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.

"investigated for cheating" This is sad, borderline criminal on part of the examination "system".

This shows a mindset of there is only one way to do it, our way.

Such people should be named and shamed.

Agreed.

enquiry vs. inquiry.

Provides for hours of intellectual discussion. Goes nowhere. Bit like the upside down quiz, which when I try and explain to another culture, I get blank stares and no discussion.

Of course it isn't. A maths exam tests method, if you can't do the method you don't get the marks.

I've awarded zeroes before in class tests where a student has started to try a question, clearly not had the foggiest and copied the numerical answer from the person beside them. Harder in an exam hall to copy from the person beside you but there's still smart watches, notes hidden in the calculator, calculators with more functionality than allowed etc.

When we suspect cheating we investigate, able students like OP's brother will be able to prove their ability and the mark can stand.

Any suspicion of cheating should be robustly dealt with for the sake of the honest students.

The point of my post was not so much to emphasise the Guardian article.

It was to highlight that Math could also be introduced by ways of pattern recognition. And that it may be an appropriate time to delve into other such methods, and look beyond rote learning.

I get some of the posters who say "just get on with it and memorise", fine for many, but not all. For the outlier cases, there may be absolutely brilliant children at Math, who are let down because they struggle to rote learn.

We work in this new field of A.I. (and Machine Learning). The little what we understand in this field, we see it being a gigantic machine simply looking for patterns via a Rote Method. Such an approach reminded us of our childhood learning. And we found the Guardian article, from an era when very little was talked about in A.I.

(Apologies to the poster who commented on my Grammar, our middle son already pulls us apart on this matter).

"if you can't do the method you don't get the marks."

And if a student deviates from a "set method", would they still get the appropriate mark?

Who is 'we'?

We have home schooled 2 of our 3 children to a certain age. It is hard, very hard. And thus we take interest in such articles.

"Rote learning" not a problem, but as parents when we try and do this with our own children, it is painful.

If we were teaching other children, not our own, it may not be a big problem for us to put our foot down. But with our own children, it is hard.

Wife and Husband, 3 children.

There are some things where rote learning is the only way something will stick. Times tables are one and irregular verbs in French (and other languages) are another.

When you conjugate a regular verb it follows a pattern, when you conjugate to be or to have it doesn't follow any kind of pattern. When DD was learning French at school she couldn't underatand why this was the case, so I just said "it just is. There is no explanation, so you just need to learn it by heart"

And if a student deviates from a "set method", would they still get the appropriate mark?

If it is correct, I think so, but I'm not a maths teacher. Perhaps @noblegiraffe can advise?

In the stuff I teach, no. If I need them to calculate the parameters by maximum likelihood estimation and they use the method of moments, then they haven't done what's asked. They might get a mark or two for the numerical answer but they'll lose all the marks that demonstrate their understanding of maximum likelihood estimation because they haven't done it.

If it's general reasoning not a specific method I'm testing, then the question won't specify a method and anything goes.

So it depends very much on the course.

Again, this is university level, I've no idea how it works at school but I assume it's similar.

I struggle with Grammar, someone here already posted. What you wrote, I cannot understand. Vowels, Consonants, Verbs etc. frankly I have no clue.

Yes, I can cobble together a sentence. And I put it down largely down to the advice I received from one of key people in the Esperanto community. "Read Fiction". Which is what I did. This saved me in English.

Taking the method you mentioned, IF a student could demonstrate a "simpler way" by use of another method when certain parameters are concerned, would they be in good steed? I guess they would need to do this in the classroom, not exam time?

If they suggested it in the classroom, I'd commend them on their knowledge but explain it's not what we're covering. They need to know methods X, Y and Z, because those three methods won't always give the same answer and won't all be suitable in the same circumstances, even if they're all suitable for a particular example. They can't just learn method X because it's easier.

For final year or postgraduate students, they are more likely to be assessed on their reasoning and critical thinking - so the question may allow them to pick a method and justify their reasoning.

It was to highlight that Math could also be introduced by ways of pattern recognition. And that it may be an appropriate time to delve into other such methods, and look beyond rote learning.

Not everything is pattern recognition. To be honest, hearing this repeatedly said is flashing me back to Umi Zumi with their box-ticking educational requirement...

Taking the method you mentioned, IF a student could demonstrate a "simpler way" by use of another method when certain parameters are concerned, would they be in good steed? I guess they would need to do this in the classroom, not exam time?

For the vast majority, they need to be able to demonstrate that they understand the method being taught. The point of teaching a variety of methods is to give children the tools they need for the future. If they only know one way (eg. Completing the Square or only using the formula) then they don't have all the tools.

This applies in so many situations - I'm a programmer, and perhaps someone I work with can sort a list using quicksort, and it'll work, but if they don't know any other way, they don't know if that's appropriate for the situation, they might (likely are) missing much better (faster, more efficient) ways of doing something.

