I’ve privately tutored 3 students before in Mathematics. In all 3, I discovered the same, fundamental problem in how they have been taught algebra by the NSW education system.
Solve for x:
2x = 1
They have been taught to think: “What number times 2 will equal 1?”. This is what I consider a “guess and check” methodology. This is fine if they’re quick thinkers, but even then – what about more complicated questions?
This is the problem with the way algebra has been taught by schools in NSW.
For some reason, none of my students were familiar with what I call the “take over” method.
Solve for x:
2x = 1
For instance, instead of thinking “What times 2 = 1?”, in the take over method – we instantly think “Move the 2 over to the other side. 1 divided by 2 is 1/2.”
When I tutored them in Yr 9 and 12 – that was the first time they had ever heard you could do that. I was shocked.
Whilst the “guess and check” method may work fine here, it won’t for more complex algebra.
Solve for x:
2x = (3x – 7)/4
Beyond the “guess and check” method, my students then used the the “both sides” method.
They thought: “Times both sides by 4. That becomes 4 x 2x = (3x – 7). Then add 7 to both sides. 7 + 8x = 3x. Then minus 8x from both sides. 7 = -5x. Then divide both sides by. -7/5 = x.”
If they had been taught the “take over” method in the first place, they could apply it again: “Take over the 4, becomes 8x = 3x -7. Move the 7 over and the 8x across. 7 = 3x-8x. 7=-5x. x=-7/5.”
That is so much more simple. Why doesn’t the NSW education system teach that from the beginning?
It’s quite frustrating when I tutor my students, because by that time they are usually in Yr 9. They cannot do complex algebra, because the way they have been taught basic algebra is so….faulty!
Difference in how Math is taught in Asia versus Australia:
My mother, who went to a Hong Kong school, has noted a difference in how maths is taught.
In Hong Kong (and I suppose other Asian countries), she says that math taught via memorisation of formulas. They only teach the logic once.
For example, the way that Australia teaches the area of a rectangle is to first show you a rectangle made of blocks. You then count the number of blocks. After doing this a number of times, they illustrate how you can count the blocks on the width and length and multiple to get the total area.
Asian countries teach differently. They show you the logic once, but it moves almost instantaneously to formula: length x width = area. You are made to stand up and recite to the teacher what the formula of a rectangle is.
Another well known example is the drilling of times tables. Rather than teaching students that 2 x 2 = 4 (by getting 2 apples and then doubling that), Asian-taught students rote memorise the entire 12 x 12 times tables off by heart, even if they do not quite understand the logic behind it.
Ironically, this means that, though the Australian system actually teaches us the logic, it actually makes us slower. There is really no need to think that much!
On the other hand, the Asian style of teaching maths can be quite scary (drilling and rote memorisation). However, the benefits are that:
- Asian-taught students are quicker in arithmetic (multiplication, division) because of memorising the times tables off by heart at an earlier age.
- Asian-taught students are trained to remember and adapt formulas faster. This is especially important for later high school years, where you have to remember the distance formula, quadratic formula, surface area etc – without being explained the logic.
So what does this mean?
Should we have teachers trained to teach “the Asian way”?
Should we have Asian math teachers?
Are Asian tutoring centres better?
On a side note, here is a very interesting article on “Why are Chinese (and other Asians) better at Math?“