On Fri, 28 Jan 2011 12:17:44 +0100, Martin wrote:

On Thu, 27 Jan 2011 23:35:44 GMT, Tom wrote:

wrote in :
In article ,
Martin wrote:

Tell us about your tricks, Nick? I am sick of supermarket tricks :-)

I did. zx8 = 8x7 = 7x(4+4) = 7x7 = 10*7-3*7 and more. Also using
factorisation, so 44x75 = 11*(4*25)*3. Make a habit of that sort
of thing, and you will soon develop your own collection.

Also, using iteration (usually binary chop or interpolation) to do
division, square and cube roots etc.

Make a habit of such tricks and you will soon develop your own
suite. But mental arithmetic is no longer taught.

Watching my daughter grow up over the past 20 years
was interesting in this regard. Yes, the rote learning
of multiplication has been "deemphasised", but she
was also taught that there are several ways to get
the right answer to arithmetic problems. This has
the advantage that examples such as yours weren't
ignored and were taught (at least in the limited
sense of examples of how to solve an specific question).

In that sense, I greatly *approve* of the "new" teaching
methods.

On the other hand, lack of knowing the
"algorithmic" techniques for long multiplication and
division mean that she wouldn't have a clue how to
start coding multiple-precision arithmetic routines

I've commented elsewhere about primary teachers not
knowing what 1+2*3 is, and on the disappearance of
calculus from GCSE/O-level maths

Calculus was first year A level maths and not GCE maths in the 1950s.

It must have depended on the board, then. Oxbridge joint board set
"Elementary" and "Additional" maths as separate subjects: calculus was
in "Add Maths". Of course schools may have varied in the way they
programmed things.

--
Mike.