Gus Hubbard: Classroom maths provides few answers

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Opinion

Recently Campbell Live contained a segment where two staff members, both of whom had been A students of mathematics at school, sat NCEA maths exams to check out if the standard of the material was declining. Both floundered at Level 2 and achieved very average results at Level 1.

This, the programme suggested, meant that standards nowadays were at least as hard and probably harder than in the past.

However, there is another explanation for their lack of achievement. When we learn material by rote, that is mechanically and without understanding, which we have no subsequent use for, then it quickly fades from memory.

Campbell Live missed the really important point: why the blazes would you want to be able to pass this exam? Apart from achieving NCEA credits.

The bulk of the paper consists of the stereotypical exercises in algebraic manipulation most of us have suffered through at school. Routines taught mechanically and endlessly rehearsed by page after dreary page of examples. Two things can be said about this.

Firstly, it is pointless and the Ministry of Education should know this. A research report, The Mathematical Needs of New Zealand School Leavers (1992), which it funded, makes it quite clear there is no application for this endless routine in the lives of those it is inflicted upon in school. That was more than 20 years ago and the message still hasn't got through.

Secondly, endless hours of students' time are spent learning to do things which they will never need and which can be done by electronic devices such as hand-held calculators anyway.

Anybody who has spent any time teaching mathematics will have been asked by students: Why are we doing this? What's it good for? When will I ever use this? The content of this exam has virtually no use in the future lives of school leavers and is the antithesis of everything that modern educational thinking says maths education should be about.

As well as the exercises, the paper has two problems which purport to be about life situations. As always they are simply thinly disguised exercises in street drag masquerading as reality.

Thirty minutes after a patient is administered his first dose of a medication, the amount of medication in his bloodstream reaches 224mg. The amount of the medication in the bloodstream decreases continuously by 20 per cent each hour.

The amount of the medication M mg in the patient's bloodstream after it is administered can be modelled by the function M = 224 0.8t - 0.5 where t is the time in hours since the drug was administered (NCEA Level 2, 2014)

Then follow questions which involve putting numbers into the given formula.

Notice that the all important first step, the sine qua non in this "problem", of turning the words into a formula, is done for the student. All that remains is the number plugging. Real life doesn't work that way.

Every occupational group has a professional body which represents its interests.

I would advise the ministry to write to each of these organisations and ask them to get their members to submit examples of the types of problem which they need to solve in their work.

Sciences, the medical profession, business, and various trades in particular should be a prolific source of material. This would tell them what the consumers of education, the workaday world, really need to know and provide a source of genuine examples for students to learn from.

And when that unmitigated disaster, the Early Numeracy Project, fades away, as School Mathematics and Beginning School Mathematics have before it, then the ministry could begin the next version by looking at its own bold, colourful front door sign: 1234567890 (http://nzmaths.co.nz/teaching-numeracy).

Does it not even know that zero belongs at the beginning and not the end of the sequence of digits and how absolutely crucial this understanding is in getting children to make sense of our number system?

Our nation's children will never be better at mathematics than the ministry's curriculum material, and enforced testing regime, allows them to be.

The ministry, not our teachers, is the weakest link in the chain.

• Gus Hubbard has spent a working life teaching maths at all levels from pre-school to tertiary. He is the inventor of a widely used maths teaching aid, BeaNZ.