A PROGRAM THAT WOULD DEVISE OPTIMAL ROUTES FOR SCHOOL BUSES WAS DEVELOPED. ONE OF THE TWO MODELS DEVELOPED FOR THIS STUDY, CALLED THE HEURISTIC MODEL, WAS A HAND PROCEDURE BASED ON THE ASSUMPTION THAT, IN AN EFFICIENT SCHOOL BUS SYSTEM, STUDENT MILES SHOULD BE MINIMIZED RATHER THAN BUS MILES. THE OTHER MODEL WAS DESIGNED TO BE USED WITH HIGH SPEED…

This paper discusses Bayesian m-group regression where the groups are arranged in a two-way layout into m rows and n columns, there still being a regression of y on the x's within each group. The mathematical model is then provided as applied to the case where the rows correspond to high schools and the columns to colleges: the predictor variables…

Most decision problems are those in which a choice among multiple-objective alternatives must be made. The central difficulty of such decision problems lies in finding single decision criteria that combine the decisionmaker's objectives and interests in an acceptable way. In this paper, a general procedure for the construction of such single…

The author gives a three dimensional analog of Pascal's Triangle as an exercise in heuristic thinking and an introduction to the multinomial theorem. The analog involves finding the number of shortest routes to various rooms in a cubical apartment house. (MN)

This article describes a one-semester junior and senior level course in applied mathematical optimization for undergraduates which provides the opportunity to test models by doing numerical experiments and to learn to use computer subroutines for solving optimization problems. (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)

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

This paper discusses how mathematics can be interpreted as an integral part of technological planning and decision making, and how mathematics therefore operates as an integral part of technology. Three aspects of mathematics in action are presented. The paper provides for the theoretical task of grasping mathematics in action and identifying how…

This paper investigates the role of teacher interaction in the development of mathematical understanding of five students who worked together on a math-modeling task. The dialogue between the teacher/researcher and students is analyzed. Preliminary findings suggest that where the mathematical thinking of the students was understood, interventions…

Special cases of the factor analysis model are developed for four selection situations. Methods are suggested whereby parameters in each case can be estimated using a maximum likelihood procedure recently developed by Joreskog. (Author)

Article gives three plans for learning stations on mathematics dealing with measurements. Exercises deal with weight, length, and comparative measurements. (GB)

This paper describes two statistics (chi square and Kendall's S) which may be used to test hypotheses about the association between two variables when observations are cross-classified in a contingency table. (CK)