Abstract
Creativity and critical thinking are the core values of science. Since mathematics is its primary language, the student of mathematics must imbibe and consolidate them. Critical thinking is consolidated in the critique of current mathematics and its foundations, creativity in the construction of a mathematical space or system. Therefore, the student of mathematics must go through the twists and turns of the critique-recti- fication of current mathematics and its foundations which in this paper focuses on the real and complex number systems that results in the construction of the contradiction-free new real number system and the complex vector plane. Since this is an expository paper on creative education much of the content is quoted from the Author’s previous works.
Highlights
We introduce and develop mathematics as primary language of science
Part of the requirements for effective mathematics education is that the subjects or courses are consistent and its axioms are adequate; otherwise, research grinds to a halt and learning is limited
This provides the right setting for complex vector analysis on the complex vector plane as extension of R*. We conclude this expository paper with recommendations on the distribution of the content of creative mathematics education into the various levels of the educational system from the primary years through graduate school. The transition to this new content of mathematics education will be quite extended as Discrete Calculus and Computation and the Complex Vector Plane are being developed and appropriate textbooks being written
Summary
Received November 1st, 2011; revised December 7th, 2011; accepted December 19th, 2011. Critical thinking is consolidated in the critique of current mathematics and its foundations, creativity in the construction of a mathematical space or system. The student of mathematics must go through the twists and turns of the critique-rectification of current mathematics and its foundations which in this paper focuses on the real and complex number systems that results in the construction of the contradiction-free new real number system and the complex vector plane. Since this is an expository paper on creative education much of the content is quoted from the Author’s previous works
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