Yesterday, The Age published an article that represents much of what is wrong about discussions of maths teaching in Australia. The only consolation, as far as I am concerned, is that I am often told that people don’t actually think these things. Here, we have documentary evidence.

The piece starts by lamenting Australia’s stagnation in PISA maths. It is debatable as to how much attention we should pay to this measure but, given this opening gambit, it makes an interesting lens through which to examine what is being proposed.

**Textbooks**

The article encourages us to ditch textbooks. Simon Pryor, executive director of the Mathematics Association of Victoria, and clearly someone who should know better, is quoted as saying, “We advocate throwing away textbooks … teaching to a textbook should not be the sole thing that the teacher is doing.”

Firstly, this is a non sequitur. You can possess textbooks without teaching to the textbook being the sole thing that you do. Secondly, there is plenty of evidence that high performing countries, as measured by PISA, consistently make use of good quality textbooks. If anything, they make more use of them than we do. Aided by a stable curriculum, these texts can be refined over time, adding to a level of curriculum coherence.

Tim Oates makes these very points in an important paper for Cambridge Assessment.

A textbook-free maths department is not a nirvana of personalisation. It is a department with a large photocopying bill where teachers are all scrabbling around at the last minute for resources that are loosely relevant.

**Rote learning **

Apparently, we should be moving away from ‘rote’ learning multiplication tables. I suspect that this is not what they are doing in Shanghai. Again, we seem to be presented with a false choice. Either children learn their tables through singing a song and cannot tell you what 6 x 8 is without singing the whole thing, or they don’t learn their tables.

Has nobody ever heard of times-tables grids where children are quizzed on their recall in a random order? Why is it not possible to both memorise the answer to 6 x 8 and to know what it means? Indeed, this is important.

If a child is busy trying to work out a simple multiplication like this from first principles then she cannot also attend to other aspects of a question. This leads to something known as ‘cognitive overload’ and is a key reason why a lack of knowledge of basic maths facts impairs performance on more complex problems.

**The ‘real’ world **

Why is maths held to a standard that no other subject must meet? We never talk of how to solve mundane, everyday problems with knowledge of Shakespeare or the history of the Australian Federation. We see these things as worth knowing in their own right. However, when it comes to maths, it’s only any good if we can directly apply it to a contrived problem about how much paint we need buy in order to cover the garden shed or something like that.

I do not buy the argument that this leads to greater motivation, particularly in the long term. I also like the quote attributed to Jim Rohn, “Motivation alone is not enough. If you have an idiot and you motivate him, now you have a motivated idiot.”

The Australian future does not need *motivated* mathematicians, it needs *competent* ones. And becoming more competent at something can indeed be motivating. This is why the children taught maths explicitly in Project Follow Through saw the greatest growth in self-concept. I suggest that we should first teach maths *well* then see what happens.

**Formulas**

The anti-formulas rhetoric of the article is pure constructivist dogma. I suspect that most maths teachers don’t simply teach formulas, they also explain where these come from. The idea that students should discover fundamental theories of mathematics by themselves, whether by folding pieces of paper or otherwise, is a recurring and damaging theme in the history of education. Let’s face it; this stuff took *professional mathematicians *a lot of time to work out. This paper by Kirschner, Sweller and Clark is probably the best on the subject.

Where is the evidence that this is what they’re doing in Singapore?

**Future fearful**

Reading this nonsense, any aspiring maths teacher could be forgiven for thinking that the future involves personalised learning in mixed ability classrooms where children play with plastic blocks rather than learn the basics. This is highly damaging and, if implemented wholesale, would likely lead to further declines on international tests.

If we really wanted to learn the lessons of PISA then we would be encouraging whole-class explicit instruction enriched with quality textbooks.

Reblogged this on The Echo Chamber.

You are bang on accurate Greg – thank you. If the educrats had their way, children would be jumping up and down and painting spotted pictures under the guise of “understanding mathematical procedures”. It’s hogwash. Unfortunately the only ones profiting from all this, are the maths consultants and tutoring centres. And truth be told, I don’t necessarily think the tutoring centres are all that happy seeing the upswing of innumerate kids.

What is wrong with these people?!?

Yes, what rubbish. The argument against learning times tables by rote is an often repeated one. My kids know their times tables by rote, no thanks to school, but thanks to Kumon and the parents. They memorized them. they didn’t sing a song, but there is nothing wrong with a song if it helps. They just went over and over them (repeated practice) until they were committed to long term memory. They do not have to go through the entire table to arrive at an answer. Nor do most kids who have memorized them. They can answer any table thrown at them out of sequence. In addition, they know exactly what the times tables are. AS quicker way of adding numbers. They actually knew this for a number of years yet they couldn’t progress as no one at school had them learn their times tables so they were stuck in limbo – knowing the meaning but unable to execute an algorithm.

Like you, I think Tim Oates’ argument for text books is an important one – it is the same argument that was made in the 1970s by the Nuffield Institute (though in their case, it was linked to an over-emphasis on discovery). Though I think the potential for digital technology to act as a medium for disseminating instructional activities will eventually trump the paper text-book.

Bang on. As usual.

Exactly! In addition, if my children had had a Maths textbook when they were at highschool, I would have been in a better position to give the help when they asked for it, instead of endeavouring to decipher what the grubby worksheet required them to do.

I’ve gone into more detail about CLT and times tables here if you’re interested: http://criticalnumeracy.com/teaching-maths/time-tables-immemorial/

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That is an excellent point. And so it now shall be.

Posted this under Andrewworsnop piece but adding it here to for feedback.

I wonder what creates this need for some to create a false dichotomy between learning facts and understanding. While learning the tables it is useful to exercise the understanding of commutative, associative and the distributive properties of integer addition and multiplication. That means you can do more interesting things involving single digit multiplication than just memory work without knowing all the tables. Jumpmath.org texts do a good job of working through the tables in the easiest order. (Hint one; leave the hardest to last and use commutativity).

Once you have the tables memorized it is not as if there are no more ideas where understanding the properties of integers is useful. Lots of basic number theory problems involving repeating decimals or fraction to decimal conversion are readily available to exercise understanding.

That is one of the beautiful features of mathematics: there is never a point where there are no more problems that require understanding as well as knowledge and these are never very far from what has become easy.

What happened to those down playing the knowing of facts so that they missed this amazing feature of mathematics?

Perhaps I am misjudging them and there really people on the other side of the debate arguing for memorization without understanding. Has anyone seen one of these people?

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I read the same article and had the same thoughts as you. One of my kids goes to one of the schools mentioned – funnily enough had to do a maths test to get in.

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