Alternate methods in maths

[TeenMinusTests]

DD is re-sitting maths GCSE as she missed y11.

New college teacher is teaching different methods for things DD can already do and she is finding it confusing & stressful. (College is already highly stressful for her - huge backstory).

So, should I say it is fine to ignore teacher, or what?

I think the annoying thing about grade 3s this year is we can't see how close it was to a 4.

I have been referred to as a 'crazy teacher' but I have my own personal theory that the more senses you involve in learning the easier it is to retain. So eat polo mints to revise and eat them in the exam too.

So ideally you don't just want to teach a method you want a child to explore, so at home, to back up the teaching, do things that involve percentages and fractions.

That could be making a sponge cake batter (weigh 2 eggs and use that weight to measure the fat, flour and sugar) and divide it into bun cases, so you have 100% cake batter, what percentage of the batter fills 1 bun case? And how much does that weigh?

Chopping things up, it could be paper, cloth, chocolate, actually chocolate cut into squares works well.

Blocks of butter / lard /marge - can you cut 25g? What percentage of the butter have you cut off?

I'm not obsessed with cooking, honestly, you can also use money, collect change and make up £1 in pennies, 2p, 5p etc then move on to mixed coins.

How many mins in 1/2 an hour? What percentage of an hour is it?

Please do make contact with the teacher, I've done lots of supply and welcome any input from students and parents as to why a student didn't achieve their potential.

IN a foundation set, those sorts of 'tricks' are often the best way for students to do basic percentages. 25% - divide by 4, 50%, divide by 2, 10%, divide by 10, (possibliy 1%, divide by 100), and then from those, make whatever percent you need. Often the questions only use 25% or 50%, especially on a non-calculator paper.

If you teach them divide by 100, many of them would struggle with that, because they might try to use bus stop method or some longer calculation like that because they aren't confident with place value. If they do divide by 100, and are then faced with a decimal, they don't necessarily know how to multiply with decimals. And then if they do know how to multiply, they might get confused with using a 2-digit number like 25. Much easier to do something like 36 divided by 4 than for them to try to do 3.6 x 25.

yes it would be great if they understood that 25% is the same as 1/4, and that finding 1/4 is the same as dividing by 4, and chances are that they've been shown that many many times ,but if they're struggling with maths and are at a resit level, chances are that it hasn't really gone in or made sense. If I had lots of time to go back to the beginning and start over with some pupils with basic fractions etc, that would help - but often they are much more interested in merely passing the exam, and don't really care about the 'why' of it. They know that there are non-calculator ways (the shortcuts) and calculator ways that may be faster, but many of them prefer the shortcuts along with 1%.

But that said, I'd be happy if someone wanted to use another method that they had remember and were correctly using, if they could do it fast enough and without a calculator. I might point out that there are faster methods (like dividing by 4), but they'd certainly get all the marks for doing it a longer-winded way.

Thank you all, this has been really insightful.

Thanks especially for noble for reminding me about the non calculator paper and why therefore these are needed rather than just faster. And thank you to other maths teachers who have explained how other pupils think too.

For clarity my DD missed all teaching in y11, and the summer term of y10 . Prior to that she was doing OK in maths due to a combination of great teaching at school and regular support from home.

Extreme rustiness, a new college & teacher, diagnosed anxiety, and some SEN mean that she really isn't well placed to be in a GCSE resit class right now - however that is where we find her due to government funding rules.

I think maybe we will need to try a 'flipped learning' approach, where if the teacher can let me know topics to be covered, I can remind DD in advance in a 'safe environment'. Though I'm not sure DD has bandwidth for that right now.

If we had done that for this, I could have ensured DD understood & remembered where the 'shortcuts' come from at her own pace, and then all would have been well.

@noblegiraffe

Why teach a bunch of shortcuts to DC who by definition aren't great at maths, thus giving them a collection of apparently unrelated facts, instead of teaching just the one method?

Tbf those methods are generally taught from primary school and I would expect even bottom sets to be familiar with them.

They're the expected method for the non-calc paper. Y/100 x Z (or converting the percentage to a decimal and multiplying) is the expected method for the calculator paper - I'd be surprised to see any student using that on the non-calc paper.

Yes, they aren't shortcuts, they are equivalences that children are expected to know off by heart in year 6.

I do know they are equivalences!
I do know they are taught in primary!

That's really not the issue.

Just because something is taught, it doesn't mean it is retained. DD has trouble retaining certain types of information.

I think that this has really highlighted for me how hidden some of DD's difficulties have stayed over the years.

It sounds like she is a very different sort of student that the type who normally have to re-sit maths, so it's not surprising that her preferred method of learning might be different than a typical student in that situation - I would quite enjoy teaching a student who had to resit but was actually more capable and wanted to know the reasons for things rather than just the tricks, but I teach one-to-one, so it would be much easier to adapt. The teacher will be used to trying to get pupils who dislike maths and just want to get through the exam enough so that they can never do maths again, and that probably involves learning some of these tricks.

Another example of tricks is the speed/distance/time triangles, where you draw the triangle, cover up the one you want to find out with your thumb, and the other two letters then show you the formula that you need. No need for algebraic manipulation or any understanding of how the things relate to each other. I dislike it for that reason, but I do also appreciate that when you have a student who isn't at the level of understanding how to manipulate equations, and doesn't really have a good grasp of inverse operations even, who has to pass an exam, then the triangles can be very helpful. See also Trig ratios in the same sort of memory-triangles.

Some of it comes down to the fact that Foundation maths now includes things that are unnecessary for that level - many of the pupils need basic practical maths, and have (for various reasons) missed out on a level of basic understanding that makes things like trigonometry irrelevant and baffling. It's not that hard for some of them to learn what they actually have to do - put these numbers in this equation, do that on your calculator - but there is no meaning to it. There is a real need for an intermediate level exam, so that foundation level can go back to being practical basics, and the teacher has time to teach them at the level that would help with understanding of those topics, such as percents and fractions and equivalences.

It sounds like OPs daughter quite possibly wouldn't be in a class with that level student had she been able to access lessons normally in Year 10 and 11, and there is going to be a mismatch in her approach, understanding and general ability, even if she is on paper at a similar level at the moment. Children who have specific difficulties in certain areas also can find that a re-sit class or a foundation class doesn't necessarily suit them - I've tutored children in a foundation class who ended up there because of memory problems or exam panic or limits on class numbers or reading difficulties or whatever other spurious reason means they ended up there, and some of them might well have been better off in a higher level class, because they chafe at the way some of the foundation material is taught, with 'just getting through the exam' as the goal rather than understanding.

A lot of people who don't fully understand percentages remember some of the common equivalences. You'll find plenty of people who know 50% is half and 25% is quarter who couldn't explain why. Particularly in a retake class, it's worth using that for those for whom it works. Understanding how to find any percentage may be less likely to stick with some of those people.
Without recognising those simple cases, you get the situation where someone has to find 25% and they laboriously divide by 100 and then multiply by 25, or worse, mis-remember and divide by 25 and multiply by 100.
I haven't checked the latest version of the curriculum, but usually children do learn first about 50%, 25%, 10%, and go on to more general percentages in later years. The difference in a retake class is that you're condensing things into a much shorter period.