BOOLEAN ALGEBRA AT SCHOOL
by Michael de Villiers
" ... a successful effort to give mathematics students the opportunity to create a mathematical system motivated by the need to solve some practical problems."
- review by Dorothy Goldberg in The Mathematics Teacher, Sept 1987.
Boolean Algebra at School aims at introducing students to the mathematical processes of modelling and axiomatization and is based on high school teaching by the author in the period 1978 -1985. It is still used by the author for in-service training of teachers, as well as other post-graduate courses. The book was also successfully used by several schools as part of the Advanced Mathematics Syllabus of the KZN Education Department in the period 1985-1995.
The first section starts of with small groups of learners being given seven "motivational" problems involving switching circuits in various contexts. Although students are normally able to easily solve the first three problems, they usually get stuck with the others. Students are then led through a gradual modelling process of the mathematics of switching circuits and encouraged to experiment and discover for themselves some of the underlying principles. Towards the latter part of the first section, opportunities for using truth tables to check their conjectures are also created.
In the second section, students are now challenged to investigate the logical relationships between the results they had up till then only verified by means of truth tables. Through carefully designed activities students are led to the identification of some statements from which all the others can be derived, i.e. the axioms. In contrast to the traditional approach where students are merely presented with pre-selected, "ready-made" axioms, students in this approach are therefore expected to identify suitable axioms for themselves. To assist students in this axiomatic analysis, novel use is made of axiomatic maps to assist students in keeping track of the underlying logical relationships and to avoid circular arguments.
Student Guide Boolean Algebra at School, Vol 1 Republished 2010, Grades 9 to College, 147 pp, soft cover @ USD 3.00 to download - printed copy also available @ USD 15.00.
Teacher Guide Boolean Algebra at School, Vol 2 Republished 2010, 121 pp, soft cover @ USD 2.20 to download - printed copy also available @ USD 11.00.