It seems like it might be worthwhile to try to summarize what CM values in a mathematical approach for the early years, meaning ages 6-9 or so. That will help anyone who wants to evaluate a curriculum to decide what to use when the school years approach, or who wants to create their own plan of instruction. This is just a rough draft.
The chief value of arithmetic, like that of the higher mathematics, lies in the training it affords the reasoning powers, and in the habits of insight, readiness, accuracy, intellectual truthfulness it engenders.
In the early years, she sees arithmetic as training the mind just as the work with language (hearing great stories, learning to read with accuracy and attention, etc.) trains the mind.
So this list she gives us helps us see at least some of the qualities we should be able to find in any math program we want to use.
She then talks about how important it is not to put the child in a situation where he does not know the right way to work the problem he is given. He must always know the right approach to take before he begins the problem.
Care must be taken to give the child such problems as he can work, but yet which are difficult enough to cause him some little mental effort.
Another point to watch for when looking at a curriculum.
The next point is to demonstrate everything demonstrable.
The child should be shown how each new concept works, using manipulatives whenever possible.
She then gives us an outline of the order in which concepts should be introduced:
* addition and subtraction together
* word problems (done mentally and without counters–or with them at first then without them later)
* notation, introduced first with money to get the idea of place value in a concrete way
Let him never work with figures the notation of which is beyond him, and when he comes to ‘carry’ in an addition or multiplication sum, let him not say he carries ‘two,’ or ‘three,’ but ‘two tens,’ or ‘three hundreds,’ as the case may be.
She discusses the importance of working with weights and measures, but doing it in the context of the real world–actually measuring and weighing real objects.
Therefore I incline to think that an elaborate system of staves, cubes, etc., instead of tens, hundreds, thousands, errs by embarrassing the child’s mind with too much teaching, and by making the illustration occupy a more prominent place than the thing illustrated.
Perhaps a warning against too much emphasis on props like cuisenaire rods and the like?
I do not think that any direct preparation for mathematics is desirable. The child, who has been allowed to think and not compelled to cram, hails the new study with delight when the due time for it arrives. The reason why mathematics are a great study is because there exists in the normal mind an affinity and capacity for this study; and too great an elaboration, whether of teaching or of preparation, has, I think, a tendency to take the edge off this manner of intellectual interest.
An interesting observation, and worth considering.
OK, this was my shot at outlining what CM wanted in basic arithmetic instruction in the early years (in this case meaning about ages 6 through 9).
All my Charlotte Mason math posts.