Chaque vérité que je trouvois étant une règle qui me servoit après à en trouver d’autres (Each truth that I discovered became a rule which then served to discover other truths). (René Descartes, “Discours de la Méthode“)
The statement from Descartes, a famous philosopher and mathematician, provides one of the ways whereby we can help this generation appreciate math by discovery rather than rote memorization. Proving theorems really develops one's thinking faculties. Teachers and parents need to stress that math is not a spectator sport. Students need to do more than just homework if they want to improve. They need to understand that math is part of everyday life and found across the curriculum. When students try to memorize math for an exam, they might get a good grade but they will soon forget everything within a few days. By proving theorems, they will remember forever, because they will be able to derive it even when they forget. Proving theorem is a way of appreciating may. It helps you to reach the "Aha Moment".
One student described a situation where she belonged to a school education system where they were made to do lots of different problems, but they were never told to try and understand the underlying theory behind them. This really made her scared of math to the point of having math anxiety. She continued to say that, what she basically had was a cookbook of a variety of wonderful recipes without realizing why she needed to add salt or sugar to a dish. This is the problem we have in some of our schools. Many students are learning all these different techniques to solve problems without really understanding the theoretical meanings behind them. So once, they get a problem that cannot be solved using the techniques they are familiar with, they get stuck and begin to fret. If they had arrived at the "Aha Moment," they would have found another approach to dealing with the problem.
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