What is mathematics anyway?

When I sit and try to come up with a meaning for mathematics, I find it rather difficult to define in concrete terms. After searching the internet for a definition and asking people around me, apparently they find it a difficult word to define as well. Some of what I found included things like:

 

"The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols." (Free Online Dictionary)

 

"mathematical procedures, operations, or properties." (Dictionary.com)

 

"Mathematics is a human endeavour, a discipline, and an interdisciplinary language and tool." (University of Oregon)

 

While all of these definitions have certain traits in common, they are all different from one another. I first think of it in terms of it's subject matter: addition, subtraction, multiplication, division and so on. This is what is taught to us in the school system which is why I think these are my first thoughts when exploring this topic. I believe it is a combination of all of these things, plus much more we are still unaware of.

 

 

So, what do we do with this information? What does it mean to do mathematics? Just as the definition of math spans wide across many areas, I feel that the concept of doing math does as well. As I remember from my school years in doing mathematics and from what I have seen through my observation days in both the primary and elementary grades, math most commonly done through a process of teaching a concept, doing examples and then working on questions from a text book or a worksheet. Since we cannot define math is concrete terms, why should try to constrict it's practice to something as basic as this? Doing mathematics involves all kinds of mental capacities such as numerical reasoning, spatial reasoning, linguistic reasoning as well as the ability to handle abstractions and when these are paired with a combination of creativity and a desire for success, students will see great personal growth in areas of mathematics. It is a variety of thought processes and actions all leading towards one final goal.

 

As I write this, I realize that I am thinking mathematically. I am wondering and reasoning about all this information I have found in order to come up with a definition, I feel, is sufficient and encompasses what I feel mathematics is. Doing math and thinking about math does not always need to involve numbers, it is about sorting through your thoughts and ideas in order to come up with one of many possible answers for a question, problem or even just an idea.

 

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

 

This quote by Bertrand Russell may say it best, and even though it seems to express a sentiment of uncertainty, when you really sit and think about it, it makes perfect sense. 

 

 

 

 

Do Schools Kill Creativity?

In class last week, we watched Sir Ken Robinson's TED Talk video "Do Schools Kill Creativity?" In this video, he shares many of his thoughts and opinions on the school system and how they treat creativity in the classroom.

 

 



Robinson makes many very interesting points throughout his talk, many of which cause us to really think about what is going on in the education system in today's society. One point which struck me as being very significant in the video was when he says "if you're not prepared to be wrong you will never come up with anything original." As we progress through the primary and elementary grades and into junior high and high school there is a notable decrease in the appreciation for creativity and originality and a move in favour of correct answers and factual information.

We have all probably heard the before that you learn more from your mistakes than your successes, and this is definitely true in the classroom. We should encourage students of any age to take risks when it comes to learning and give them the opportunity to express their creative thoughts without worrying about being wrong or embarrassed if their answer is incorrect. As a future educator, I feel that we should never look to instill fear in our students of any age. The classroom should always be a safe place for them to be who they are and express their thoughts with creativity and imagination. While there will be many times where we will need them to arrive at a certain answer for a question, we must teach them to do this with a sense of encouragement and an openness for learning.

I most definitely see the significance in showing this video to us, as future teachers, because it raises our attention to some of the issues within the school systems that we will very soon be working in. I realize that the issue Robinson has presented in his video is one that can not be solved quickly nor easily, and I feel that there is a shift beginning to be made, but is something we can continue to work towards as we enter into our profession.

To end this post, I will leave you with another quote from Robinson, which I feel sums up very well my thoughts and feelings on this subject:

"Creativity is as important in education as is literacy, and we should treat it with the same status."

Math Autobiography

When looking back at my experiences in mathematics throughout the primary and elementary grades, I quickly realized that there is not much that I do remember. From what I can recall, however, it seems to be quite opposite of the experiences of many other people I have discussed this with.

I completed the primary grades in a school in a small community on the Burin Peninsula and we were always told to work quietly and independently through various worksheets and only ask for assistance from the teacher. The only lessons where we were encouraged to work together was when we were using various manipulatives, such  as blocks, counters and cards (which we were all very excited about when we would see the teacher pull these from the shelves!), and that seemed to be only because there was not enough materials for each student to have their own. My family and I moved to a town just outside of St. John's before I began grade four where I completed the elementary grades in a much larger school than I had previously attended. This school and my teachers gave me a very different experience in learning mathematics. All students were encouraged to work together through the various problems, offering assistance to each other wherever we could. For me, it transformed math into an interactive and enjoyable experience. The energy was always very high in the classroom throughout every mathematics lesson.

That seemed to be a turning point for me in how I viewed mathematics. I was always described as being someone who was "good" at mathematics and it was a subject which came quite easily to me and this was reflected in the marks I received throughout school. After my experience in the elementary grades, I began to enjoy the subject and this continued throughout my junior high and high school years.

In reflection, I find it quite difficult to gauge how my teachers in the primary and elementary grades seemed to feel about teaching mathematics. For some, it seemed as though they were going through the prescribed curriculum simply because it was something they were required to do. For others, they clearly had a passion for the subject and loved teaching it to their students. This was reflected in the creativity of their lessons. One of the most inspirational teachers I had throughout high school was my math teacher in grade ten. She shared with us that she had been diagnosed with dyscalculia, a specific developmental disorder where one has difficulty in areas such as understanding numbers and learning how to manipulate them. It was her love of the subject which drove her to overcome these difficulties she faced and through sharing this with us she taught us that we can truly become whatever we want in our lives no matter what obstacles may stand in our way.

No matter how the teacher conducted their math lessons, it seems that assessments always looked the same. It began with worksheets, assignments and unit tests and as we progressed into junior high and high school we were also required to write mid-term and final exams, all of which would be marked by the teacher. Tests and exams typically consisted of short answer questions where we were graded on our workings as well as the final answer. If there were any other forms of ongoing assessment completed by the teacher in the classroom, it was never seen or discussed with the students.

Although I would describe my experiences with mathematics throughout my school years as being mostly positive, I have only taken two mathematics courses since entering university, both of which were required for my degree program, Math 1050 and 1051. I don't feel as though there is any reason as to why I did not continue my formal education in mathematics, I guess it just comes down to the choice to pursue other interests through my chosen courses.

Math seems to have a rather poor reputation in our society today, probably because it is perceived as being difficult and detached from the real world. I'm sure we have all heard the same complaint I remember hearing countless times throughout school (and I am sure I have uttered it myself a time or two), "when am I actually going to use this in my life?". What many of us do not realize, however, is that math is all around us in many things we do. We use it in our jobs, when we make purchases, telling the time and even checking the weather. As an adult, I definitely see the importance of having good mathematical skills in our world and as a future teacher, it is a subject I will try to give my students positive experiences in, such as those I had in school, so my students can also enjoy mathematics!



Welcome!

Hello and welcome to my blog!

 

My name is Laura and I am a fifth year student at Memorial University of Newfoundland, currently completing my B.Ed (primary/elementary). This will be used for the purposes of the Education 3940: Math in the Primary and Elementary Grades course and will further explore my thoughts and feelings about topics covered in class.

Enjoy!