Hi Karen,
The handbook goes through CM’s deliberate and measured method of teaching multiplication from the introduction of multiplication, the use of manipulatives and mental work, how to use money problems before moving onto abstract numbers, the written multiplication table and its memorization. I think the handbook would give you all you need and you could stay textbook free. A large part of CM’s methods in this area is that the child will get ideas and then you will be able to obtain from him or her how the problems are worked rather than you doing all the explaining. Here are some tidbits:
Irene Stephens, who was the lecturer in mathematics at Ambleside and wrote the handbook on teaching arithmetic to children used by the PNUS showed how to present multiplication as repeated addition:
“Multiplication is at first presented as an extension of addition. e.g., ‘If 4 children had 6d. each, how much had they altogether?’ would be worked
6d. + 6d. + 6d. + 6d. = 24d. = 2s. Several examples like this are given before we suggest that it may be written down more shortly, thus 6d. × 4, where ‘ × 4 ‘ means multiplied by 4, i.e., each of the quantities mentioned is to be taken 4 times, so that 6d. × 4 means 4 sixpences, 2s. × 10 would mean 10 2s. pieces, and so on.
We work a few simple questions, getting the children to write them on their blackboards with the multiplication sign and using easy numbers for which a knowledge of the multiplication table is not necessary. These elementary examples give to the children an idea of what “times” indicates and we can then begin Tables” (Stephens, 1911, pp. 9-10).
Here’s a taster regarding the multiplication table:
“There is no royal road to the multiplication table; it must be learnt by heart. This is a fact which faces every teacher of elementary arithmetic, and which each must prepare for in the best way possible. They must be learnt by each child individually and not in a chorus. The tables are learnt both forwards and backwards as it were, i.e.:—
6 times 1 = 6.
6 times 2 = 12, &c., and also
One 6 is 6.
Two 6’s are 12.
Three 6’s are 18 &c., &c., and are said not in consecutive order,
but in a variety of ways, e.g.—
Four 6’s are 24.
Three 6’s are 18.
Six 6’s are 36.
Seven 6’s are 42.
Ten 6’s are 60, &c.,
and then again in another order” (Stephens, 1911, p. 10).
Warmly,
Richele