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T34:

bgy1mm:

You need tables for two reasons, to do tiny multiplications in your head, and  to do long multiplication and long division with pencil and paper.

 

You've missed one, I think.

In science you do a lot of estimation and approximation.

After (or before) you use a calculator or computer to get an exact answer you do an approximation in your head (hopefully). You also do a lot of "back of a beermat" calculations.

For example,

6965 * 7,900,000 / 31.3

coould be approximated to

7 *10^3  *  8*10^6 / 32

Knowing the value of 7*8, or that 56 and 32 are both divisible by 8 is rather useful in this case.
If a KS3 or KS4 pupil does not know his tables he is hopeless at estimating.

 

Though logarithms are more useful. I'd like to see ten to the three times ten to the six, that's ten to the nine, take off one, ten to the eight.

Also, this works for all numbers, not just when someone has cooked the figures.

bgy1mm:

T34:

bgy1mm:

You need tables for two reasons, to do tiny multiplications in your head, and  to do long multiplication and long division with pencil and paper.

 

You've missed one, I think.

In science you do a lot of estimation and approximation.

After (or before) you use a calculator or computer to get an exact answer you do an approximation in your head (hopefully). You also do a lot of "back of a beermat" calculations.

For example,

6965 * 7,900,000 / 31.3

coould be approximated to

7 *10^3  *  8*10^6 / 32

Knowing the value of 7*8, or that 56 and 32 are both divisible by 8 is rather useful in this case.
If a KS3 or KS4 pupil does not know his tables he is hopeless at estimating.

 

 

Though logarithms are more useful. I'd like to see ten to the three times ten to the six, that's ten to the nine, take off one, ten to the eight.

Also, this works for all numbers, not just when someone has cooked the figures

?? You have mystified me. Logarithms are more useful than what?

According to my calculator the original expression evaluates to 1.719 * 10^9

My approximation gives 56/32 * 10^9, which if you know your tables simplifies (in your head) to 1.75 * 10^9

What is this 10^8 you quote?

And the whole idea of an estimate is to cook the figures, whatever the original numbers may have been.

weebecka:

When discussions get stuck, as here where OldAndrew is pushing the importance of fluency in solving quadratics and I (and others) am suggesting instead that a connected understanding of the varied contexts and processes of quadratics is sufficient and that an appropriate level of fluency will come with the development of higher order skills, grounding our viewpoints in our contexts/experience helps to move the conversation on. 

Actually I was just illustrating the fact that fluency in times tables might be useful when doing a more advanced type of maths later. 

I wasn't expecting to have people suggesting that we could also skip the more difficult type of maths as long as we had a phone or computer to hand.

I mean, I guess we could always keep skipping things, never getting efficient at working anything out, I suspect, however, that such an approach won't make anyone any good at maths. But I get the impression that certain people have a very different concept of being good at maths than I do.

weebecka:

Why is teaching all 7 methods (including this one)

http://www.youtube.com/watch?v=NkPfW40DFyk

dumbing down?

Where has this red herring come from?

Being unable to do even routine problems without a calculator or computer is dumbing down. What you choose to do with the extra time created by leaving your students poor at simple factorisation is up to you, but you will have trouble selling me the idea that doing 7 methods badly is better than doing 2 or 3 fluently.

You asked about my blog, and I have to say this teaching approach makes me think of this entry. It is an unfortunate habit of illusionists to be able to boast that their students are covering really advanced material, even though they don't actually have a firm grasp of any of it. I can just imagine the delighted top set teacher declaring that their year 10s have done quadratics in seven ways including an iterative numerical method, perhaps handing around an exercise book to prove it. Then when the class fail to do even easy factorising in their exams the excuse will come out that exams don't really test understanding properly and that it's really unfair they failed to get a grade B at GCSE when they were "doing" A2 or degree level work in lessons.

oldandrew:

Then when the class fail to do even easy factorising in their exams the excuse will come out that exams don't really test understanding properly and that it's really unfair they failed to get a grade B at GCSE when they were "doing" A2 or degree level work in lessons.

The point is that the people setting the exams have decided to test quadratics with easy factors, as opposed to, say, quadratics with real or even with complex roots.

That's a decision that weebecka and I might want to challenge. You can't do a square root in your head, and even if you know Newton's method it's very tedious with pencil and paper. But it's very easy with a calculator. That changes the places it's appropriate to use the formula method rather than the hand-factoring method. It changes hard quadratics to easy ones and easy ones (with no calculator) to hard ones.