Little children doing something mathy with dollar-store jewels, a long, long time ago
You might be interested to know, first of all, that Charlotte Mason did not teach mathematics using living books. Math stories can be quite engaging and useful, and I will list a few that we particularly liked at various levels and for various reasons, but as Harmony notes in the post linked above, Charlotte Mason largely taught mathematics using the language of math.
In fact, in her vision – and it strikes me as a really sensible vision – math learning is a lot like language learning, in which the child moves by stages from vocabulary and communications related to concrete and physical realities (mama, dog, tree, hungry, cry), to vocabulary and communication related to the level of ideas (dignity, justice, virtue, heroism, causes and effects, symbols and representations).
Here is what she herself has written about the sequence of math learning. (you'll have to scroll up a tiny bit to catch the beginning)
If what you notice is that the sequence she describes sounds like more or less every math curriculum ever . . . well, yes. She doesn't have some rarified mythological approach to teaching math. Start with the concrete, move to the abstract. Start with things the child can relate to and do and gradually move beyond that. That is roughly the idea here.
Of the many math curricula we have used over the years, my hands-down favorite, especially for K-8, or the pre-algebra stage, is MEP, a British program based on a Hungarian model.
What do I like about MEP?
It features:
Scripted, highly detailed lesson plans, which contain the meat of the math teaching.
A gentle spiral structure for Years 1-6, granting about a week to a concept before moving on, but returning to the same concept to review and build on it multiple times during the year.
Practice books which accompany the lessons, and which provide extensive opportunity to work at a concept, in problem sets that increase in difficulty as you move from left to right. A child encountering a concept for the first time, or a math-struggling child, might stick to the left-hand column of practice questions the first time or two through a concept. A child who has become confident in that concept, or a math-gifted child, might move quickly to the problems on the right. The last problem in the right-hand column is generally an "extension" question, aimed at the mathier child, who might like to stick his neck out to explore the concept in a way that hasn't necessarily been taught or explained yet.
It's also all free for the cost of printing.
The earliest "year" in MEP is Reception, which is analogous to kindergarten, though British children start at four, not five. The Reception year offers math lessons at a rate of roughly two or three times a week. These lessons are gentle, hands-on, and concrete, with no writing required.
Year 1 represents a real step up in seriousness, though the first few pages look deceptively simple! Longtime MEP users recommend that anyone starting this program with a child in first through third grades begin in Year 1. This Year lays down foundational concepts to which subsequent levels of the program will refer, and although it stays in single-digit operations far longer than the standard American early-grades math program, it invites children into algebraic thinking quite quickly.
Years 4-6, meanwhile, introduce pre-algebra, so that they are not too "young" even for a middle-schooler, especially a not-particularly-math-gifted child. More advanced students might jump up to Years 7-9, which offer pre-algebra, algebra, geometry, trigonometry, statistics, set theory, and other concepts as units, again with scripted lesson plans. Years 7-9 also offer "tracks" for remedial, "standard," and advanced or gifted students.
I do know home educators who have used MEP's upper-secondary levels for high school, though they are keyed to stages of British schooling, and some of the sequence may not correspond as clearly to the kinds of topics American students need to know for the SAT and other college-entrance exams. For this reason, I hesitate to recommend it as a high-school program as readily as I recommend it for K-8, as a curriculum corresponding to Charlotte Mason's vision for math learning.
For high school, we have used, variously, Teaching Textbooks, Saxon, and dual-enrollment courses.
Other popular programs among Charlotte Mason home educators:
Right Start Math
Singapore Math
Math U See
Math Mammoth
Beast Academy
The Art of Problem Solving
We have also enjoyed math stories such as
for Pre-K and K:
Anno's Counting Book (any counting books)
One Odd Day
Usborne First Numbers
Oxford First Book of Maths
for lower primary:
the Life of Fred series
Anno's Mysterious Multiplying Jar
for upper primary and middle school:
Famous Mathematicians
String, Straight-Edge, and Shadow
plus books for logic, like The Phantom Tollbooth and The Westing Game
for high school:
Flatland
Anno's Mysterious Multiplying Jar
for upper primary and middle school:
Famous Mathematicians
String, Straight-Edge, and Shadow
plus books for logic, like The Phantom Tollbooth and The Westing Game
for high school:
Flatland