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. 

Welcome

Welcome to Jody's Mathematics Blog 

Hello and welcome to my Math blog. In this blog I will be discussing and sharing some of the key concepts that are covered in my Education 3940 course. These concepts will surround learning to teach mathematics in the primary/elementary classroom setting. I look forward to viewing and learning from similar blogs available on this topic. I hope you enjoy my blog and that you discover some valuable resources and information valuable to you in your future teaching careers.

Jody's Math Autobiography

Often, it is not easy to recall what took place in our own primary/elementary classroom, but reflecting on this information is incredibly valuable. Through reflecting on your past experiences as a primary/elementary student, as well as hearing about the experiences of others, reminds us of the impact that different methods of teaching had on us as students. Using this information we can modify our own teaching methods to become more effective teachers in the future. One does not always have to make a mistake themselves to learn from the mistake.  

The first question you could ask yourself could be: How did my primary/elementary Mathematics classroom look? For myself, the appearance of mathematics changed drastically over the course of my primary/elementary school years. During the primary grades, math was taught in various and creative ways. To learn the basic concepts of math we sang songs and played games about numbers and their relationships. We used manipulatives often to make the learning hands-on and to make the concepts visible.We complete an abundance of group work. Classrooms were noisy, and inquiries and discussions with our peers and instructor were encouraged. These are the years which initiated my love of math. As I began my first year of the elementary grades math became much different. Students were encouraged to sit independently and not to speak. Math consisted mainly of doing independent work from the text book. Teachers would dryly teach a new concept on the chalk board and the remaining classes in that week would begin with: "Turn to page 364-365 and do all of the problems numbered with even numbers on the page." The "good" student was the one who finished quickly and asked few question. Munipulatives became a thing of the past, and memorization became significant. All of the beneficial methods used to teach math in the primary grades were labelled and "childish" and my excitement for math began to falter. 

Although this new approach toward math may have harmed my excitement toward the subject, I still excelled in the subject and found it understood math concepts rather easily. I was often the first to finish my work and achieved high grades in the subject. Yet, it was my success in the subject that lead to the worst experience that has happened to me during a mathematics class. My grade four teacher paired me up with a small group of students who were struggling. He gave me the instructions to assist the three other students with the current math concept being taught as I had a good understanding of what was being taught. I was very shy when I was at this age, and the group I was working with were students who were known to be "popular" in the class and often the students who bullied me outside of class. At first, I tried to explain to them how to solve the math problems but it quickly became obvious that the boys did not want to learn and they certainly did not want to be taught by me. To avoid further frustration and embarrassment, I took each of their worksheets and completed it for them. After seeing how well the boys had done on their work sheet, my teacher assumed this grouping was working well for everyone involved. Rather than tell the teacher that I had written most of the answers myself, I continued to do my groups' math worksheets for the remainder of the year.

In the story I've just shared with you, I believe that the teacher was not effectively fulfilling his role as a primary/elementary mathematics classroom teacher. In the primary grades, a teachers role as a mathematics teacher involves teaching students the basic concepts about math such as the concept of numbers, simple arithmetic, as well as some simple terminology such as measurements of height and weight and problem solving. A math teacher's role in elementary is to expand upon what the students already know, making the arithmetic slightly more complex and adding to the students math vocabulary. But I believe primary/elementary math teachers have more responsibilities than just teaching the concepts of math. I believe that they should find creative and fun methods of teaching math that reach all types of learners. I believe primary/elementary math teachers should try to create a love for math in all of their students. 

My experience with math in high school varied tremendously depending on the teacher that I had. One of my high school math teachers was very enthusiastic about math and this was evident through his teaching methods. He often used creative and interesting ways to teach us the concepts such as using technology to show video or play interactive games, or by giving us opportunities to learn in a hands-on way (such as using a ruler to measure distance). Once again math became both interesting and enjoyable. The following year, I experienced a teacher who did not have the same passion for math. He taught through explicit instruction, worksheets, or by doing endless problems assigned on a page in the math text. I once shared with him that I wanted to be a math teacher in the future, and he warned me against the choice saying that he felt that becoming a teacher was a mistake. 

Although I was a little discouraged by what my teacher had said, I did not allow him to change my mind. Before I began attending MUN, I did well on my math placement test and had planned to begin Math 1090 that semester. I was blown away by how much more information I needed in this math course and how quickly the semester was going. By the courses drop date I was not pleased with my mark and drop the course. I completed Math 1050 and Math 1051 that I needed to apply for the faculty of Education and did not complete any more math courses.

Although I have not completed any other math courses in MUN, I encounter math on a daily basis. Math is involved in all of my money transactions such as buying food or comparing sales at the grocery store. Often over the weekend my friends and I get together and play card games which require a lot of mathematics, and often being good with mathematics gives you the advantage. At times I draw, practicing my symmetry. I do a lot of measuring and weighing because I enjoy baking, and my dad enjoys to work with his hands and often we build furniture together which requires many math concepts such as measurements, angles, and problem solving. Although we do not think about it often, we all utilize math skills in various everyday situations.

Although I have had some great experiences with math, and other not-so-great experiences, I still enjoy math quite a bit. I am enthusiastic about teaching primary/elementary aged students about math, and showing them that learning about math can be fun and exciting. I will make sure that a child's love for math is not threatened by repetitive, silent seat work, but instead I will thrive to make math interactive, dynamic and interesting for my students.