The Problem with how Maths is taught in Australia

The Problem

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:

  1. Asian-taught students are quicker in arithmetic (multiplication, division) because of memorising the times tables off by heart at an earlier age.
  2. 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?

10 comments for “The Problem with how Maths is taught in Australia

  1. Shannon
    August 11, 2009 at 11:11 am

    This idea is completely ridiculous. I figure you are smart as you tutor maths however you seem unable to think about what your saying. Are you indeed asian cause obviously your logic seems to be equal to null. We may have our errs within the Australian education system however we are not breeding a generation of robots where thought is chastised and how minds are only able to go as far as thinkers before them have as they are limited by the formula’s they possess. Australia is creating thinkers. Thinkers that go beyond what they already know to discover and create other things that may aid humanity. It is fairly obvious that western cultures are more advanced with their teaching methods as you can never find in history the theory of relativity or any discovery of high level maths within asia as they tossed it aside to become a race of copiers and drones. To even suggest we should teach like asians do is completely ridiculous. I hope that people who can actually make a difference is far from your frame of thinking because it will be a sad day when we begin migrating to the asian “way”.

    • tutortales
      August 12, 2009 at 1:03 am

      Firstly, thanks for commenting and sharing your difference of opinion.

      However, I don’t believe that the “Asian way” of teaching necessarily churns out “robots” and “drones”. Whilst it does sound depressing, I think it actually lays really good foundations for grasping the “basics” of Maths (or any subject) at an early stage, rather than limiting them as you claim. There are necessarily some things that require rote memorisation (e.g. the times tables in Maths). This is especially so when you consider how the NSW HSC exams are built to test students upon memorisation in practically all subjects (may be this is a problem of the HSC exams itself). For instance, English exams practically test your ability to remember a prepared essay.

      I have no problem with teaching students to be thinkers. That’s fantastic. Unfortunately, the NSW HSC seems to rewards students 70% on memory and 30% on ingenuity. Our prepared English essays are 70% of the what we write and the other 30% is how we’ve changed it to answer the given question.

      You also claim that Western teaching methods are “more advanced” based on “history”, without explaining in any way what it is about Western teaching methods that has resulted in these “great discoveries”. What is the causal link?

      I’m not arguing that the Australian education system should be completely replaced with an Asian one. I’m firmly believe that both have advantages and disadvantages and maybe the best answer lies in a careful study and integration of the two.

      That way, we don’t end up with a society, where students accelerate at Maths yet lack creative thinking, or a society, where students can think outside the box, but are slow in grasping the fundamentals. In both situations, students are disadvantaged, because they lack one or the other.

      TT

  2. August 11, 2009 at 4:46 pm

    Damn, I am caught between what I want to tutor people next year after my HSC. On the one had, I’ve seen some really really bad essay writing. Like I wouldn’t even consider them essays…

    On the other hand, teaching maths is less stressful but I don’t really feel tutoring people for Prelim and HSC Maths, especially Extension 2 which can be so frustrating to teach. Ideally, I would love to tutor people for selective but that seems kind of overkill. Maybe Yr 7-10 if I can find willing people.

    The Asian thing is so true though. I remember when I was 5, I learnt my times table off by heart in one day when my mum went out shopping. Although she threatened to “punish” me if I didn’t learn it by the time she got back. Plus now I have to literally translate the times table from Chinese to English. No problem now as I do all my Maths in Chinese but was a bitch in primary when we had to say our times table out loud. I ended up adding through the times table rather than translating. Dunno if you understood that.

    In answer to your discussion.

    1. Teachers are meant to teach “the Asian way” aren’t they? Memorising formulas is faster than what you said but I guess understanding the theory behind the formula helps you remember how to do the question. Although I’ve never had a problem sticking to the formula, so yes, Asian way ftw.

    2. Asian maths teachers are not the solution. We have a fob Maths teacher here at school and sometimes, we have to strain alot to understand her theory lessons. What we need is qualified teachers with higher standards and expectations. We have the best Maths teachers at James Ruse and they are excellent because the expect the best from us students.

    3. Asian tutoring centres only seem to work purely because they apply the “work factor”. Thomas Jefferson did say that a genius is just someone who does their homework. By dumping booklets of questions on you, you naturally adapt in order to survive. Quite frankly, I wouldn’t know what non asian tutoring centres are like. I’ve always had private tutors my whole life.

    P.S Reading your blog is quote interesting and has taught me some language forms and techniques I had discarded/forgotten/ been unaware of.

    Lots of thanks, from long time listener, first time commenter =D

    • tutortales
      August 12, 2009 at 12:29 am

      Thanks for taking the time out to reply! Your comments are really interesting.

      I’ve actually started drafting a post about whether it is “easier” to tutor Maths or English! I find English tutors are more in demand, but Maths is a lot easier to tutor (maybe because I only tutor up to Yr 10…). With English, the syllabus changes, there’s texts you’ve never read etc….

