Background
Villiers, Michael David De was born on August 6, 1956 in King Williamstown, South Africa. Son of Pieter Jan Albertus and Elleleen (Van Schalkwyk) De Villiers.
(The main focus of this book is on actively engaging stude...)
The main focus of this book is on actively engaging students in the mathematical processes of modeling and axiomatization. The book starts off with some challenging problems involving switching circuits. Students are then engaged in gradually developing a mathematical model in order to solve these problems. Suitable notation is firstly introduced for series and parallel switches, and then followed by truth tables, and the discovery of several interesting mathematical properties related to switching circuits. After development of the model and solution of the original problems, a section on systematization follows where students are led through some proof activities to identify a suitable set of axioms. The book concludes with a short historical overview of the development and application of Boolean Algebra.
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(How do you know if an election is fair? Or if the result ...)
How do you know if an election is fair? Or if the result truly represents the choice of the people? In Making Democracy Fair students use elementary mathematical methods to explore different kinds of ballots, election decision procedures, and apportionment methods. In the first half of the book, students are introduced to a variety of alternatives to the "winner take all" strategy used in most elections. Determining which strategy is fairest is usually a very difficult question to answer, and many times the strategy chosen determines the winner. In the second part of the book, students investigate different methods of apportionment. How many representatives from each state will there be in the United States House of Representatives? How do countries using a proportional representation decide on the number of representatives from each political party to be seated in their government bodies?
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(This book seeks to actively involve the reader in the heu...)
This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.
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mathematics educator researcher
Villiers, Michael David De was born on August 6, 1956 in King Williamstown, South Africa. Son of Pieter Jan Albertus and Elleleen (Van Schalkwyk) De Villiers.
Bachelor of Science, University Stellenbosch, 1977. Bachelor of Education, University Orange Free State, 1982. Master of Education, University STellenbosch, 1984.
DEd, University STellenbosch, 1990.
Mathematics and science teacher, Education Department, Karasburg, Namibia., South Africa, 1980; mathematics and science teacher, Cape Education Department, Kimberley, Cape., South Africa, 1981-1983; mathematics education researcher, U. Stellenbosch, Cape., 1983-1990; lecturer, U. The University of Durban-Westville, South Africa, 1991; senior lecturer, U. The University of Durban-Westville, South Africa, 1992-1993; assistant professor, U. The University of Durban-Westville, South Africa, since 1994.
(How do you know if an election is fair? Or if the result ...)
(This book seeks to actively involve the reader in the heu...)
(The main focus of this book is on actively engaging stude...)
(Book by Leslie Johnson Nielsen, Michael de Villiers)
(1st)
Elder Dutch Reform Church, Kuilsriver, 1988-1990. Member Association for Mathematics (journal editor since 1987), Education of South Africa (convenor of journal committee since 1994), American Mathematics Society, Consortium for Applications of Mathematics.
Married Pearl Sophia Smith, March 28, 1981. Children: Michelle, Rikus.