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The mathematical experience Gian-Carlo Rota, Philip J. Davis, Reuben Hersh
Publisher: Houghton Mifflin Company

They are not for everyone, but if teachers and parents are sensible and sensitive, they can, for many kids, enhance the mathematical experience. By guiding students and asking them questions the teacher can lead students to a successful and powerful mathematics experience. Math is bogus, and used by science to make . The exemplary case of thinking occurs within the sciences. The science of physics consists of theories, concepts, mathematical formulae, technical apparatuses, and experiences. Hofstadter is not inimical to mathematics as the lingua franca of science, which we think is detrimental to human thought, and a contrivance that is unreal, a concoction that gives scientists a mantle of authority that it doesn't really deserve. But it never hurts to make some points explicit. The teacher's role is NOT to do the work for the students or just tell them the answers. The preceding dialogues are both from works of fiction. That being said, they may in fact truly represent how the majority of mathematicians experience their work. I've mentioned this before, but I have taught every level of mathematics course from algebra 1 (to students ranging in age from 9th to 12th grade) right up through multivariable calculus.