Math is an area that is all abuzz in the Charlotte Mason community. To tell you the truth, I chose our math curriculum before digging into Home Education again. I picked the curriculum that I used as a teacher. Our situation is somewhat unique, because I would love to send my children to the school where I once taught. If that happens, I would like my children to have experience with the curriculum they use.
If anything, reading about math in Home Education assured me that Charlotte Mason's recommendations aren't there to be followed as a recipe. This idea stood out to me because after she gave her recommendations for teaching math, she recommended a math curriculum that looked very, very different than what she said. So, as you choose a math curriculum, know that we can have grace for ourselves, as Charlotte Mason had grace.
You can see the rest of this series, which outlines a curriculum based solely off of Home Education, here.
"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. " Home Education, page 254
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Math instruction, according to this volume, begins with simple math problems that children can do on their own. Charlotte Mason said that these problems are within a child's grasp. These lessons serve as a little warm up to get ideas moving, yet they don't focus on merely sums. They set up a story problem that will require a child to think through it.
After this opportunity to complete a problem, the skill is demonstrated using what are now called math manipulatives. Charlotte Mason recommended beans, but there are now so many options. I like Unifix cubes, although so do my toddlers, and they end up all over the house.
We can demonstrate the skills before introducing more challenging problems. Here is an example:
"A boy had twice ten apples; how many heaps of 4 could he make?' He will be able to work with promiscuous numbers, as 7+5-3. If he must use beans to get his answer, let him; but encourage him to work with imaginary beans, as a step towards working with abstract numbers. Carefully graduated teaching and daily mental effort on the child's part at this early stage may be the means of developing real mathematical power, and will certainly promote the habits of concentration and effort of mind." Home Education, page 257
Charlotte Mason continued to describe learning about money, and weight and measurement.
The modern-day curriculum that she mentioned was ABC Arithmetic, which seems to appear under the name The Science and Art of Arithmetic (perhaps Charlotte Mason mentioned the teacher version, and now only the students' version is available.) If you take a look at the book, you'll see why it doesn't seem to exactly follow Charlotte Mason's recommendations. It begins with Roman numerals, and then is off into different forms of notation, that as well as being mostly unnecessary today, would be very confusing to teach a young child who does not yet understand counting, let alone multiplication. Saying, 1 is 10 and 3 is 11 would most likely do nothing more than confuse a child who is still developing number sense.
Home Education Curriculum: Math
Singapore Math- Similar to Charlotte Mason's approach, this math program moves from a problem demonstrated in a concrete way, to a pictorial representation, then moves to the standard notation. Some say that this curriculum "is not Charlotte Mason," but those statements are always subjective. Charlotte Mason wanted US to decide whether something fit into her principles or not, which is why she gave us Four Tests for Lessons.
Other Math Options:
MEP- This is a free, online math curriculum that many people think highly of. It seems to do a good job of establishing number sense for young children. The lesson guide is also free, so you really only need to print it out.
I hesitate to recommend other math curricula that I haven't personally looked at. There are several more that I've used and have seen as a teacher, but that I wouldn't necessarily recommend.