My Shifting View of Mathematics

As our course progresses and I continue learning more about mathematics and how it should look in the classroom, I find myself contemplating concepts/ideas that I had never really given much thought to before. Before reading chapter two in the text and attending class on Thursday, I would have been one of the first people to say math is a "black and white/right or wrong" kind of subject. I guess that opinion stemmed from my experiences with mathematics growing up. There was only one right answer and one way to get to that answer. Any "workings" that didn't support the teacher's method and any answer that didn't match the one in the back of the book was automatically wrong. Honestly it never really bothered me though, because I was one of the lucky ones who easily got the right answer, showed the "right" workings and never really asked questions. However, after reading the text, math is not about regurgitating facts without even thinking about the process or why we use it. As our text states:

"Doing mathematics means generating strategies for solving problems, applying those approaches, seeing if they lead to solutions..." (pg. 10, 3rd ed)

Because of my past experiences, I am still programmed to worry about the right answers of problems instead of on the strategies and processes created to solve them. When completing the problems in chapter two, it was actually really bothering me that the answers were not in the book. I especially wanted to know the answer to the "Two Machines, One Job" problem on page 13. It really bothered me that the two different answers given could be backed up so well... how could they both be right? Or could they? I guess this is where it finally clicked for me that the creating of strategies and being able to "back up" the process is equally (or more) important than the answer itself. We all have to use mathematics everyday in our lives to solve problems. When we try to actively solve our day to day problems there are no easy methods/answers - there are only strategies and approaches that we have to come up with and test on our own. Students should be taught to solve problems in the classroom like they will have to do it in the real world. Therefore, "right" answers shouldn't be everything, nor should one method be considered the ONLY method to get there.

As a final thought, I believe that mathematics can indeed be considered a humanity. Math is always changing. New methods and theories are constantly replacing old ideas and it isn't as black and white as some might believe. With new teaching methods requiring students to think about, analyze and test possible solutions to problems, it suddenly becomes less of a repititive 2+2=4 "just because" but rather a way to solve everyday problems in more than one "right" way.

Video Response

Hello everyone!

This entry is in response to Sir Ken Robinson's video about the role of schools in nurturing creativity within students (watched in class). I'll start out by stating that I agree with Robinson's view that the education system today extinguishes the creativity that children naturally possess. From my own experiences growing up and from what I've seen/learned so far in the education faculty, I feel as if young students start out thinking creatively and channeling it through everything that they do. But as they age and progress through elementary and jr/sr high one can very quickly see most of that creativity vanish. I think that imigination can be used powerfully but for the most part schools don't value imigination, they value facts and correct answers. 

When I was young, I didn't show much creativity in my work for fear of being wrong. I felt as if being 'wrong' was the worst thing that could happen when completing schoolwork. As a result, I never took chances, I always completed my work in the most straightforward way. I would assume that many students feel this way. One thing I feel that we should do as future educators to promote creativity is to encourage risk-taking in our classrooms. Students shouldn't have fear of making mistakes. Mistakes are proof that an effort was made. I also believe that a lot of creativity can show through the arts, but many times the importance of arts is neglected in school. I believe that creativity would have a larger chance of persisting with children if more emphasis was given to music, drama, dance, etc. 

Although I have little experience in the subject of mathematics, to promote creativity  in my math classroom, I would try to:

-Allow students to use different materials to solve problems/demonstrate their understanding of concepts.

-Allow input. Students should make some of their own choices in the classroom. Don't constantly give a lot of restrictions with assigned work.

-Be open-minded. (Don't assume there is only one way to do something correctly.)

-Encourage risk-taking - mistakes are ok to make!




"Every child is an artist. The problem is staying an artist when you grow up."
                                                                                 -Pablo Picasso
                      

Mathematics Autobiography

When I reminisce on my mathematics experiences from primary/elementary, I realize I actually don't remember all that much. What little I do remember from primary is sitting at tables with a group of classmates filling in brightly colored workbooks that used a lot of visuals/pictures to help us out. I can remember using manipulative materials such as blocks, counters, and card games to help us solve problems and learn new concepts. (I would get so excited to see my teacher pull materials from the shelves to hand around during a lesson!) I can also remember being asked by my teacher to help peers who needed a little extra time with assigned work when I finished mine early.  I liked being able to help my peers but, being shy, I didn't enjoy being put on the spot. Math was always interesting and enjoyable to me, fun even, in the primary grades. However, as we aged, and progressed through the elementary years, math became more boring. It became less interactive, as most work was done individually, "in our heads", on "boring" lined exercise books, and manipulative materials became a rare treat. I found that attitudes in the classroom about math quickly went downhill by late elementary/junior high.

It's hard to remember much about my primary/elementary years, but it seems as if my mathematics teachers enjoyed teaching it. It is hard to tell how they really felt about it because they were responsible for teaching everything - but if they didn't enjoy it, they hid it well. High school was different though, teachers were specialized in the area and it was very obvious that they loved it! Some of the math teachers I had in senior high would get so happy when teaching their favorite units/concepts. In high school, I found a new appreciation for math in my last couple years. I transferred from NL to AB in grade 11 and they put me in pure mathematics. It was so different from the math I had taken in NL and it was difficult for me to adjust to a completely different curriculum in the middle of high school but I loved the challenge.  

Math was always something that came easy for me. I knew I was "good" at it because I always excelled without having to put much effort into it. I know I was lucky in this respect, many of my friends couldn't say the same. That doesn't necessarily mean I loved it though. Math was always that subject that I neither loved nor hated, I never really thought much about it - it was just something we had to do. I enjoyed the feeling of success I would get from making my teachers and parents proud when I'd bring home my 90's & 100's, but it wasn't the subject itself that brought me joy, it was knowing I was good at something that not everyone could be good at.

As for assessment, it was always the same. Worksheets, open-book assignments (which were basically the same as worksheets), unit tests, and as we got older: finals. Tests and exams usually had some multiple choice and some short answer questions. It was always the same and generally straightforward. I'm sure there was probably on-going informal assessments in the classroom such as observation and checking of homework etc. but as a child I can only remember worrying about things I knew were being marked: the assignments and tests. 

Since university, I've only taken two mathematics courses: the recommended 1050 & 1051. For my focus area a few years ago I was debating between math and english. In the end I chose english, but I've always kind of regretted it.

Overall, I've had good experiences with mathematics. However, no particular memories stand out in my mind from primary/elementary. I do think that mathematics is an extremely important subject to teach children because it's all around us: we use it to count money, to buy things, to tell time & dates, for baking, for clothing sizes, for weather, and so on. Numbers are everywhere, I consider it a literacy all on its own.We use it everyday without even thinking about it - so as an adult, I can see why it is emphasized so much in grade school.

Welcome to my Blog!

Hi everyone!

My name is Amy and I'm a forth year student at Memorial University of Newfoundland, currently completing my B.Ed (primary/elementary). This blog is required for my Ed 3940 course - Mathematics in the Primary and Elementray grades. I've always enjoyed math and have been looking forward to this course since the beginning of my program! I'm quite interested to learn about approaches to take when I begin teaching mathematics to my future students. I've never written a blog before so please bear with me as I try to figure it all out!

:)