MATH - Is about spotting patterns. Not learning Times Tables. Opine.

[HarrowToCroydon]

MATH - Maths is not about learning times tables, it’s about spotting patterns in everything we experience and using them to plan and invent.

From a 7 year old Guardian article,
Reckon you were born without a brain for maths? Highly unlikely | Students | The Guardian

Would you recount your experiences where you or your loved ones were traumatised by Math.

I love maths.
Absolutely loved it

English and media studies traumatised me.

DD3 moved school in year 4. In her old school, they worked on a times table and when they got 12/12, they moved to the next one. She was at the head of the class, on her x times tables. Every week they would be tested. She would get several wrong. When I asked her about it, she said "It doesn't matter Mummy. Kieran is only on his X times table and he's the nearest one to me, so I'm not going to lose my place."

When she moved to the new school, they used Times Table Rockstars. They did questions on all the times tables. She came out of school saying "I didn't even finish my test and some of those kids finished with time to spare!" I said "Well, baby girl, you've got some catching up to do, haven't you?" Within a couple of weeks she was finishing the test and soon she was either top or in the top 2 each week.

Times tables are only effective if you can recall them quicker than you can work out the sum. It isn't enough to know them, you need to be able to call them to the forefront of your mind very quickly.

I know this was common and I'm sorry it happened, but sometimes there's a reason. For example, multiplying by 10 by adding a 0 works just fine until you get to decimals, when it doesn't work at all. Moving the figures one place left works every time and reinforces place value while you're at it.

Workings matter if you get the answer wrong. So you make a slip up on the first part, then carry the error forward.

My brother was investigated for cheating in his a level Maths for being able to skip steps in his written workings. Fortunately the school could prove hes always been able to do that...

From experience in seeing how my son was taught Maths at primary, they do seem to beat about the bush too much. Take number lines, yes, absolutely brilliant at the start to teach basic addition and subtraction and eventually, yes, negative numbers, but primary school still had them using number lines up to around year 4 or 5, even using them for multiplication and division. Then they moved on to several different ways of doing multiplication and division, all of which seemed pretty convoluted and complex and I kept saying to myself "just teach bloody long multiplication and long division" throughout years 5 and 6 (I remember we did it at primary school around that time). Of course, first thing they were taught at secondary was long multiplication and long division - just why waste so much time on "alternative" methods that are more difficult and protracted?

So, yes, I can see where you're coming from with your "just bloody learn them" comment. As I said above, same with prime numbers, not difficult just to rote learn, say, the first 10, but no, they don't do that, they teach an equation which takes longer and less accessible to less able students, which is capable of producing all prime numbers, yet, for school purposes, even to GCSE and A level, only the first 10 or so prime numbers are needed for the kind of algebra they're doing most of the time.

You have to get into the habit of showing your workings so that as problems get harder into multi step ones you know how to do it. It is good practice to unpack how you get an answer you can just 'see' so that when you can't see the answer you know what steps you need to work it out.

Furthermore once you get to GCSE level if you get the answer wrong (e.g. by a simple adding mistake) you can still get method marks.

It's maths.

The basics are the foundation, like the foundation of a house or the roots of a tree. Without it, you're never going to get far with Maths. Yet, the "foundations" are pretty easy to learn (unless you have a learning disability).

My son crashed and burned in Maths in year 8. He'd been "so-so" until then, but he just didn't "gel" with his year 8 maths teacher, and his year end test was a disaster, worst mark/grade he'd ever received in any subject (something like 30% when he was working at 75/80% in other subjects, including Maths in the past).

We spent that Summer doing "remedial" maths with him, nothing intense, just maybe 30-60 minutes per day maybe 3/4 days per week, going right back to tables, prime numbers, long multiplication, long division, etc. I printed off loads of worksheets of ever increasing difficulty (I think they were from Corbett Maths on the internet who had them graded according to age/difficulty).

In year 9, he started confidently and ended up top of his class and scored 95+% in the year end test. Then he went on to grade 9 at GCSE, A* at A level, and just got a First in his Maths degree at Uni!

Well that makes no sense. How can you get a mark for method if that method got you the wrong answer? Also doesn't explain how a method can be "wrong" if the answer is right. As both me and PP said, we were told off even when we got the right answer, because we hadn't used the "correct" method.

People seem to confusing ability with attainment
You can be lower attaining at this moment but have a very great ability

My point was that my "methodology" was entirely sound and acceptable, just different to the teacher's marking example they were following. I know the importance of showing workings, etc to get a few marks even if the end result is wrong as you can indeed still get pretty close to full marks if there's just a minor/accidental error along the way, due to ECF.

As for following a method, then yes, I always did that for lessons, etc., after we'd been taught a particular way, as obviously the teacher wants you to use that particular method if the questions are linked to a particular lesson. I was talking more about progress tests, end of year exams, etc., with just random questions based roughly on your cumulative knowledge, where any kind of logic should be acceptable.

Both are equally important IMO. Pattern spotting is crucial but many many problems in life are easier if the times tables are easily recalled.

We never argue about whether children should be doing spellings, or reading, or comprehension - we accept that literacy education should encompass all those things and ideally foster a love of reading.

Numeracy education is never treated in the same way and it drives me crackers. I was reading the homework in primary school thread earlier and there were so many comments saying only reading is important, or talking listing three important literacy tasks and no or maybe one on the numeracy side. It seems maths is to be tolerated and reading embraced.

So many adults are happy to say they're rubbish at maths but would never proudly admit to being bad at reading.

