I think Mr Yamazaki is onto something.
I have five children and in my opinion, the way they were taught maths did them no favours.
There are so many things on the curriculum and each of them with their “helpful little tricks” to speed up the way our children can answer questions.
But none of the tricks make even the slightest contribution to a deeper understanding of the subject and surely, that must be our goal!
Son number three gave me the sharpest understanding of the situation. He was definitely a bit(!) lazy and refused all my offers of help in the run up to his exams (for 16 year olds).
With less than a week to go, I could stand clear no longer and asked him to show me his progress. After some heated debate, he confided that he had abandoned maths months before as the battle was irretrievably lost. I was not convinced it was the case and he agreed to spend 6 hours with me (bribery may have played a part).
We took the past papers to my garden office and started to work out what he knew and didn’t know. There was a lot that he didn’t know.
After some soul searching, I concluded that I would help him to learn one thing in detail and then how to apply that one thing to a specific class of problem. Respectively, they were:
- How to transpose formula
His understanding of transposition was almost non existent and had been corrupted by the helpful tricks.
We spent many hours with fruit and counters and the whiteboard transforming mystical strings of letters and symbols into real world things he could understand:
- y = mx + c > or > cost of night out = beers * cost of beer + taxi
And that if he knew how much he’d spent, the cost of a beer and the cost of a taxi, then he could work out how many beers he must have drunk.
First we just did it intuitively (because our brains are smart enough).
Then we deconstructed it to extract what we’d actually done.
Then we generalised.
We did it again and again and again with different examples.
I introduced the formulas for triangles and trigonometry. The concept of a function and reversing a function. How to rearrange depending on what you know.
He worked harder than I’ve ever seen him work (not a very demanding comparison at that time!).
At the end, he was like a different young man. The battle was definitely not a foregone conclusion. If he was lucky with the questions he could do quite well. He would have to be quite unlucky with the questions to actually fail.
He got home after the exam: “I absolutely nailed it dad!”.
He doesn’t really suffer with lack of confidence so we waited for the results.
Maths: Grade B
By focusing on fundamentals, and with the luck of a fair wind, we went from almost nothing to a Grade B in one evening.
Mastery of a few principles must be better than a ragbag of party tricks.
I have no confession, this story is true!