To have a Charlotte Mason approach to math, it does not matter so much which math book you use as HOW you use it. From the things she wrote about math, I’d say that Mason especially appreciated two things:
(1) In many math problems (though not in all!), our children come up against a firm rule or law, something that is solidly right when any other answer is wrong. She felt that this was a valuable and humbling experience.
(2) Math gives children the chance to grapple directly with ideas, to learn how to justify their reasoning.
These two ideas are related, since it is the justifications (or proofs) that convince us an answer is right or wrong. How do we know that we got a sum correct? We can take the numbers apart and add them another way, to see if we get the same answer. Or we can subtract one of the numbers from the sum and see if we get the other number. Or… well, how would YOU prove it? From the very beginning, children should be doing this sort of informal proof, explaining how they figured things out. Don’t wait until high school geometry to let your children wrestle with ideas!
This is why stories and manipulatives are so important when working with elementary children. Do not rush to abstract math notation, because children cannot reason with it. They need the physical presence of manipulatives or the mental images of a story to give them something “real” to reason with, so they can grapple with ideas and make justifications. Not until MUCH later will they be able to reason using only abstractions.
This is true for teenagers and adults as well. As W. W. Sawyer wrote in his wonderful little book, Mathematician’s Delight:
Earlier we considered the argument, ‘Twice two must be four, because we cannot imagine it otherwise.’ This argument brings out clearly the connexion between reason and imagination: reason is in fact neither more nor less than an experiment carried out in the imagination.
People often make mistakes when they reason about things they have never seen. Imagination does not always give us the correct answer. We can only argue correctly about things of which we have experience or which are reasonably like the things we know well. If our reasoning leads us to an untrue conclusion, we must revise the picture in our minds, and learn to imagine things as they are.
When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touched. One can begin to reason only when a clear picture has been formed in the imagination. Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination.
Also, be sure to take into consideration Mason’s approach to all learning, not just the things she said about math. For instance, the use of narration is very important in math as well as other subjects. When children put their thoughts about a math problem into words to explain what they did, this solidifies their understanding of the concepts. I’ve written a blog post about how my family uses narration in math, which you might find helpful: Buddy Math.
