Math should be students learning through discovery, problem solving, and logical reasoning at every level. Five of the most significant milestones in math to me are the discoveries of Neutral versus Euclidean geometry, integrals to find the area under a graph, different groups of numbers and their properties, Discrete Mathematics, and limits of sequences. One common thing among all of these discoveries is that the people who discovered them have a way to justify why their math is correct. Since I was able to learn these concepts through discovery based activities and logical reasoning I was able to understand where these concepts come from making them more important to me. Therefore, if every class was taught with discovery based activities, problem solving and logical reasoning, then students will be able to understand why things work in math allowing students to apply the mathematics they learn to real world problems. Then students will see the significance of the lesson instead of thinking it is just a horrible subject that is not understood by anyone.