Teach Roman Numerals in Primary Maths: Gove

[noblegiraffe]

A story in The Guardian today has a charity expressing concerns about Michael Gove's plans for a new numeracy curriculum in primary school.

Among other things, the classically educated minister with a Latin obsession has decided that primary school children really need to be able to read Roman numerals up to 1000.

Baffling. I can't say it gives me any confidence about the quality of the rest of it.

DD1 doesn't know her tables, and it hasn't held her back from a Maths degree (she used to write out the ones she needed down the side of her exam papers ).

Learning imperial measurements seems to be to show how to convert numbers, so around Y5/Y6. It's not teaching imperial measurements in order to actually use them.

When I did my engineering undergrad, we can use a graphing, programmable calculator. We are also allowed a standard issue formulae book. There really isn't much memorisation expected. I have never been able to do mental arithmetics, but have always done really well in maths.

But Gove is talking about primary school maths. I think they don't teach much other arithmetics? Or maybe a bit of algebra?

It is incredibly useful to know your tables because it's not just about multiplying numbers together, it's about being able to split numbers into factors. It's not just about knowing 4x6=24, it's about being able to say that 24 is 4x6. Or 3x8, or 2x12.

Imperial measures weren't taught when I was at school in the 80s but they've been taught for at least a decade I reckon, mainly converting between metric and imperial. I think it's roughly a level 6 skill. Last year's foundation GCSE paper asked students to convert a speed in mph to kph without giving the conversion factor.

We were taught all maths by formulae.

I got put into the lower set for GCSE, and then ended up doing the olympiad in the sixth form. I was the only student in my year to get any grade - a silver. I still didn't know enough rote learning to have been thought good enough to do the proper GCSE or AS level. So clearly for some teachers rote learning is very important.

noble, you don't need to know tables to see 24 is 4 lots of 6. If you see it as a pattern or a process, you're already there.

noble how do you explain to children -6 lots of -4 is also 24? I can't remember how I was taught negative numbers.

I agree, DD gets confused with too many numbers to think about, she sees it all as patterns. Thankfully degree level maths doesn't seem to involve many numbers at all, so she's coping .

It's not just about knowing 4x6=24, it's about being able to say that 24 is 4x6. Or 3x8, or 2x12.

You don't need to memorise tables to be able to do that - you need to understand numbers and how they work. You need to know that 4x6 is the same as 2x2x6 is the same as 4x2x3 is the same as 2x2x2x3 (to break it down to primes).

In my experinece the best way to learn tables is to use them in manipulating fractions - that involves a lot of multiplying and dividing and really put it in context, which rote learning just doesn't. If you use them often enough they just stick (just like learning any other language !).

If you think of the - as a direction change (ie turn and face the other way) then you have 6x4 and two changes of direction (so you end up facing the same way).

checked with DD3 (10) -she can add and subtract negatives, but not multiply; DD2 (14) can multiply them, knows that the two negatives cancel each other out, but not why, she just remembers what to do with them. Both started with a number line which went down below zero, and "froggy jumped" the addition and subtraction till they were able to do it in their heads.

Also neither of them really know roman numerals, and certainly can't do arithmetic with them without turning them into ordinary numbers, doing the sum, and translating the answer back. DD3 did know that there was no zero, but only because she read it in Murderous Maths.

DD1 isn't around to ask (thought it would be interesting to see what she though as a much more "instinctive" mathematician, whereas the other two are more "learn it and do it").

IShall the way I think of it is that multiplication (of real numbers) is scaling. So you have 2y being doubled y. y/2 is half of y towards zero, y/4 even further until you reaches 0 and then pop out the other way. The cancelling out wouldn't make much sense.

PS. The real number bit is in case your 14yo is doing calculus. Multiplication of imaginary numbers is a rotation. So multiplication is a combination of scaling and rotation on a plane.

I wonder how your DD1 (I assume it's the one doing a maths major) would explain this negative number business.

