This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

The students of a Mathematical Modeling and Problem Solving class investigate and explore the mathematics involved in fitting a box spring mattress up a stairwell by solving various optimization problems and by using The Geometer's Sketchpad. The results show that a very small fraction of the class was actually able to solve the problem without…

Three constructions using thread are given for the hyperbolic paraboloid in addition to a method for constructing an approximation for the third-order saddle surface. (MN)

This is the fourth and concluding article in a series on using mathematical techniques from history to provide an interesting way for middle graders to practice math. (Editor)

Included are brief articles on multiplication of negative integers and testing knowledge by asking true-false questions that involve a relatively high level of abstraction. A number of specific examples are included. (MNS)

A model for directed numbers, using a sentry moving along the number line, is described. (MNS)

A model is offered which can be used for teaching addition, subtraction, multiplication, and division with directed numbers. Illustrations for all operations are given. (MNS)

Twenty-nine reports yielding 112 studies were analyzed with Glass's meta-analysis technique, and results were compared with predictions from Ausubel's model of assimilative learning. Overall, advance organizers were shown to be associated with increased learning and retention of material to be learned. (Author)

A mathematical model of a soccer-league competition results is set up and investigated using simple randomization techniques. The hypothesis that winning the league championship was purely luck was statistically tested. (JP)

Before judging a student's diagram correct or incorrect, the mental associations made by the student between his diagram and the problem should be known. This is a follow-up to the author's article in the November 1970, Arithmetic Teacher." (RS)