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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 10:36 am 
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Joined: Sat Aug 10, 2013 11:46 am
Posts: 237
Lots of extremely good mathematicians were taught algebra early.

Children from state schools taking the 11+ are competing with those from private schools and those with parents who have either got tutors or taught their child themselves from the internet or books like CGP. They have no such qualms about teaching maths early.

To give the impression they should not try because they will get it wrong is putting them at a disadvantage. Primary maths is not rocket science. I like Yes's ideas of using diagrams and illustrations as much as possible. But to any parents thinking of teaching their child, get a book and see if you could.

There are also good maths videos online for bits where you might need help in explaining.


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 10:37 am 
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Joined: Tue Dec 16, 2008 5:08 pm
Posts: 1714
Guest55 wrote:
If you want your children to really understand algebra [as a mathematician] then it is totally inappropriate to use algebra before it is introduced at school.

I now understand some of the 'issues' I've faced in teaching algebra in a GS - so many more misconceptions!

Teachers are trained in pedagogy - often tutors aren't trained and don't really explain what algebra really is about.


Unfortunately, I don't buy into that G55. I do not agree a child can't fully grasp algebra, if it wasn't introduced at their school - in fact this is the first time I have come across such statement. I have taught many mathematical concepts to my children, way before their school did, and they use the same concepts, with a fair amount of confidence, to this day.

Sorry crossed with KenR


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 10:43 am 
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Joined: Fri Jul 04, 2014 10:45 am
Posts: 144
The pros and cons of teaching algebra are a little off topic.


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 10:48 am 
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Joined: Fri Mar 17, 2006 5:12 pm
Posts: 1435
Location: Birmingham
below is an actual Independent School 11+ Maths question from many years ago(Solihull School). It's the last (scholarship level) question in paper.

Quote:
T is a town on the shore of a large lake, and various boats and hovercraft stop at T in their journeys around the lake. The total distance round the lake is 180 kilometres.

At 10:00am a boat starts from T and travels clockwise round the lake at a speed of 15kph. At the same time a hovercroft starts from T and travels round the lake in the opposite direction at 60kpm.

(1) How far has the boat travelled by the time the hovercraft gets back to T?

(2) When do the hovercraft and the boat meet each other?

(3) How far has each vessel travelled when they meet?


You could probably solve by trial and error, but using Algebra is a far more elegant and faster solution.


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 10:55 am 
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Joined: Tue Dec 16, 2008 5:08 pm
Posts: 1714
Moderators wrote:
The pros and cons of teaching algebra are a little off topic.


Do you see any harm in discussing them Moderator?


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 11:13 am 
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Joined: Mon Feb 12, 2007 1:21 pm
Posts: 16126
KenR wrote:
below is an actual Independent School 11+ Maths question from many years ago(Solihull School). It's the last (scholarship level) question in paper.

Quote:
T is a town on the shore of a large lake, and various boats and hovercraft stop at T in their journeys around the lake. The total distance round the lake is 180 kilometres.

At 10:00am a boat starts from T and travels clockwise round the lake at a speed of 15kph. At the same time a hovercroft starts from T and travels round the lake in the opposite direction at 60kpm.

(1) How far has the boat travelled by the time the hovercraft gets back to T?

(2) When do the hovercraft and the boat meet each other?

(3) How far has each vessel travelled when they meet?


You could probably solve by trial and error, but using Algebra is a far more elegant and faster solution.


So not really appropriate for the vast majority of students?


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 11:26 am 
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Joined: Sat Aug 10, 2013 11:46 am
Posts: 237
Guest55,
I took it that KenR had cross posted with the mod, but would it not be polite to respect the mod's post about not discussing this until they have replied to MSD's request?


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 11:33 am 
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Joined: Mon Feb 12, 2007 1:21 pm
Posts: 16126
russet wrote:
Guest55,
I took it that KenR had cross posted with the mod, but would it not be polite to respect the mod's post about not discussing this until they have replied to MSD's request?


He clearly didn't looking at the time - he's a mod :)


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 11:44 am 
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Joined: Mon May 16, 2011 1:05 pm
Posts: 6208
Location: Reading
MSD wrote:
Moderators wrote:
The pros and cons of teaching algebra are a little off topic.


Do you see any harm in discussing them Moderator?



Agreed there’s no harm in ‘discussing’, unfortunately neither side in this argument with ever agree, and probably won’t even agree to disagree. :roll: I was attempting to just get the thread back on track and end what is another pointless argument that will just rumble on with no conclusion.


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 Post subject: Re: Ratio problem
PostPosted: Fri Nov 30, 2018 11:54 am 
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Joined: Sat Aug 10, 2013 11:46 am
Posts: 237
I am quite happy to agree to disagree and leave it to individual parents to decide whether or not to teach algebra to their child and at what age.


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