contains 17 figures and 2 tables.)

In the context of a three-year professional development program in mathematics, practicing elementary teachers persistently engaged in collaborative inquiry and reflection to build connected meanings for slope. One teacher invented a compelling representation for slope as a process of repeated addition, using Cuisenaire rods, based on teachers'…

We report a dissociation between higher order mathematical ability and language in the case of a man (SO) with severe aphasia. Despite severely impaired abilities in the language domain and difficulties with processing both phonological and orthographic number words, he was able to judge the equivalence of and to transform and simplify…

This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.

The article deals with issues concerning the abductive-inductive reasoning of 42 preservice elementary majors on patterns that consist of figural and numerical cues. We discuss: ways in which the participants develop generalizations about classes of abstract objects; abductive processes they exhibit which support their induction leading to a…

This article presents a project for a differential equations class using an inverse problem based on the second order differential equation that models an electrical circuit. (Contains 2 footnotes.)

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with A's chosen x- or y-axis. It becomes necessary in such cases to develop…

This article describes concepts exhibited by seventh-grade prealgebra students as they approached algebraic-thinking tasks. (Contains 7 Figures.)

Two related sequences of definite integrals are considered. By mixing hand-work, computer algebra system assistance and websurfing, fine connections can be studied between integrals and a couple of interesting sequences of integers. (Contains 4 tables.)

In early years' (primary grade) classrooms in Australia repeated patterns are commonly explored as an early introductory activity to mathematics. Most young students have an extensive knowledge of and exhibit success in copying, continuing, creating and transferring patterns into other media. By contrast, research indicates one of the most…

In this paper methods and algorithms for identifying the main elements (edges and facets of any dimension) of a cone and a polytope, and calculating the corresponding hypervolumes are presented. The cones and polytopes are supposed to be given as the non-negative linear combination and the convex hull generated by a, not necessarily minimal, set…

This reprint from the June 1912 issue of "Mathematics Teacher" gives readers a sense of the timelessness of some of the issues relating to teaching for computational fluency.

TESTS ON ALGEBRA WERE PREPARED TO ASSIST TEACHERS PARTICIPATING IN THIS PROJECT. TWENTY-TWO UNIT OR CHAPTER TESTS, 6 CUMULATIVE REVIEWS, AND 1 FINAL EXAMINATION ARE PRESENTED. OTHER REPORTS ON THIS PROJECT WERE ASSIGNED ACCESSION NUMBERS ED 003 197, ED 003 237, AND ED 003 198. (JM)

See JC 690 392 above.