If you were to ask a child which subject was their favourite in school, what would they say? Would they say language arts, mathematics, or would the ever popular subjects known as gym or recess take first place?
If you asked an adult what they thought of math, would they respond positively or negatively? When you were in school did you have a ‘love it’ or ‘leave it’ opinion on the subject?
Have you ever caught yourself or heard someone say “Math is hard”? Math gets a bad wrap all the time. Sometimes I wonder if we are predetermining the fate of our society by allowing these types of phrases to be acceptable. I hear math is hard, so I’m just going to give up because I don’t stand a chance to ever ‘get’ this. Do we teach math, with an undertone that only the ‘smart’ kids will excel? I certainly hope not. Let’s keep fear out of learning.
The fact is we need a basic understanding of math to survive adult life. The grown-up world is full of numbers games. Yes, it may be true that you rarely use the calculus or the algebra that you learned in school. Numbers are never imaginary anymore and when you hear the word “pi” your brain thinks of the eating variety not the 3.14 kind.
And with math comes problem-solving, and we all know that as adults we need those skills too. As grown-ups we are always forced to ‘fix’ problems.
Fast forward to today… and today’s students.
Each year in the Province of Ontario students in Grades 3 and 6 write a standardized test often referred to simply as EQAO which is administered by the Education Quality and Accountability Office (EQAO). In the latest round of results released, the media outlets took no time to let their readers know that only half of the Grade 6 students were able to meet the provincial standard. (Here is the Globe and Mail‘s take on the results).
I won’t speculate on why our provincial math scores are declining. But some common questions have been raised among us “outsiders”. Is the way we teach math today the problem? Or is it the standardized test? Is this test set up for our children to fail rather than succeed? What can we change?
I have heard many parents today complain about “new math”. Yes it is true, that for many parents, the way they see their children learning mathematics appears very different from their experiences in the classroom years ago. But it isn’t new. Math is still just math.
Marian Small, a leading Canadian mathematics educator, speaks regularly about how you can support your child to achieve success in mathematics. She doesn’t use the term “new math” but rather calls it “alternate strategies”. She points out that “Children are learning different strategies since different ones are more efficient or more meaningful in different situations and different ones make more sense to different kids.” (Check out her website for past presentations.)
The problem with mathematics, is that it’s just one of those subjects where a one-size fits all approach doesn’t always work. Finding the materials and resources needed to build a solid mathematics foundation will likely be slightly different for each student. Using only one strategy to teach a mathematics will almost certainly lead to cracks in the foundation.
Although it may appear very black and white in terms of identifying the answer to a problem, the route to get there can be very diverse. Have you ever argued with your GPS (or your family) on the best directions to take to get to your end destination. There is rarely only one way to go, although it may be argued that some ways are better than others (but this is merely an opinion). The point is, all routes get you to your end destination!
Dr. Small gives a simple addition problem to show some different approaches to tackle the very same question. How would you solve this problem?
The approaches used in Methods #1 and #2 are much easier to visualize. Simplifying and breaking down the problem into smaller steps is the strategy. These ‘tricks’ have been employed for years (as my husband attests) to be able to more readily perform math in your head. Although, when written out, these explanations may look complicated, surprisingly it does make it easier to get to the answer. It isn’t ‘new’, it’s still just math. But for many students, making things a bit simpler to visualize is the intention.
Method #3 is how I was taught in school, and admittedly, it is the method I am most comfortable. Because it is familiar. But as you can see three different methods, one common answer.
I have graded enough midterms and final exams over the years to know that when a mathematical question is presented, I will see a collection of approaches that all arrive at the same, correct answer. Sometimes seeing things a little different, thanks to my students, gives me a fresh understanding to the logic needed to solve a problem.
Don’t rush to the end of the journey, enjoy the trip and all the stops along the way.
I always say (even to my university students), yes the answer is important, but it is also very important (especially when you are still learning) to understand the steps involved. Learn to ask the right questions. Learn to see the trees among the forest. Make things simple, take it slow. Don’t rush to the end of the journey, enjoy the trip and all the stops along the way. If you don’t understand the process, you will never successfully solve the problem.
Math is just like that. And what works for one student, may not be clear to another. Don’t be afraid to mix things up. Be different. Make analogies to something more ‘real’.
My primary concern is whether each student is building a strong enough foundation in math to allow today’s students to quickly build up from that foundation. Or have we left them on very shaky ground?
Yes, there is a negative connotation when you say ‘memorize’ but sometimes it just needs to happen. For example, the days of memorizing timetables are gone. Which, honestly, I can’t wrap my head around. Every subject area, requires some level of recall. Do you love to memorize? Probably not, but sometimes it’s just a necessity. Once you understand the process, and a solid foundation has been built, recall allows you to spend more time problem solving rather than getting hung up on the details. I clearly remember, sitting in math class in Grade 8, a subject taught by our music teacher. To the beat of a meter stick tapping on the ground we all sang out in unison, our timetables. It was fun. And you know what? We remembered them.
Why learn you timetables, when you have a calculator? Again, you need a solid foundation first, before you can enlist the help of electronic devices. I am guilty today of grabbing a calculator to do math that was once straightforward. But if I can’t find a calculator, I can just as easily solve it with a paper and pencil. Could you? Could your children?
How do you improve math for the next generation? Be patient. Learning takes time and practice. You may need to try a few different approaches before that ‘light-bulb’ moment. And if you and your child need a break. TAKE A BREAK! Our brains (and our patience) need some down time too. Every little bit counts when building that solid foundation.
So for the entire month of December, we at STEM Play Every Day will be engaging in Math related activities. To my kids, it’s just a bunch of fun games. They won’t even realize that brick by brick we are building that foundation.