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Sample Grade the Proof Type Question

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I learnt about "Grade The Proof Type Problem" in an article American Mathematical Monthly in late seventies where it was discussed as a means to train the  students to write correct proofs of mathematical theorems.


The process of creation

This assignment was created by from the answer sheets submitted by the in response to an earlier tutorial problem. A close scrutiny of the answer sheets revealed that while almost all students had no difficulty with basics method, but in actual application to a simple problem, they made mistakes (or wrote equations which were valid for small angles only)  without realizing the nature of mistake/ approximation(s) provo

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