      I agree about the “work factor” in Asian tutoring centres. The one I currently work at is incredibly organised and systematic (it’s impressive but scary at the same time). They find out the weaknesses of the student and then completely eliminate it through revision, revision, revision until they get either 0 answers wrong, or only 1 wrong in a “booklet”. I found this method actually worked really well, as some students just need revision that can only be done through “doing more work” coupled with an engaging tutor that explains their errors to them. Sensibly, this system only applies to Yr 10 and below students.

      TT

  3. August 12, 2009 at 6:19 am

    Yeah, English tutors are more in demand and the pay is far better with better working conditions (1 on 1 or 1 on 2) , but requires alot more work and preparation. Since I’m familiar with the new syllabus, being the first year to sit through the new English syllabuses, I’ll probably try tutoring English mainly to help fund my materialistic wants next year. Although that plan falls through if I end up going interstate… =.=”

    The Australian education system for maths really should involve more memorisation of formulas rather than spending alot of time behind the theory. The problem is how low the Maths standard has fallen as a cohort. Most of the State don’t go above 2U Maths. A big problem is that the standard expected of students each year are dropping. There really are only three things tutors are meant to do.

    1.Go over topics students don’t understand or revise forgotten knowledge
    2.Push students to work harder
    3.Provide insight on exam and study techniques

    Through more memorisation of formulas, the time saved would benefit students across the state. As students, we are accessed on how well we do. If we understand the whole theory behind one topic, yet fail to correctly implement another, I rather students acts like “drones” and regurgitate memorised formulas. I believe Shannon does not give enough credit to students and memorisation. Coming from a school that tops the State every year, memorisation has become our backbone. Creative thinking is crucial. Yet by knowing the formula and repeatedly cycling through questions, one will eventually understand the theory behind it naturally. We are not trying to produce the next Mathematicans here. We are trying to get most students in the State to rise above the level of 2U maths. When presented with challenging questions, good students will think outside the box.

    I do however see Shannon’s point in creative thinking. Whilst this is not apparently obvious in Maths, it is in English. Everyone in my school memories their essays. That being said, the majority of students don’t act like “drones”. Whilst ideally, I would love to learn and understand a module very well, write a variety of different essays and turn up to the exam without having to memories prepared essays, there just isn’t the time for that and is far too risky. Our teachers at school teach us to address the question, with us regurgitating points rather than whole essays and I have found this has worked very well compared to people to write word for word what they wrote previously.

    P.S I don’t see how Shannon’s point of Western Culture has any merit behind it at all. Western Culture is not “far superior”. Most of the world’s greatest inventions has been a result of non western invention and the hypothesis that it’s because they create ‘thinkers” compared to the “drones” of Asia is utterly ridiculous. Take the best of both worlds and chill. I think the stereotype that Asians are “good at Maths”, speaks for more than itself that we must know generally know something about the subject.

  4. mishmashmosh
    August 13, 2009 at 5:16 pm

    I discovered the same problem when I was teaching my students. The “Asian method”, I find is more straight-forward, more logical and easier to comprehend.

    I agree with materix01 (HI HI! I don’t memorise my essays!) about Asian Tutoring centres and the “work factor”. I used to work at Pre-Uni and every single week, the kids would get a module in each subject (approx 6 back to back pages) to hand in the following week. How good/accurate/speedy you are depends on the quantity, and the effort you’ve put into practising and revising. Once you learn something, you won’t remember it forever; you have to keep practising it and make sure you don’t become rusty. Asian tutoring centres are good at pumping oil in those easy-to-rust areas and that’s why kids who get tutored there can get such good marks.

    I think hammering a formula into a student’s mind is only useful when they understand how it works; what’s behind it, the working out behind that. I guess I opt for the more “intuitive” way of education :) But once you get the hang of the concept, formulae are quick and useful. I believe there is a need to grasp the logic and to understand how it works. Sort of like driving a car. You want to know what that pedal does before you step on it, right?

    I totally love my dad for making me memorise all my times tables in year 1.

    So that’s my 2c worth.

    • August 14, 2009 at 8:40 am

      It’s you mishmashmosh
      Lol, shouldn’t you be studying for trials?
      Wait, shouldn’t I be studying for trials?
      You have exams everyday… I’m excused because my next exam is on Monday XD

  5. Blehs
    November 2, 2009 at 4:37 pm

    The Asian style of working has its pros and cons, but im willing to bet that out of the top 50 students in NSW, at LEAST 45 of them will have adopted an asian style of working.

    It might not be the best, most enjoyable way to work, but memory is what gets the marks in the HSC.

  6. D
    June 17, 2011 at 12:02 pm

    Shannon, you must realise you are being prejudiced.

  7. Ted
    July 26, 2012 at 7:18 pm

    Mate you’ve got this completely wrong, If all you want is for kids to remember formulas then they don’t develop the part of their brain that helps deal with complex situations and things they haven’t encountered before. For example, how could you expect a student who remembers formulas to excel in the ext 2 maths course when a large part of it is actually problem solving rather than memorising formulas.

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