Going back to times tables and why it may be useful to learn them ... the way I introduce it to my class (Year 3 and therefore lots of tables to learn) is to emphasise how 'just knowing' multiplication facts frees up time and brain space to do the rest of the maths in the problem. It's not 'necessary' (as in all of them can be worked out) BUT by knowing them by heart, there is more time and effort available for the more complex / more fun parts of maths. So we work on it more as a 'hygeine factor' than as an 'end in itself' IYSWIM?

Say if I was working on multiplying a decimal by a small number, and it is new to the children. If child A knows his 6x table, then the only thing that is 'new' in multiplying 4.7 x 6 is the place value (possibly the partitioning, too, but we always do lots on that first). So they can quickly go '24, + 42 divided by 10, so that's 28.2'. A child who doesn't know their 6x table has the extra labour of working out the 6x4 and the 6x7, and in doing so may well lose track of the overall task they are trying to accomplish. OK, if the working out mentally is very quick, then the difference between that and instant recall is pretty small ... but 4 jumps of 6 is......followed by 7 jumps of 6 is..... can take some time.

It's a bit like spelling (or any other individual skill, like letter formation, or punctuation) within writing. If a child can spell short, common words that they will use every day in their writing 'automatically', or form all their joins correctly and automatically, then they have time and effort to spare for the 'higher order' skills within writing of story structure, selecting vocabulary, voice, genre etc. If they have to go back to the basics of phonics every time to spell 'and' or 'but' then while doing that it is very easy to lose focus on the higher order parts of writing.

you don't need to know tables to see 24 is 4 lots of 6

How would you do it, out of interest? I can't see anything that isn't going to involve a faff that's going to get in the way of answering the question.

For example if I see the number 56 I instantly know it's 7x8. If I see the fraction 21/56 I quickly realise that I can take out a factor of 7 from both numbers to simplify it to 3/8. If a student doesn't know their times tables then what should they do to simplify it? Surely knowing your times tables is the easiest way to go about it?

how do you explain to children -6 lots of -4 is also 24?

I introduce it in terms of patterns, I get them to draw a multiplication grid from -3 to 3 (top and side, although I fiddle the order from positive to negative to make the pattern more obvious) and then get them to fill out the multiplications that they know (the positive ones) and the zeroes for the zero times table. So they have a cross of zeros and one quarter filled in. Then they just continue the number sequence by counting on into the negatives for the neg x pos. Then they continue the pattern into the neg x neg and realise that the answers in the neg x neg quarter must be positive. Because if they weren't there wouldn't be a pattern and maths is all about patterns.

If they ask why, you can talk about forgiving debts. Or I like the example of a water tank losing 10 litres a day, so the volume changes by -10 litres per day. How much will you lose in 3 days? 3 lots of losses of 10 litres gives you a loss of 30 litres (3 x -10 = -30). How much was in the tank 3 days ago? -3 lots of -10 = 30 -> there was 30 litres more in the tank 3 days ago.

noble you sound like a great teacher!

spoke to DD1 last night - she "just knows" factors of up to 4 digit numbers, 5 and above she needs to work it out; she's probably better at times tables than she thinks she is, as she can work the answers out immediately without having to think about it; multiplying negative numbers - she deals with the digits and works out the sign afterwards (so having learned the rules of how it works, rather than understanding why and how); she calls herself a "conceptual mathematician" rather than a "numbers mathematician", and then started explaining what she meat,but as it was nearly midnight, and the concepts she was trying to tell me about weren't covered in my Standard Grade Maths back in the dark ages, it went over my head .

She laughed a lot at the idea of having to learn roman numerals up to 1000 though (presumably in order to be tested on it?) and started quite a long rant about how non maths people shouldn't be allowed to interfere with maths teaching, as it was bad enough as it was, and if they wanted to do the history of maths, there were plenty of famous mathematicians DC could study instead as that was Much More Interesting and Had A Point.....