Article Discussion- Balance is Basic

Okay so today was my day to lead the discussion and the article I read was Balance is Basic. What I gathered from the article was the emphasis on having math be a balance between 3 core ideas. These ideas include understanding mathematical concepts, being able to compute math and lastly being able to problem solve or apply the math. Near the end of the article, they add in 2 more accessories which were engagement and reasoning. Engagement being the idea that the individual will want to try harder questions and push themselves beyond their limits because they are "engaged" in math.

So I completely agree with what the article is saying, it makes perfect sense and is totally logical in what it's attempting to argue. All three aspects it touches on are key to a persons understanding and "relationship" with math. The article nicely points out that if a student memorises how to multiply fractions, one must strictly go "straight across" and multiply. Simple. Answer is done. Vice versa, if you want to divide, all you must do is flip the second fraction and go straight across. It is easy to do these simple tasks, however if you don't understand the reasoning behind it, then you are missing the fundamentals of mathematics. Additionally when more complex math is introduced and you don't have a solid foundation, well I think you might be in trouble.

This was also highlighted in class today when V asked us to multiply 18 by 5 without using a pen and paper. I mentally calculated the 10x5 and added it to the 8x5. When Phil mentioned that he wrote it out in his head like a typical multiplication setup, and carried the 4, I agreed that is what should happen. Here's the thing, I couldn't explain why that happens...it just does! It wasn't until V actually explained that the 4 represents 4 (10's) that I was like OHHHH!!! ding ding ding!!! But in my 28 years of existence, I didn't know that and I never cared enough to ask...until now that is.
Another thing V mentioned in class today was that you cannot come into class assuming that students have the same level of math interest or ability as you do. He spoke to the fact that when he was growing up, he was fortunate enough to have a father that asked him solely about math and this in turn might have helped him succeed in math. So not having that notion that all students will have even a fraction of interest in math will help us as educators to try to see things in different way and motivate us to come up with various ways of explaining something.

In terms of my discussion, I wrote 4 questions that I asked my group.

1. Do you agree with the article in the sense that we need an equal balance of all 3 strands of math: understanding, computation and application? Justify your answer

2. In what ways does this way of thinking about mathematics make your job more challenging or difficult?

3. What issues do you see arising with having this model as a standard model for all math teachers?

4. In what area of math (out of the 5 mentioned- understanding, computation, application, reasoning, engagement) do you feel is your strongest and why?

We had some interesting discussion, and I will just touch on a couple of the questions that I asked. So in terms of the first question, some mentioned that they disagreed with the article in that you don't need to have all 3 aspects fully developed because we don't use all three everyday. We also have the lovely thing called the internet and Google at our disposal if we need to look some rule up that we have forgotten. Another member said that she wished she had a stronger computation skill set because she finds that she struggles with some basic math arithmetic like being able to currency convert. In my opinion, I think ideally one should have a balance of all three aspects, but does this mean that you are going to fail miserably in life if you don't? Of course not!! I didn't know why I had to carry the little 4 in today's class yet I managed to get an A- in first year calculus. So to me you can still succeed even if there are some tiny minor gaps....(please let me know your thoughts on this!)

For the second question, I think we mostly agreed that it would make our lives a bit more challenging only because we have been trained as professionals to see things as separate entities. So for example when we are marking students work, we always separate the knowledge, application, thinking and communication pieces. We are conditioned in society to have things organised and in their own compartments but I think once you get over seeing math as these three aspects that one MUST focus on and instead try to see it as a holistic approach, it might be slightly easier. We also mentioned that for some standardised testing, they are very much set up in a way where everything is compartmentalised and separated which might again make the transition tougher. 

Lastly for the third question, we discussed that because it isn't explicitly stated in the curriculum that math should be thought of in this way, it might be challenging for some teachers to accept. I sort of struggled with this argument because I took the article to be somewhat of a guiding  tool as opposed to "this is how it needs to be done" tool. So I took from it that you can still teach everything in the curriculum but make sure you are looking that students are able to understand concepts, can compute math and critically think on their own. We also jokingly said that many math teachers will be retiring and when they do, then this whole shift will occur because many are still very focused on the computation aspect of math. 

So here is a picture from today's exercise on how a simple multiplication question could be seen in a different way.