A discussion of the classic probability hat check problem. The paper shows how the hat check problem can be viewed as a problem about enumerating certain members of the symmetric group of permutations on n symbols, with an ensuing generalization. (PK)

An elementary school mathematics program can be structured to allow students to practice computational skills and also become familiar with concepts that need to be mastered in algebra. The activities described begin with students' life experiences, continue through concrete and pictorial experiences, and conclude with abstract activities and…

An activity is described as an example of an application that draws on the behavior of current in electrical circuits to create a symbolic algebra. Five worksheets are included, with discussion of their use. (MNS)

The problem of controlling the grizzly bear population at Yellowstone is described. The results are presented in graphical form and discussed. A computer program is included. (MNS)

The various roles and uses of mathematics in developing global awareness in students are considered. Mathematics as a unifier of human experience and problem solving with a global emphasis are discussed with many illustrative examples. (MNS)

In its empirical part this paper establishes a general weak understanding of the process of applying a mathematical model. This is also evident in the way teachers regard the application of alternative sharing in their own problem solving and in relating to children's answers. The theoretical part analyses problems that are considered as…

This book is designed to help adults gain the range of math skills they need to succeed in life and work and on standardized tests, including the GED. It is expected to help students overcome math anxiety, discover math as interesting and purposeful, and develop good number sense. Lessons are organized around four strands: (1) skill lessons that…

This paper briefly reviews research grounded in cultural and socio-constructivist theories carried out to investigate the phenomenon of suspension of sense-making when doing school arithmetic word problems. It begins with ascertaining studies documenting and marking out the phenomenon, then provides an explanation of the observed effects that are…

This research report presents a study of the work of agronomy majors in which an extension of linear models to non-linear contexts can be observed. By linear models we mean the model y=a.x+b, some particular representations of direct proportionality and the diagram for the rule of three. Its presence and persistence in different types of problems…

This paper describes a models and modeling framework that has been applied to various areas in teaching, learning and problem solving. It examines the implications of that framework on metacognition and higher order thinking during everyday problem-solving situations that required teams of students to produce complex solutions in approximately 1-2…

How a computer randomly generates numbers to turn off lighted blocks on a graphics display is discussed. A computer program is given after reviewing a definition and two theorems and applying them to the problem. (MNS)

An approach to teaching problem solving to preservice and in-service middle school teachers is described. They examined an unsolved question as a class research project. The process of developing the solution is detailed, and difficulties contained within the process are noted. (MP)

Seven applications problems are presented for gifted students to solve by writing microcomputer programs. (MNS)

The game of Yahtzee is analyzed to some extent through methods of elementary probability. Several different problems are posed, and these serve to illustrate both mathematical concerns and game play strategy. Solutions are provided to all questions at the conclusion and suggestions for further questions are presented. (MP)