Final Post

What was your greatest 'learning' this semester with regard to teaching children mathematics? How has your thinking shifted?

I came into this course with a love of mathematics. I wasn't afraid of it, it didn't make me uncomfortable, I just didn't have a clue how to teach it. If you asked me now if I feel prepared to walk into a classroom and start teaching math, I'd still probably say no. But that doesn't mean I haven't learned anything about teaching math from this course. I've learned so much I don't even really know where to begin. The distinction, I believe, is that I will simply never feel confident or knowledgeable on those topics until I actually get to try out some stuff in a real classroom with real kids. 

I found this diagram months ago, and was saving it specifically for this blog. I think it sums up our experiences with this program so far in general. We're gaining a whole bunch of those little knowledge dots, and now it's time for us to go get some real, meaningful experiences to tie it all together. 

Looking back now I can't believe it didn't really occur to me that math can be more than it was when I came up through the school system. The security of having one "right" answer was something I took solace in during my own math classes, but it's so near-sighted of me to not realize that not everyone learns that way and thrives in that environment, and there is indeed room for creativity in mathematics. I realized that while coming up with activity ideas for the math fair and the team-teaching assignment, I naturally gravitated towards problems where there were multiple answers, because it was more exciting! I was looking forward to exploring all the solutions that my classmates came up with, and didn't want to box everyone in with a question with one solution. Math becomes less competitive this way, and problem solving becomes about finding out cool new information, and new ways of thinking. This is something that I hadn't realized about myself and I think it's neat to know that I think about math a little differently now.

Another incidence that impacted my learning this semester was participation in the math fair. I'm so pleased that we actually created the problems and got to try them out firsthand. If we hadn't had that experience, I don't know that I would have realized what a neat concept it really is. I love the idea of science fairs and heritage fairs, and now I have a whole new idea to add to the list. Looking back, mathematics was always the type of subject that was fun to the people who considered themselves competent in it, but was not considered particularly exciting to the rest. The idea of math fairs changed that mentality for me, and I'd love to see it in action with real children!

Math Resources

In class on Tuesday, we were provided with the opportunity to examine the curriculum materials for K-6 math in Newfoundland and Labrador. It always surprises me when a professor shows us what we will actually have available to us as teachers, because in the first year of the program I didn't really think we would have much of anything. There must have been a miscommunication somewhere, because I (and some others I know) thought that we were pretty much given the curriculum guide and textbooks and more or less told to come up with all of our own lessons and buy our own resources.

So, it's comforting to know that I'll have more than nothing at my disposal. Some of the material is so guided that it actually gives instruction for every page of a read-aloud to a kindergarten group. I think that might be overkill, but I get the idea. It's certainly detailed. A big part of being a teacher is examining the way that others teach something and then deciding whether or not you wanna teach that way, or what changes you would make. I think that's one of the benefits of having rich lesson ideas, it allows you to take it and change it and turn it into something that works for you in your classroom.

Something I noticed progressing through the grades is that once you reach grade three, the picture books disappear. It gets a lot less colourful and fun. Math becomes a little serious. Is this necessary? I've met children in grade three and I think they wouldn't consider themselves too mature to have a bit of colour in mathematics. I feel like the point of having these picture books in the first place is to add some realism to the subject so kids can understand it. I don't quite understand why that focus is taken away at the point where it is. But perhaps that offers the opportunity to supplement the existing resources with fun things I find on my own.

Personally, I noticed an awful lot of arithmetic in the documents. Not saying that's not important and obviously it's a large chunk of the curriculum, but I just felt like I couldn't find that many examples of how to implement other aspects, interactive aspects, or problem solving beyond asking the arithmetic question in words(which I remember was considered problem solving by a few of my teachers in the primary grades). I can just see how it could be easy to fall into the routine of following everything these teacher guides say to do, and not really ever breaking out into your own lessons. Not saying they are not great resources, but certainly they can't encompass everything we should be teaching in math classes. I think, perhaps like most concepts I've encountered in education so far, a balance needs to exist.

YouCubed

When I first visited the YouCubed site, I didn't quite understand what it was. As you scroll down the page, more and more information is provided about what exactly the site provides. I like the way the home page is organized. You scroll down in a logical fashion and links explaining more information are provided throughout.

I was very impressed with the math lesson plans found on YouCubed. They are very detailed but written in a totally accessible way and include everything you need to know in order to engage with the lesson. I loved the example of "A Google Dilemma". One of the big complaints about mathematics education is that it doesn't relate to the "real world", but Google is completely relatable for kids and is a more accessible issue for their generation than some of the standard textbook examples.

Along with lesson plans, the site offers videos of YouCubed at work in classrooms, information and ideas for parents, math games, and overall suggestions of making mathematics more engaging. One particularly interesting idea is that when the site becomes fully operational, YouCubed will feature the math worked on in today's innovative companies. In many of our courses we are exploring the idea of students working together in innovative ways to solve real-world simulated problems, and constructivist education in general, and I can see how this feature would be useful for that type of activity.

The site also provides up-to-date news and research articles, and I like the idea of having a user-friendly site to visit when I want to explore what the latest research is for mathematics instruction. 

I think the article titled "Parents Make Math Fun" could be provided to parents at the beginning of the school year to set the stage for a new perspective on mathematics. A revolutionary method of math instruction probably won't succeed without earning the support of parents, and it's important to provide them with the current research so they understand why we're teaching the way that we are. I think that sometimes parents become frustrated when their child struggles with a mathematical concept, and it doesn't hurt to provide parents with research saying that it's perfectly okay to encourage mistake-making. 

