With due respect to all the distinguished members who are either renowned mathematicians or professors active in teaching and promoting quality mathematics education, do not come to the conclusion that my above analogy of the story of the "6 Blind Men and the Elephant" that the blind men are these members who posted their various viewpoints!
One very "heated" but very interesting discussion that brought out many aspects of Mathematics as a subject, and of the relevance of mathematics to society and to its practicality in life, and how and why we should or should not teach mathematics is at the post titled :
"Seen This?" (<= click to view)
A very excellent book "The Number Sense: How the Mind Creates Mathematics" by author Stanislas Dehaene (1999, updated 2011), will make you really think about what mathematics really is and to realize how unique we human beings might be in the natural world because we created (and continue to evolve) language and mathematics in a special way that has no parallel in history in the evolution of any other living thing ! Do correct me if I am wrong.
Dr Dehaene's work continues and he is the Director at
INSERM-CEA Cognitive Neuroimaging Unit;
where research continues on high-level human cognitive functions using experimental psychology, neuropsychology and neuroimaging approaches (functional magnetic resonance imaging, fMRI; magneto- and electro-encephalography, MEG & EEG). We can find research publications, and many leading edge discoveries shared at the site.
I needed to add on this :
The difference between teaching and instruction at the blog, Devlin's Angle which is maintained by mathematician Keith Devlin , who is the Executive Director of the Human-Sciences and Technologies Advanced Research Institute (H-STAR) at Stanford University, and is The Math Guy on NPR's Weekend Edition.
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