"Wonder, Discovery and Intuition in Elementary Mathematics"

A major problem today concerns educating the next generation of engineers, mathematicians and researchers.The value of our concentration on drilling and testing appears questionable.Some students perform well on tests but do not understand why the various algorithms work.Others do poorly, become overwhelmed and give up with feelings of hopelessness.Conceivably, computational ability may not reflect mathematical insight or be a reliable measure of creativity.With readily available calculators, the next generation may not be well served if young people are trained and judged on the speed and accuracy of their computations.Perhaps we should be nurturing analytical judgment and the ability to recognize errors.Unfortunately, current public discussion involves repeated testing and not the genuine joy of discovery.Areas of mathematics contain wonderful concepts and ideas, which can pique the natural curiosity of young students and enchant them into furthering their mathematical studies.The inner structure of mathematical objects, properly introduced, should suffice to captivate young minds.My proposition is that with appropriate additional explanation, many youngsters could comprehend and take delight in visual presentations of mathematical concepts.Why not start the analytical education of our children early in elementary school?Accordingly, I have been designing sets of slide shows with the aim of providing a visual framework, which will illuminate the essence of some mathematical concepts.Each of the slide shows introduces a surprising mathematical fact.In the spirit of mathematical strategy, the progression of slides builds on established facts to explore the unknown.It is hoped that students who view the slides might develop the insight, intuition and confidence needed to successfully explore other analytical situations.