I'll definitely be checking back when YouCubed becomes fully operational to avail of their free resources, especially when trying to bring my own ideas and methods to my internship.

So... What is Math?

I asked Google the above question and it said, "the abstract science of number, quantity, and space. Mathematics may be studied in its own right (pure), or as it is applied to other disciplines such as physics and engineering (applied)". Oook. Seems fairly straightforward, and not far from how I would define mathematics myself. The term "abstract" throws me off a bit, so I do some more research.

Now I stumble upon Bertrand Russell's definition of mathematics: "the subject in which we never know what we are talking about, nor whether what we are saying is true". Then this quote from Charles Darwin: "a mathematician is a blind man in a dark room looking for a black cat which isn't there". 

We only discussed this briefly in Tuesday's class, but we touched on the idea that our base ten number system didn't just appear out of thin air. Humans invented the terms and parameters surrounding mathematics, and if these terms and parameters didn't exist, mathematics as we know it would not exist. 

In my opinion, another vital aspect of mathematics doesn't involve numbers or symbols in a necessarily concrete way, and that aspect is problem solving. Problem solving is beyond math, it's an imperative life skill that we tend to teach and learn through mathematics, but genuinely applies to every school subject and beyond that, every experience in life. 

The mathematics that I experienced in school operated on a simpler definition, and none of the above concepts ever came into play. It was just solving problems with numbers. In elementary school there was usually a purpose for the math we were performing (such as counting money), but in high school math was seemingly performed for the sake of being performed. I remember sitting in my level three "advanced" math class and whispering to my friend, "what in the world is sine, or cosine? what does it represent? why do we use it?". These answers were not provided. We were just expected to know how to solve the equations.

Math is more than just numbers and problems, and it sure makes life easier. We have discussed in class that math always has an absolute answer, and there isn't exactly room for debate unlike in almost every other subject. However, variation can exist in the methods used to obtain the answer, and this is key. Solving math problems teaches logic and reasoning, which can be applied outside of mathematics. 

Sir Ken Robinson: Do schools kill creativity?

In class we watched Sir Ken Robinson's TED talk titled "Do Schools Kill Creativity?". Most of the class had apparently watched this video before but this was my first time. First of all, I thought his sense of humour was great, which always resonates with me. I've always been impressed with teachers and professors who can incorporate humour into their message (when applicable). He makes it relatable and doesn't pretend the field of education doesn't have faults. 

Our education system doesn't leave a lot of room for creativity. What particularly struck me was his story about the four-year-olds performing the nativity play. Instead of saying, "I bring you frankincense", the child said "Frank sent this". Ken Robinson went on to explain that when children are not sure of something, they will come up with some sort of response and try anyway, without a fear of being wrong. Schools tend to destroy this innate creativity by insisting that there is always a "correct" answer and giving children poor grades and reprimand when they are "incorrect". By doing this, children develop a fear of being wrong, and therefore never receive the opportunity to make the mistakes necessary to come up with something truly unique.

This video makes sense in a class about mathematics because math is one of those "hard" subjects that is given high priority in the schooling system. It is held at the opposite end of the spectrum from an artistic subject like math. In order to give these artistic subjects more precedence in the education system, it seems like a logical option to incorporate these subjects in some way. There was very, very little room for creativity in the way that I was taught mathematics. Learning as much as possible about creative thinking is a way to learn to incorporate creativity into the mathematics classroom.

Something that occurred to me during my second viewing of this video is how effective Ken's messages are. Most of the video consists of comedic anecdotes, and the important points are delivered in a few simple, albeit very profound lines. 

Math Autobiography

I really like math. I miss doing math. I don't know why I don't do more of it in my spare time. 

I do not remember a lot of specifics from my K-6 mathematics classes, but what I do remember was generally positive, and I predict that positivity exists because I was "good" at it. When I attempt to envision what my mathematical experiences involved during primary/elementary grades, I conjure up images of manipulatives and numbers on a chaulkboard. I remember those little multicoloured blocks intended for describing place values. I never liked those blocks, I found it easier to just visualize the numbers and write them down. 

I remember "mad minutes" for multiplication, and sometimes even the dreaded division. I didn't mind practicing the multiplication tables but to this day I don't quite understand why it's so important to be able to recite them so fast. My third grade teacher would reward the first three students to complete the task. When I think about this now all that comes to mind is an image of the last child to pass in their mad minute --with possibly every question correct-- feeling downtrodden and embarrassed. This concept is something I see as an issue in math assessment. From my own experience(and, I can imagine, the experience of many others) math assessment = math tests. Math tests are stressful. I've always had a lot of confidence in my mathematical ability but I still remember sitting next to an open window waiting to enter the gymnasium for my Math 1000 final exam, trying not to pass out from nervousness.  

If I thought I had the answers for the problems on that test and I felt that way, I can only imagine how someone who was struggling was feeling.

I haven't taken a math course in a while and surprisingly often think about how I miss it. In university I've taken Math 1000 and 1001, two linear algebra courses (for fun), and two introductory stats courses (as electives). I interact with math in my life as much as any average person I suppose, but not in any real major way. 

So, I like math. However, I'm not even remotely confident in my abilities to communicate mathematical concepts to others, especially children. I'm eager to learn what I can and start preparing myself for that.

Welcome!

Welcome to this blog focusing on mathematics in primary and elementary grades. The purpose of this blog is to express ideas and address issues about K-6 mathematics in accompaniment with the ED3940 course in Winter 2014.