Reasoning and Proof in Mathematics
Have you ever think why the Phytagorean theorem is a2 + b2 = c2, and how the theorem can be found?. Usually, teachers during the time of graduation high school only give formula to students, and they need to use it to solve the problem without understanding the formula itself. Consequently, students though it not important to applied because they did not know what the formula use for. In this case, is very important to mathematics teachers to make the students understand and know the formula use for by add reasoning and proof when teaching mathematics.
Reasoning is part of the beauty of mathematics where when something happens, it should be good reason exist. In teaching process, teachers need to give instructions for train students to give logical reasoning that logic and relevant to a mathematics problem. Often, students give reasons to mathematics question like “Why this theory is true” by answer “Because my teacher said that it is true”. Teachers should play the role the students to give synthesis reasoning to every mathematics problem that they solved.
Proof is the things that do after students have the reason of their mathematics problem that wants to solved. Different with reasoning, proof only requires students to can conclude the reason that be got from reasoning mathematics problem. Sometimes students have a difficult when proof mathematics problem, even though they have a lot of reason to solve it. In this case teacher play role in direct the students to can conclude the reasons that they get. This is very important because sometimes people only see the proof rather than reasoning.
To sum up, reasoning and proof are very important in mathematics, especially for students. Both reasoning and proof will make learning process of mathematics more meaningful because students will more involve to it. Besides that, reasoning and proof will train the students to be logic and systematic in solving the mathematics problem. Learn mathematics is not only know the formulas but also understand them by doing reasoning and proof from the formulas.