Fwiw, my eldest is in P2 and I've been really impressed with the way they've tackled early numeracy, they're clearly focusing on a very solid grounding in basic tasks (and, yes, pattern spotting) before moving on and I think it will really work in their favour.

Oh and the maths Vs math crowd can feck off, both are fine, both are clear and both are used in different regions. Just tedious to be carping on about that on what is an otherwise interesting thread.

The poster you replied to said getting it wrong due to a simple arithmetic error rather than using an incorrect logic, so that's entirely right to be awarded most of the marks if the logic worked (or would have worked except for the simple error).

As for getting the logic "wrong", well it shouldn't really be down to someone with only GCSE or A level in Maths to dictate what logic is wrong and what logic is right. The "logic" used by a pupil could well be sound, but just something that someone without a Maths degree (or higher), didn't know - after all, even the best Mathematicians won't know everything and won't "see" every pattern/logic.

Personally, unless there are signs of cheating, I'd say full marks should always be given for the right answer supported by some kind of workings/logic, even if the marker doesn't understand the thought process. Obviously, if the marker has proper grounds for believing there was some cheating, or just a pure fluke guess, then that's different.

It's a massive kick in the teeth to be down-marked when you got the right answer, by following your own logic, just because the marker/teacher expected you to work it out a different way!

@ColleenDonaghy

Fwiw, my eldest is in P2 and I've been really impressed with the way they've tackled early numeracy, they're clearly focusing on a very solid grounding in basic tasks (and, yes, pattern spotting) before moving on and I think it will really work in their favour.

Yes, it's good that all the "progressive" teaching nonsense has been scrapped for the younger generation. I was at school in the 70s, which seemed to be the tail end of the "traditional" teaching methods, and I remember some teachers saying they were still going teach "the old way" even though they'd been told to teach using modern methods (and not teach some things at all). Even through to secondary school, I remember teachers starting a lesson with "this topic isn't on the curriculum anymore, but I'm teaching it anyway because ....."

We've really screwed over a generation or two with "trendy" teaching methods that have proved not to work.

A method can easily be right and still get the wrong answer.

Say you had to solve 2y + 3 = 31

correctly subtract 3 from each side 2y = 28
divide each side by 2, y = 14

or subtract 3 from each side 2y = 28
divide each side by 2 but do it wrong y = 13

Right method to solve algebra, but you screwed up the easy division. Still get 1 mark out of 2.

Now the 'correct' method issue:

When you get to secondary they broadly speaking don't care what method you use as long as it is valid and thus consistently produces the right answer.

However at Primary they can be concerned with teaching a toolbox of methods for people to pick from. If they are trying to teach eg Napier's method for multiplication and you do it by a different method, then you have got the right answer, but failed to show you know the method they are trying to teach.

Some methods can work fine for 'smaller' problems but are too unwieldy for larger ones.

And at the other end of the scale, I teach a mathematical subject at uni and frequently the method is what I want to examine. The question will state the method to use and there will be zero marks for using another one.

Numerical slips will only lose a mark, that's not what I'm testing.

Method more important than results.

Well there is a difference between arithmetic and mathematics. Arithmetic is adding, subtracting, multiplication and so on. Maths is about much more than that - it’s a language almost, the language that expresses how the physical world works. It is much more than spotting patterns that’s for sure.

My Director of Studies at university (RIP, who was massively involved with STEP papers) used to have a saying 'don't worry about the 2s'. When integrating and differentiating you tend to get powers of 2 all over the place, and when teaching he might end up with a 4 where there should have been an 8 etc. But it didn't matter, it was the method that was important for us to understand.

Surely it’s both?

I agree with this! My Ds 18 struggles with times tables, cannot do mental arithmetic, cannot tell the time on an analogue clock yet got a B in advanced higher maths without actually putting much effort in, both his AH maths teachers said he could get an A if he bothered putting the effort in!

Well if doing say engineering it is both of course.

However it is a bit like if a teacher asks for a piece of writing.
They may want the pupil to concentrate on a specific aspect, and be less bothered about others: Use of imagery, use of connectives, SPaG, handwriting etc. English teachers don't necessarily mark / correct all aspects all the time. Also, even if they are marking everything, they may still not correct all errors. Is it worth correcting the spelling of picturesque if the pupil still can't spell house?

Question for the primary school teachers. .
Is there any reason why children don’t rote learn times tables for 5 minutes every day from year 2 (or whenever it is the start to learn times tables). I mean literally chant out loud (perhaps using songs etc) from year 2 to year 6, every single morning, without fail.

I’m sure this is what they used to do in my parents and grandparents generation, & it seemed to work.

My children did this at primary, but only intermittently, not consistently/every day.
My younger child still doesn’t know her times tables securely. We did rote learning at home for months until she learned them, and then a few months later she’d forgotten them which was such a surprise to me. We did them at home again - sane thing happened. It seems to be a retention issue rather than a learning issue.

I guess we need to reinforce the learning at home intermittently every few days, but given it’s such a fundamental party of maths which is this not done at school?

Workings matter because even if you get the answer wrong, you can get points for workings.

I have this argument with my son quite often, because his mental arithmetic is very good (Excellent teaching at primary school, coupled with natural ability I think - although my mental arithmetic isn't good). He's dyspraxic, so finds the writing extremely tiring and would prefer to shortcut, but it's important that he doesn't, and that even though it's hard, he works neatly, as otherwise the teachers can't give him marks if he makes a silly mistake.

And actually, it's not just about marks - it's also about being able to re-trace your steps to check, instead of having to start over. Sometimes the mistake will shine out at you as you look at your step by step workings again.

AND it's about being able to follow a process - which stands you in good stead for anything from cooking to physics to knitting or following/giving directions.