“Of all his early studies, perhaps none is more important to the child as a means of education than that of arithmetic. That he should do sums is of comparatively small importance; but the use of those functions which ‘summing’ calls into play is a great part of education…”
Charlotte Mason asserts that the chief reason for mathematics is to train the mental powers of reasoning and developing habits of accuracy and honesty, because “…There is none in which slovenly teaching has more mischievous results. Multiplication does not produce the ‘right answer,’ so the boy tries division; that again fails, but subtraction may get him out of the bog. There is no must be to him he does not see that one process, and one process only, can give the required result.”
The point of mathematics is not to give the child complex equations to work which are often frustrating and incorrect, but to start small and help them understand the purpose of mathematics so they can visualize what is being asked and what method should be used. “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.”
Miss Mason believed in teaching children the reason of why sums are done rather than just teaching them the mathematical equation. Using manipulative is a great way for children to visualize and think about mathematical problems.
“Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the ‘Captain’ ideas, which should quicken imagination. Mathematics are a necessary part of every man’s education; they must be taught by those who know; but they may not engross the time and attention of the scholar in such wise as to shut out any of the score of ‘subjects,’ a knowledge of which is his natural right.”
The mathematics book Charlotte Mason recommended for her day was the ABC Arithmetic by Sonnenschein and H.A. Nesbitt. You can find the full text of the same authors’ book The Science and Art of Arithmetic (it seems as though the ABC book was the teacher’s edition which is not available) on google books. It can also be purchased from Amazon.com.
Math U See: I plan on using MUS the whole way through because it goes through advanced math levels, uses manipulative’s and includes DVD instruction. I like the mastery approach of really getting the child to learn a concept before moving on. But, I don’t like how repetitive this process can be so we tend to skip a lot of pages, in fact I can use one workbook for two children because we usually skip so many pages. My oldest son gets concepts very quickly and doesn’t need a lot of practice to remember so I usually have him do one or two exercises and then the review or exam and if he gets them all correct, he can move on.
MEP Math: I really really like this program. It is free, which is great, but you have to print a lot, which is not great (fortunately, I have a fast laser printer). The reason I like this program so much is because it requires my kids to THINK. MUS simply requires them to work exercises, this requires them to visualize and come up with the solution- it requires understanding rather than just working of sums. My oldest gets really frustrated with this program because he just wants to work equations, but I love that it forces him to use his brain. So we combine, half the week we do MUS and half the week we do MEP. The teacher’s manual includes ideas for teaching the concepts and I find that with my math background it doesn’t take me much time to prep- I hear others say it takes them longer, kind of depends on your comfort level with math. I keep the tabs pinned on my browser for each level teacher manual, exercises and answer sheet so that I can easily reference it each day without printing everything out.
Singapore Math: This is very similar to MEP except you have to purchase it. If you don’t like to print, then I think this is a great program. I hate the teacher’s manual and there is no DVD instruction, so I think it’s best for people who have a solid math background. The colors and graphics are great for kids who learn visually.
Life of Fred: This is such a fun series for kids. It tells silly stories while working math problems. I find that it goes through math concepts very quickly so if you use it for your primary math program you really need to do some work creating exercises to reinforce the concepts. My kids just kept reading through like a novel so we stopped using it for a math program and I just let them do it for fun.