Throughout my life as a student the word math has meant a lot of different things. As an elementary student it meant doing a lot of memorizing numbers and procedural work, such as adding and subtracting. As a middle school student math meant a lot of homework (which involved procedural skills) and lecturing in class, In high school math was the class that almost every student hated because no one could understand the procedures being taught and couldn't understand the context of a new real world problem that would be assigned as homework. Class would consist of the teacher going over 5-10 of the homework problems we did not understand out of the 30 assigned, then continue to lecture the whole hour about the next lesson, giving a brief reasoning of why we can use some shortcut (procedure) to solve the math problems. It was not until I entered college that I actually learned what math is not a procedure or mainly memorization or about a teacher lecturing and showing examples. I learned that math is about discovery, problem solving, and logic reasoning.

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.

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.