Proofs and "Puzzles"

It is well known that mathematics students have to be able to understand and prove theorems. From our experience we know that engineering students should also be able to do the same, since a good theoretical knowledge of mathematics is essential for solving practical problems and constructing models. Proving theorems gives students a much better understanding of the subject, and helps them to develop mathematical thinking. The proof of a theorem consists of a logical chain of steps. Students should understand the need and the legitimacy of every step. Moreover, they have to comprehend the reasoning behind the order of the chain’s steps. For our research students were provided with proofs whose steps were either written in a random order or had missing parts. Students were asked to solve the \"puzzle\" – find the correct logical chain or complete the proof. These \"puzzles\" were meant to discourage students from simply memorizing the proof of a theorem. By using our examples students were encouraged to think independently and came to improve their understanding of the subject