2. A good teacher teaches the child, not the program.
Charlotte Mason talked about using a method, not a system. I am going to write about the implications of this for math later in the series, so I won't write too much about it here. For now I'll just say that we have a great advantage as homeschooling parents. We know our children as “born persons.” We know their strengths and weaknesses, we know what they know and what they don’t know. We have an opportunity to deal with them one-on-one.
What does this mean when you are choosing math curriculum for the early grades? It means that the curriculum isn't everything. It's a tool to help you reach your goals for math. You will be able to see if your child is mastering the concepts. If not, you will not push him through without mastery. You will find other resources and ideas to help in areas that seem difficult. You will not insist on endless drill of concepts your child already understands. The bottom line is, you do not need to find the perfect curriculum. You just have to find one that works, and work with it.
3. A good teacher “quickens the imagination” with great ideas.
“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.” (6, 233)
"But we, believing that the normal child has powers of mind which fit him to deal with all knowledge proper to him, give him a full and generous curriculum; taking care only that all knowledge offered him is vital, that is, that facts are not presented without their informing ideas..." (6, xxx, Principle 11.)
“I have so far urged that knowledge is necessary to men, and that, in the initial stages, it must be conveyed through a literary medium, whether it be knowledge of physics or of Letters... ...mathematics seem to fall outside this rule of literary presentation; mathematics, like music, is a speech in itself, a speech irrefragibly logical, of exquisite clarity, meeting the requirements of the mind.” (6, 334)When we think of the early grades, it sometimes can be difficult to see what the inspiring "captain ideas" are, much less pass them on. How can we avoid passing on the simple facts of addition and subtraction without their informing ideas?
The first way at this age is through the use of manipulatives. When a child is handling beans or rods or pennies, he grasps the idea not only that 3+4=7, but also that 4+3=7, and that 7-3=4 and 7-4=3. For a young child exploring his world, this can be a very exciting discovery. I know it was for my son!
A second way to provide inspiration in math during the early elementary years is to use everyday situations like playing games together, cooking together, and measuring all the children, or paying with cash at the grocery store. I am not talking about calling a cooking session a "math lesson" because you used fractions (Does that drive you crazy, too? As if cooking together wasn't valuable in and of itself.). I just mean that these everyday situations often will allow your child to make math discoveries on his own... living ideas that appeal directly to his mind with little or no explanation needed.
Do these thoughts make a difference in the curriculum you choose? First of all, you do not need to choose a math curriculum that weaves the concepts into a story in order to pass on its living ideas. (Though I'm not saying you can't use such a thing...) It will be more important that you use manipulatives, whether you choose a curriculum that utilizes them, or whether you use beans or buttons alongside your more traditional math program. You may have your own ideas about activities and games using math, or you may use a resource book for inspiration and ideas like I do. What matters is that your child has a chance to discover some living ideas for himself. Math is not just about dreary, endless pages of drill in arithmetic facts, it is about inspiring ideas waiting to be discovered and explored. These ideas give meaning to the facts and make practicing them interesting and worthwhile.
This post is part of the series "Choosing Elementary Math Curriculum with Charlotte Mason's Principles in Mind"
You are *still* here >>A Good Teacher - Part 1, Part 2, Part 3
A Method, Not a System
Atmosphere, Discipline, and Life in Early Math Education
Spiral or Mastery?
Putting it all Together: Choosing Curriculum and Resources