Homework approaches in secondary school

[Stevie77]

I'm genuinely interested to hear about your child's secondary school approach to homework.

My son started Year 7 in Sept. I also have a Year 11 child in a different school. My son's school uses Seneca and Mathswatch as their main platforms for homework, with other work being on Google Suite, or other platforms. But all on digital platforms.

I've reached out to school (they have a dedicated Yr 7 transition lead) querying it as it seems like the reliance on an automated platforms leads to a lighter-touch approach to homework overall. I can see how it is convenient for teachers not having to mark books, but I am concerned about the lack of written homework, lack of personalised feedback, no teacher-guided assessment or the chance to meaningfully learn from mistakes etc. I also don't think that Seneca alone provides the level of academic challenge or the development of independent study skills needed further down the line. I also don't think it promotes focused work, as the system is really distracting - you get celebratory pop-up memes when you answer correctly, when you type an answer it automatically completes the end of the word for you etc. It seems like a useful for revision and quizzing, but for all homework?

School have so far replied reinforcing (expected, I guess) this school-wide approach, stating that they find Seneca to be a highly effective, interactive online platform that supports learning and revision. They say they also utilise a Seneca Plus model, where while they have a core approach, individual faculties incorporate specific independent learning strategies tailored to their subject area.

So, am I right to be concerned? I can't see how this approach prepares the students for what sitting GCSEs and the level of studying needed in the coming yars - which I am seeing with my older child now. Assuming I am correct in my concerns, where else can I take this next? Governors? Happy to be told I'm wrong!

I don't care that DD1 uses a grid method for long multiplication whereas DD2 uses Napiers method and I do it the compact way. They all get the right answer.

I had a kid excitedly showing his mates Napiers for multiplication the other day, and I went 'oh yes, Napier's bones, I love that method' and he said 'why've we never been taught it then?'

'Michael Gove'.

I see your point, it seems we have different ideas about mental maths - DC's teachers often emphasised they needed to practise mental maths for faster calculation, but maybe it's just for top sets.

I'm still interested to know how maths can be "inappropriate" or "contextual" @Octavia64

I personally don’t consider speed important.

i am aware that the government currently is emphasising speed in particular for the times tables test in year 4 but many mathematicians don’t consider speed important and a notable minority describe themselves as slow thinkers.

the classic example is Maryam Mirzakhani who described herself as a “slow” mathematician.

see the wiki under her personal life.

https://en.wikipedia.org/wiki/Maryam_Mirzakhani

You sent me down a rabbit hole of BBC bite size - if I’d had this sort of stuff as well as the other methods I’d have enjoyed maths more.

I had an uncle who was a Professor of Maths and would tell me aged 7 or 8 about the problem he was setting or marking <very old nothing online at all> and it was interesting. I’m not brilliant at maths, stopped at GCSE but liked the idea of a puzzle.

Ok.

so, to give a few examples. I’m going to use maths curriculums and countries I am familiar with as these are examples I personally have experienced.

firstly, mathematical modelling is part of maths. This means that an important part of doing maths is translating from the problem to the mathematical structure before being able to work on the maths itself.

ao in Ghana, for example, I came across this problem:

there are some tuktuks and bicycles parked outside the shs. If there are 20 wheels in total how many tuktuks could there be? How many bicycles?

i didn’t know how to begin working with it because I didn’t know what a tuk tuk was and how many wheels it had. That’s fundamental knowledge needed to solve the problem.

or when I was hosting some Shanghai teachers and we were rewriting Chinese maths lessons to be appropriate for English students one that slipped through the net was “how many shoes will a family have?” In China the answer is 6. Two adults one kid. One child policy.

when we did it in England they got a whole variety of answers.

so that’s example one, that part of maths is working out when and which bit of maths to apply to “real world problems” and that’s variable by culture.

example two, different education systems teach different bits of maths at different times. In Shanghai algebra starts in grade 1 (5-6 year olds). I have seen this with my own eyes. This means that Chinese textbooks for secondary assume a level of proficiency in algebra that English kids do not have because the English system largely leaves it until secondary.

Singapore sort of has a midway between the two model in that they use a visual algebra known as bar modelling (which is becoming more popular over here) which permits manipulation of unknowns in a very intuitive way but isn’t the full on algebra from the beginning approach of the Chinese.

ok.

so let’s take eg quadratic equation.
lets go with

x squared plus 7x plus 12 equals 0.

what is the “best” method to solve this? How do we define best? Is it the quickest? The most computationally efficient if implemented in a computer? The one that makes the method clearest?

now consider another quadratic equation.

x squared plus 7x plus 23 equals -27

does this have the same best method? If not, why not - surely all quadratics have a single method to solve them?

now let’s consider this quadratic:

6x squared plus 7x plus 23 equals 76.

can we use the same methods? Does the graphical representation help here?

it’s not as simple as there being one “best” method.

We're not really discussing Fields medalists or Stanford professors here, as a parent of a gifted mathematician I can only say what you probably already know - they are VERY different from other people and the whole discussion about teaching maths at an ordinary school is largely irrelevant to them (my gifted DC never learns in a way you described, understanding simpler concepts then moving higher, it's the other way round for him) so I'm not sure what you're trying to say giving examples of Stanford professors or linking Tao's pre-print :))

The OP was about an ordinary homework at an ordinary school. Tbh I'm not even that interested in maths HW, it's straightforward as I said before. Humanities and languages are changing much more dramatically.

