What IS mathematics anyway?

When you think of mathematics what do you think of?

When I think of the question "what is mathematics?" I immediately think of concepts such as formulas, problem solving techniques, geometry, numbers and simple equations such as addition and subtraction. I've never truly thought deeply about what math is or how one could define it. After conducting some research I feel I have reached a better understanding about what math is.  

The first idea that became obvious during my research is that there are many different definitions of mathematics. Math is defined in many different ways for many different people. An article called "What is Math?" by Wendy Petti claimed that Bertrand Russell defines math as "the subject in which we never know what we are talking about, nor whether what we are saying is true." I believe that this definition alludes to how little we know about what exactly mathematics is or how to define it. 

It is important for teachers to define what mathematics means to them, so they can decide how to provide their students with the best education in the subject. Like all subjects, a teachers over all plan for a school year will be much more effective, deliberate, and purposeful if the teacher has a clear objective for his/her students, than if a teacher is basing what they teach toward on various opinions and definitions on what math is. 

What are some of the definitions of math?

The online dictionary (dictionary.com) defines mathematics as:

"The systematic treatment of magnitude, relationships between figures and forms, and relations between   quantities expressed symbolically."

This definition is what many people think of when they think of math and covers very important aspects of what Math is, but it is through definitions such as the definition given by  Elaine J. Hom in his online article titled "What is Mathematics?" that we realize that math can be defined as much more than this. Elaine Hom defines Math as:

 "...all around us, in everything we do.'Math' is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports." 

This definition points out that math is more than just math equations on a worksheet, but math is a gigantic aspect of our daily lives. All of us use math on a day to day basis; when shopping, playing, reading time, through music and counting, in art, and in many other everyday activities. Usually during these daily activities we don't even realize how heavily we're relying on mathematics. 

I made the important realization that math was much more than numbers and formulas but a necessary concept that we use on a daily basis. This realization is important to realize as a future teacher because this shows the possibilities of relating the subject to what is relevant in our students daily lives. This discovery also helps to guide the definition I create for myself as a future primary/elementary mathematics teacher. 

What is mathematical thinking?

 

Mathematical thinking is what students need to perform the math activities they encounter in the classroom and in their daily lives. It is a teachers goal to teach their students to think mathematically, but what does mathematical thinking mean? When I think of mathematical thinking I think of trying to figure out how to approach a problem, and then deciding the steps to take in order to solve a problem. An article by Kaye Stacey titled "What is Mathematical Thinking and Why is it important" states that mathematical thinking includes "components... such as reasoning, modelling and making connections between ideas."

Although its important to teach in a way that recognizes and enhances these processes, it is important to realize that we take part in mathematical thinking often in our daily lives as well. When I decide what time to leave my house to catch the Metrobus in the morning before school I am taking part in mathematical thinking. Because mathematical thinking occurs in our everyday lives, it is possible to teach the skill in a way that is natural for the students. 

Having a better understanding of math has many implications for me as a future teacher. I learned that there is not one specific definition of math and that teachers must create their own definition to create a plan with direction and purpose. I learned that math is defined as more than numbers and formulas, and mathematical thinking is more than processes, but these concepts take place in our day to day lives. I believe that this is important to me as a future teacher because now I will teach to the real life implications of math as well as the "technical" aspects of mathematics.