In teaching, including subjects with correct answers, the point of the exercise isn't just to get the answer, but to know how you got the answer, so you can apply it to other situations.

And as to AI - yeah, I've worked with it - it's useful for some things, it's good at some things, but it won't be replacing the people who have put in the effort (and have the ability) to get an answer multiple ways, to evaluate the options and pick the best way for the situation, and anyone relying on it to get their answers for them is setting themselves up for a massive fall.

Re: set methods. I think in KS2 SATs (correct me if I'm wrong please, primary teachers!) the govt wanted children to use e.g. column multiplication for long multiplication so if you use that on a 2 mark question but make a silly mistake (e.g. 2x3=5) but the rest is correct, you will get 1 out of 2 marks. If, however, you used Napiers or a grid method correctly but did 2x3=5 in the middle you'd get 0 marks.
At GCSE, however, we don't care about column multiplication and all of those methods with one arithmetic mistake would get you 1 out of 2 marks.

For other questions, generally any valid (i.e. mathematically correct) method that gets you the correct answer will get you full marks. The correct answer with an incorrect method (i.e. something that makes no sense but coincidentally gives the right answer) will get 0 marks. However, the correct answer given on its own with no method will get full marks, unless the question specifies that you must show your working.

There are instances however where method is specified e.g. "using an algebraic method, solve these simultaneous equations" to stop kids using trial and error, or at A-level "show detailed working" on e.g. integration to prove that they can integrate algebraically and not just stick it into their calculator.

Methods that are outside the scope of the course are fine - if a kid used vector product which is not taught at maths A-level to solve an A-level vector problem, that would be ok.

Why do we want kids to show their method? Because maths is about presenting solutions and not answers. It's about logically arguing that your answer is correct.

It's useful in many situations - e.g. if your builder presented you with just a bill for £5000 you'd say "hang on, can I see a breakdown here?"

If a mathematician said "I've proved Riemann's Hypothesis!" Likewise you'd be keen to see the working.

@ColleenDonaghy

Of course it isn't. A maths exam tests method, if you can't do the method you don't get the marks.

What if they use a different valid method? What if they see an alternative method which the teacher/examiner doesn't know/understand themselves?

I can understand a specific test, say, after a lesson, that only examines the exact method taught in that lesson, but totally disagree with penalising a "different" method in an end of year test or formal exam.

I've explained this above - understanding method is just as important as giving the right answer.

The stuff I teach is accredited by a professional body, they need to demonstrate they understand methods X, Y and Z they can't just choose X.

They absolutely do and, in England at least, the government checks they do:

What does this even mean? By low ability I mean children who do poorly in maths. They might be rich or poor. I mean children who I've taught and taught and taught but who remain at a level several years below their year group.

Apologies for mis-reading your post.

As a secondary Maths teacher, with 2 children in Primary a lotbif what is said on this thread doesn't ring true to what I have experienced.

I do lots of pattern spotting in my teaching, tables I reiterate by using a pattern spotting exercise.

My children were reception/yr1/yr2 during covid so I saw a lot more of what they teach and how and it makes sense. Some if it as a maths brained parent in my head I queried, but it really breaks down the systems so understanding is hugely improved.

I've been teaching 15 years, I can see a massive improvement in the maths skills coming in from Primary with the new curriculum.

To the PP whose child is at Oxbridge, saying Primary teaching is done badly, firstly its changed since they were there, secondly I've worked with maths teachers who went to Oxford and they struggle to grasp why students don't just see things they do, same with incredibly bright students they lack the empathy in understanding how to unlock what they can just see. Teaching maths is vastly different to being able to do it.

Another PP asked if in an exam students would miss out if the question was answered using a different method - as a GCSE examiner - it depends! If you have been asked to calculate something using a certain method and go off piste you won't get full marks possibly one if you have the right answer unlikely though. If no method stated as long as you show how then multiple methods are allowed, one exam I marked had 6 alternative answers and you could switch as well as once you figured out 1 value, you could use it differently! Workings show your train of thought, my two best students last year used workings to figure out how rose it would work, considered what ifs.

Lots of comments on this thread are related to how you learnt maths, or memories off it. In practice things are similar bit also have moved on hugely. Processes are the same but explanations are vastly different.

"I've been teaching 15 years, I can see a massive improvement in the maths skills coming in from Primary with the new curriculum."

Your comment is heart warming, in that change is happening.

Kudos to the British Education system, where they take risks, some which do not work out.

Compared to the French and Indian education systems, where change is slow.

Teaching maths is vastly different to being able to do it.

IMO teaching maths - or any subject is a very much under-appreciated skill.

It was to highlight that Math could also be introduced by ways of pattern recognition. And that it may be an appropriate time to delve into other such methods, and look beyond rote learning.

Pattern spotting is literally what happens in primary. But there comes a point when you have to cut your losses and just learn the values.

RE method marks. If a method is valid (any method), unless the question asks for a specific one, then yes you get marks.

There's so much BS in that article and your thinking OP.