In teaching primary teacher trainees, an awareness of the characteristic features, especially commutativity and associativity of basic operations play an important role. Owing to a deeply set automatism rooted in their primary and secondary education, teacher trainees think that such characteristics of addition are so trivial that they do not need…

In this workshop, we will continue to reflect on a models and modeling perspective to understand how students and teachers learn and reason about real life situations encountered in a mathematics and science classroom. We will discuss the idea of a model as a conceptual system that is expressed by using external representational media, and that is…

The presentation of physics content knowledge in conjunction with the lack of examples in solving problems leads high school students to struggle with mathematical problem solving in physics courses. This paper explains the importance and necessity of having mathematical courses for all high school students. (YDS)

A brief history of the development of our present day Gregorian calendar is given. Methods are then given, based on congruences, to determine such things as the week-day for any given date and the date for Easter in any year. (LS)

An investigative activity dealing with where to pitch a tent at a campsite is described. (MNS)

Presented are solutions to variations of a combinatorics problem from a recent International Mathematics Olympiad. In particular, the matrix algebra solution illustrates an interaction among the undergraduate areas of geometry, combinatorics, linear algebra, and group theory. (JJK)

Revisits and discusses the polar bear problem that was published in the March 1997 issue. The problem concerns a riddle: If you walk one mile south, one mile east, and one mile north, and end up in the same spot as you started, what kind of bear would you see? (ASK)

Teachers should not assume a problem is difficult for the students just because it appears difficult. A teacher solves one such difficult mathematical problem, an egg dilemma problem.

The majority of research on mathematics practice in everyday situations within cultures has investigated the use of arithmetic and geometry concepts and processes. To extend this research to a situation using measurement ideas, this paper investigates the mathematics practice of a group of carpet layers in an effort to detail how ordinary people…

The approximate nature of measurement is stressed, with examples given of elementary school mathematics problems which confuse reality with its mathematical model. Examples relating measurement to mathematical structure are given. (DT)

Part I reviews the mathematical definition of function, and then presents some practical uses of functions in such areas as substitution in a formula, equation solving, and curve fitting. Part II gives examples of functions that can be used to describe some real life situations. (RP)

A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

Presents a mathematics problem involving speed of a walking student versus speed of light reflection in a high school hallway. (MKR)

Poses a practical woodwork problem in which maximizing the perimeter of a square-based pyramid is required. The pyramid is constructed from four identical trapezia to be cut from a given rectangle of wood. A simple mathematical analysis suggests a number of different strategies for the solution of the problem. (Author/NB)