Abstract
What is mathematics? For many secondary school pupils, it is solving equations, evaluating determinants, using synthetic division, or finding a derivative. All too frequently what the student does is more closely related to bookkeeping than to real mathematics. Perhaps this is why we have so many prospective mathematic majors at the university level who breeze through calculus but who never seem able to cope with “abstract mathematics.” Their manipulative skills are adequate, but their ability to think has never been developed.
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