Critics claim that the reform efforts put little emphasis on learning basic mathematics and algorithms and, instead, encouraged reliance on calculators, student-directed activities and discovery learning processes. ... Knowledge of math facts proves to be a more effective tool than a calculator. ...
Introduction Somewhere between Vygotsky and Piaget; somewhere between Newton determining the laws of the universe alone with his apple tree, and Andrew Wiles proving Fermat's last theorem with the aid of his colleagues around the world; somewhere between learning the 3Rs by rote under a strict schoolmaster beating down the slightest whisper, and the neo-pragmatist's "knowledge is conversation" ideal mathematics lesson of total discourse; somewhere between these opposite ends of their various spectra lies the true role of language and conversation in the mathematics class. ... Biggs ...
After graduating from GÖttingen, Dedekind felt that his knowledge of mathematics was still insufficient for advanced study, and so he spent the next two years attending lectures and filling in the gaps in his education. ... Newton, however, was reluctant to publish, so Leibniz became recognized as a co-discoverer because he published his discovery of differential calculus in 1684 and of integral calculus in 1686. ...
