Importance of trial and error/ guess and check method, another maths question

[user789653241]

How important is it? Do all the children need to be able to do it that way?

My ds was doing the word problem meant for YR6.

Q:There were red and pink roses. The number of pink rose was 4 times as many as red roses. There are 21 more pink roses than red roses.

My ds done like this.
P = 4R

P = R +21

4R = R + 21

3R = 21

R = 7
A: 7 red roses, 28 pink roses

But it isn't really trial/error method, more like simple algebra. Is this acceptable?
But I can't really explain to him how to do it the way the question is asking.
Or if the child is capable, are they allowed to skip trial and error and apply algebra in primary maths? Do they have this sort of question in YR6 sats that requires different working out? (or do they lose points if they did it this way?)

As I am not native English speaker, I really struggle to explain concepts to my ds. He learns maths by himself, but I really want to help.

Can anyone explain how to do the trial and error method rather than algebra way? Or can I just leave it to him?

Given the support for Singapore maths and the methods used there, then I'd guess that trial and error will be used less and less.

Plenty of schools would encourage using a bar model to solve that question which is essentially a pre-algebraic model.

In the long run there's absolutely no need for him to learn the trial and improvement model. I teach secondary school students and even some decent GCSE students would struggle to tackle the question algebraically (not because the algebra is difficult but because it wouldn't occur to them to convert the question into algebra).

Your son is probably very unusual to be tackling it that way so young but good for him. It would be ridiculous to make him tackle that question by guessing when he can do it analytically.

Just thinking about that, hard do you suppose teaching trial and error might actually harm students' mathematical thinking? So they'd be more likely to use algebra for a question like that if they'd been taught to approach it differently from the start.

Thank you, sounds like I could let him do as he wants.
My ds has been coding since 6, so he has proper understanding of variables.
Even block type programming like Scratch uses x and y, so I wonder kids these days find algebra easier than older generation.

Rafas I'm not an expert in primary teaching so take this with a pinch of salt. I think trial and error is an OK method to teach in general but I have seen many able students put off all the way through to GCSE because the more advanced and unequivocally better method they want to use is "wrong" according to the mark scheme.

My DH learned variables via coding so you're probably right that that's helped him (although a kid that wasn't technically minded would never be convinced to start programming at 6 in the first place), I still think it's unusually impressive for a Y6 student, as I say I'm not expert in primary!

He is YR4! Like I said on other thread, he is probably 2e.

No worries, I was just questioning my own assumptions, really. I'd assumed that once children had been taught and were confident with algebra they would switch methods, but I can see why that might not be the case.

I wonder whether switching from trial and improvement to something like the bar model might be better for children's thinking in the long term.

If ds can work with algebra this well at that age do not worry too much about trial and error. The capability is obviously there to someone of that ability, but the hunger on this occasion/question for an accurate and straight forward answer became the easy priority. School books ask for the trial and error chapter to be taught so why not double check that ds understands the methodology involved and then let ds's sharp mind continue down the algebra route. Algebra will be a very large part of the coming years.