After being subjected to mathematics for practically my entire life, I have never actually thought about, "What IS mathematics?" ...Uh, a subject with numbers and stuff? (Jokes).
Off the top of my head, I would define it as an important subject that involves numbers and practiced equations that we can use to benefit our daily lives. To be honest, I could not think of a good, elaborate answer to this question on my own. Therefore, I done some research to expand my knowledge on mathematics. I know that Wikipedia is considered a "non-creditable source" in university, but I seriously love Wikipedia. So, the various users have defined Math as, "the abstract study of topics, such as quantity (numbers), structure, space, and change" (Wikipedia, 20 January 2014). After hundreds of years of theories and practice, mathematicians have created what we know as math today. We have been learning bits and pieces of math since that first day of Kindergarten (and maybe even before that, learning the concepts of numbers at home with your parents/guardians).
So, what does it mean to do mathematics? It involves a wide variety of mental skills and abilities. It's not just putting that pencil to paper to answer a multiplication question or plugging in some numbers on your calculator. We actually reflect on what we have previously experienced and think about how we can apply that knowledge. Within our course textbook, the authors (Van de Wall, J., Folk, S., Karp, K., Bay-Williams, J., p. 11) say that to do mathematics, it involves a number of verbs to understand the task at hand. The list is as follows:
explore represent explain
investigate formulate predict
conjecture discover develop
solve construct describe
justify verify use
Each one of us remembers using at least some of this actions to "do" our math at some point. I have used 14/15 verbs that I can remember, for sure.
If a person is thinking mathematically, I think that they are using their mathematical/logical intelligence described by Howard Gardner (1983). We use our knowledge about numbers and try to get an answer based on our mathematical skills. For instance, when I go to the grocery store and compare the price of two items of different weights to see what the best deal is, I'm thinking mathematically. When I count the hours of sleep I will get every night if I went to bed at a certain time or when figure out what bus I need to take to school to make sure I get to my classes on time (given that the buses are usually running late or that there may be traffic), I am thinking mathematically. I believe that every person thinks mathematically to some degree. If we were not exposed to math throughout our lives, then we would not possess this ability. Therefore, it is important for our future students to "do" math and learn different ways to get their answer to be successful members of our society. MATH IS EVERYWHERE.
After our class today (January 23rd), we shared our ideas about mathematics. In our group, we summed up what we learned in the following web:
It may be hard to see, but we said that it is human created, an art, misunderstood, and abstract. Even though we had plenty of similarities, it was nice to see how everyone else in my class viewed mathematics. This activity helped me realize that we all have some idea of what math is, what it means to do math, and think mathematically. Hopefully by the end of this course, we will all have a good understanding of mathematics and how to use this knowledge to teach our prospective students.
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