This question is one that can be easy to answer, or hard, depending on your view of the subject. To me, math is everything, and everything is math. We use math in all areas of our life (spoken like a true math major). We use math to cook, to create everyday products, to drive, to buy groceries, and even when we set our alarm to sleep at night! At first glance, many of us believe that math is purely numbers, counting, equations and operations. But if we take a closer look, we see that math IS all of those things, but it is also what helps us reason and use logic in our everyday lives.

One of my favorite things about math is that it teaches us to ask WHY something is the way it is, not just accept that it is true. I think one of our biggest problems as a society is that the majority of people accept things to be true without further exploration. As a future teacher it is my goal to encourage my students to dig deeper into what they are learning, and ask questions! Not only in math, but in all subjects they encounter. This will develop their reasoning and logic skills and help them become independent thinkers.

There have been many great mathematics discoveries, but these are the five that I feel are most significant to my future as an educator:

1. The discovery of numbers and counting. Numbers themselves are the backbone of everything we do. Without numbers, we would not have math. This discovery has led to our ability to sort, calculate, and draw conclusions among other aspects of life.

2. Shapes and their attributes. I feel this particular aspect of geometry is very important. The discovery of the different shapes and all of their characteristics is crucial to our understanding of their relationships to other shapes and how they fit into the world. We use shapes for many things, like road and traffic signs, building, and cooking.

3. The four basic operations. I feel that this discovery is pretty self-explanatory. The four basic operations: addition, subtraction, division and multiplication, are just one of the ways we integrate numbers and use them in our daily lives. Without these operations, math would be quite different from what most people know it to be.

4. Proof Writing. This is the aspect of mathematics that pushes us to find truth in things we already accept to be true, and things that we want to decide if they are true or not. It encourages us to ask the why and the how, rather than just knowing the answer.

5. Calculus. I feel that calculus is a beautiful aspect of mathematics. Newton and Leibniz developed a subject that can be applied to many different situations and is not arbitrary.

I chose these five mathematics discoveries because each one relates to how I want my students to view mathematics, no matter which grade I teach. If I teach first grade, I want my students to recognize the math that is in our classroom, such as the shape of the clock, the progression of days on the calendar, the way the table is built. If I teach high school mathematics, I want my students to be able to connect all of the different aspects of math together, and realize that it has a purpose.

One of my favorite things about math is that it teaches us to ask WHY something is the way it is, not just accept that it is true. I think one of our biggest problems as a society is that the majority of people accept things to be true without further exploration. As a future teacher it is my goal to encourage my students to dig deeper into what they are learning, and ask questions! Not only in math, but in all subjects they encounter. This will develop their reasoning and logic skills and help them become independent thinkers.

There have been many great mathematics discoveries, but these are the five that I feel are most significant to my future as an educator:

1. The discovery of numbers and counting. Numbers themselves are the backbone of everything we do. Without numbers, we would not have math. This discovery has led to our ability to sort, calculate, and draw conclusions among other aspects of life.

2. Shapes and their attributes. I feel this particular aspect of geometry is very important. The discovery of the different shapes and all of their characteristics is crucial to our understanding of their relationships to other shapes and how they fit into the world. We use shapes for many things, like road and traffic signs, building, and cooking.

3. The four basic operations. I feel that this discovery is pretty self-explanatory. The four basic operations: addition, subtraction, division and multiplication, are just one of the ways we integrate numbers and use them in our daily lives. Without these operations, math would be quite different from what most people know it to be.

4. Proof Writing. This is the aspect of mathematics that pushes us to find truth in things we already accept to be true, and things that we want to decide if they are true or not. It encourages us to ask the why and the how, rather than just knowing the answer.

5. Calculus. I feel that calculus is a beautiful aspect of mathematics. Newton and Leibniz developed a subject that can be applied to many different situations and is not arbitrary.

I chose these five mathematics discoveries because each one relates to how I want my students to view mathematics, no matter which grade I teach. If I teach first grade, I want my students to recognize the math that is in our classroom, such as the shape of the clock, the progression of days on the calendar, the way the table is built. If I teach high school mathematics, I want my students to be able to connect all of the different aspects of math together, and realize that it has a purpose.