Background/purpose: In modern mathematical education, it is important to develop students' ability to understand the fundamental properties of geometric objects deeply. This makes it relevant to study the additivity of the area of triangles as a property inherent in various kinds of quantities and ways of representing it methodologically in the…

In this paper, we aim to contribute to the discussion of the role of the human body and of the concrete artefacts and signs created by humankind in the constitution of meanings for mathematical practices. We argue that cognition is both embodied and situated in the activities through which it occurs and that mathematics learning involves the…

Our work is inspired by the book "Imagining Numbers (particularly the square root of minus fifteen)," by Harvard University mathematics professor Barry Mazur ("Imagining numbers (particularly the square root of minus fifteen)," Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of…

The purpose of this note is to outline further enrichment exercises with rhotrices and thus to stimulate ideas on mathematical arrays and structures. Rhotrices provide students with examples on how to imagine new forms of arrays and their classifications as abstract structures.

A lawn-mowing problem is discussed in terms of clarifying the problem; making initial conjectures; experimenting; developing a solution; and supporting formulas, theorems, and corollaries. (MNS)

The formula used by the telephone company to determine long distance charges is presented and several sample problems are included. (MP)

Shows that the ratio of the area of the quadrilateral formed by joining the kth points to the area of the original quadrilateral is constant whether it is convex or concave quadrilateral. Presents many geoboard or dot paper diagrams and geometrical expresssions. (YP)

Discusses the calculation of pi by means of experimental methods. Polygon circle ratios, Archimedes' method, Buffon's needles, a Monte Carlo method, and prime number approaches are used. Presents three BASIC programs for the calculations. (YP)

The harmonic mean, neglected in favor of arithmetic and geometric means in modern mathematics, is defined and its historical relationship to music as presented by Pythagoras is described. Two geometric constructions present a picture of harmony, and an application in calculating the square root of a number is given. (MDH)

Unified Technical Concepts (UTC) is a modular system for teaching applied physics in two-year postsecondary technician programs. This UTC classroom textbook, consisting of 10 chapters, deals with mathematical concepts as they apply to the study of physics. Addressed in the individual chapters of the text are the following topics: angles and…

Presents activities to teach the formula for the area of a rectangle that require students to determine the cost of refurbishing their school's tennis courts. Students collect their own data, organize information, and make decisions individually and as a group to solve the problem. Worksheets are provided. (MDH)

The second of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Overall course goals are specified, a course outline…