I'd say example 1 would require a very basic editing of books so not a problem (AI can do that in seconds 😁 )

Example 2 is a real problem indeed - British kids are so behind on maths that they cannot really catch up, the whole system would need a complete overhaul right from the early stages and no one is going to do that. Our STEM is doomed I think, we cannot compete with Asia as we simply don't teach STEM as they do - and we don't want to, even though some schools try to integrate some ideas. Tbh I don't think it's about easier presentation like bar modelling, it's more about maintaining the logical structure and interconnections between maths concepts in learning environments.

The maths is still the same though, it's still the same algebra they teach, not something esoteric. And I'm not sure eg sine can have any cultural variables.

Thank you for the detailed answer, it was interesting to see the examples.

British kids are so behind on maths that they cannot really catch up

This is untrue, England outperform the vast majority of countries in the OECD in maths.

I don't think parents of gifted mathematicians are in the best position to judge teaching of secondary level maths.

Jumping to conclusions much? :) And not reading other ppl posts - I specifically said that Fields medalists, Stanford professors and other gifted mathematicians examples were irrelevant to this discussion.

DC2 has an average ability and learns as an average pupil does, but is in top set nevertheless, partly because our schools have never used apps and online platforms and were setting homework after every lesson from y1, even in lockdowns. They never used CGP either 😁

Unless all kids in the school are in top set then one wonders how not using online apps and marking all that homework has nonetheless resulted in children in that school being in middle or even bottom set.

You may say that, it doesn't mean it's true.

If I have understood you correctly you have one gifted mathematician and one apparently 'average' ability who nevertheless is in top set maths (can't quite work out what type of school as you listed a whole bunch).

Why bother figuring it out if you don't believe it anyway? 😁

Logic is not being taught in schools at all, I know...

I guess my position comes from
. trusting schools who see far more pupils than any parent have a reasonable idea as to what is or is not working for them
. being an interested parent who paid attention to what and how my DC were being taught and seeing whether it worked for them or not
. being an able mathematician myself but also having 2 DC who are average / below average academically and having seen what they have needed to grasp and master new concepts
. having used CGP books across a number of subjects to help DD1 revise (not be taught) for her various GCSEs

I think I said right at the start that online didn't really work for DD2, I am guessing due to her SEN. However if the teachers here say it is effective for the majority of their students I don't see why they should be wrong. I have used the online videos occasionally to understand new-to-me methods (eg Napier and a method whose name I forget for solving quadratics) and I think the combination of clear voiced explanations plus real time writing was excellent.

I don't believe one of them is a teacher or perhaps I should say I do hope they're not as their online behaviour is out of order for a teacher.

DC1 went through state+grammar and read pure maths at uni.

DC2 went to pre prep hot house then top 15 (at the time) super selective private then academically average private.

I refer to my experience at those schools as well as our friends' experience in various grammar and private schools and even in home schooling. And the national stats on literacy and numeracy. This is how I know that the statement "this is how maths has been taught everywhere" is simply incorrect, full stop. And from the stats we all know that the approach described here by teachers is not working, otherwise we would have had 90-95% of school leavers without SEND perfectly numerate. We all know the reality is nothing like this. Of course there are different factors contributing to this, not just the lack of homework or chaotic teaching methods, but they play their part for sure.

The schools are shifting to platforms because they have no money. Even posters on this thread confirmed this a few times.

@Octavia64 made me read some comparative research on teaching algebraic skills in China and the US and even though maths is not my special interest it's still an interesting read.

Our homeschooled friends here in the UK (not Asian or S Asian) do GCSE maths aged 13-14. You may argue that's because they get 1 to 1 teaching but if it was impossible from a cognitive point of view no individual teaching would help achieve that. Human beings have enough cognitive capability to do that, that's why the Chinese achieve that. They're not super human, they just set high expectations and teach, that's it. I'm not in favour of teaching formal algebra from year 1 but yes, human brain is capable to do that too, and more.

I guess I am thinking about working within the current system limitations.
You are arguing what could be possible if you throw away all the limitations.

Home Ed is broadly speaking nothing like the school system in approach, tutor time, how they do exams. For various reasons they tend to do a few exams over a number of years rather than the standard approach of 8-10 GCSEs in y11.

Private and grammar schools do not tend to have the same range of children in them that even the leafiest comp does (in terms of ability, parental interest, parental income, and probably behaviour).

I don't believe one of them is a teacher or perhaps I should say I do hope they're not as their online behaviour is out of order for a teacher.

You mean me, right? That's pretty funny.

I think I said upthread I was comparing top sets in leafy state to private, top set innate ability is very similar to "normal" selective schools (not Westminster, SP and the like).

Anyway, I'm not arguing or advocating for anything, I'm just presenting facts for comparison. The only reason I do this is because other people may read those claims and think "oh the system is great, the methods are clear and it's the only way to teach maths but my child is struggling, then there must be something wrong with my child or maybe they just don't have any aptitude for maths". I guess what I wanted to tell is that it's not necessarily the case.

I don't have any opinion on other books eg Collins either as I haven't done any research. The online apps I've seen are harmful to primary school children cognitive development, I can tell this as a neuroscientist, not as a maths teacher. But again, I haven't seen all of them even for primary so am not arguing they're all equally bad. There is no authoritative comparative research on the outcome of platform based learning vs book based as the new reality is still in babyhood so no longitude exists yet. Any claim "online is the best way" is frankly bonkers as no one really knows yet. I've just read a recent research on typing lecture notes vs hand writing them - the latter leads to better outcomes. It's a very niche topic though and not a large longitude either so I won't be going about waving this result and claiming writing is the best and only way to do everything, it would be utterly ridiculous. I'll just make sure my DC does as much writing as possible :)

Human beings are evolving and changing too of course, it may be possible the majority of population won't be able to read, write and calculate at all in the near future, and it would be perfectly fine as they won't be needed in the workforce anyway. Who knows what lays ahead.