Teaching math

Two passages in Charlotte Mason’s writing about math are in my opinion widely misunderstood. The first relates to the proper use of manipulatives.

Mason believed strongly in the importance of physical objects and oral work (mental math) in early math education. In her priorities, the use of written calculation fell in distant third place.

“A bag of beans, counters, or buttons should be used in all the early arithmetic lessons, and the child should be able to work with these freely, and even to add, subtract, multiply, and divide mentally, without the aid of buttons or beans, before he is set to ‘do sums’ on his slate.”

 — Charlotte Mason, Home Education

Continue reading Charlotte Mason Math: The Trouble with Manipulatives

“Teachers have seldom time to give the inspiring ideas, what Coleridge calls, the ‘Captain’ ideas, which should quicken imagination. How living would Geometry become in the light of the discoveries of Euclid as he made them!”

 — Charlotte Mason, Towards a Philosophy of Education

The Captain ideas are the great Truths of a subject, the things that make our minds wake up and pay attention, that energize our thoughts and make us yearn for more.

In math, living ideas are the big principles that tie together many branches of the subject. Things like:

• Proportion — where two quantities are connected so they scale up or scale down in tandem. For instance, if we double the number of cars in the driveway, that automatically doubles the number of tires.

• Transformation — how we can change things while keeping important attributes the same. Like, if we shrink a square, its area will change, but the angles stay the same.

Continue reading Charlotte Mason Math: Finding Time for Big Ideas

Even in Mason’s day, testing drove much of educational policy, but we must not allow ourselves to fall into the trap of teaching for a test. Just as we do not study history in order to win a trivia contest, so we do not study math merely to produce answers on an exam.

“Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.”

 — Charlotte Mason, Towards a Philosophy of Education

Remember Mason’s twin goals of rightness and reason. Even if you use a math book that focuses on memorizing rules and cranking out answers, you and your child can look for the ideas behind the rules: “Why does this work? How can we know for sure?”

Not just because the book says so, but because you search out and discover the innate sense of it. That is the essence of mathematics.

Continue reading Charlotte Mason Math: How Shall We Teach?

“Therefore, we are limited to three educational instruments––the atmosphere of environment, the discipline of habit, and the presentation of living ideas. The P.N.E.U.* Motto is: Education is an atmosphere, a discipline, and a life.”

— Charlotte Mason, Principle 5

This principle is the key to a Charlotte Mason education. Most of her books consist of drawing out the meaning and implications of this motto.

When we think about applying Mason’s educational principles to math, we must focus on providing the right atmosphere, developing appropriate habits, and presenting living ideas.

What is the mathematical atmosphere of our home or classroom? Is math a natural and welcome part of life? Or does it exist only in schoolbooks and in some nebulous “future” for which our children must prepare?

What about the people in our children’s lives? Do we adults enjoy and use math, or do we dread and avoid it? Is our mathematical worldview positive, eager to learn and grow, or negative, seeing math as a chore to endure?

Continue reading Charlotte Mason Math: Our Educational Tools

In our search for a Charlotte Mason math education, we must take into consideration Mason’s approach to all learning, not just the things she said about math. We must be guided by the core principles of her philosophy, even in math

“We hold that the child’s mind is no mere sac to hold ideas; but is rather, if the figure may be allowed, a spiritual organism, with an appetite for all knowledge. This is its proper diet, with which it is prepared to deal; and which it can digest and assimilate as the body does foodstuffs.”

 — Charlotte Mason, Principle 9

For instance, we must offer our students living ideas (not mere facts) in math, just as we do in literature and history.

Masons “20 Principles” outline the essentials of her educational philosophy. If we truly apply these principles to math, it can radically transform how we teach the subject.

Let’s examine a few of her principles in more detail…

Continue reading Charlotte Mason Math: Practice Your Principles

“The Principality of Mathematics is a mountainous land, but the air is very fine and health-giving. People who seek their work or play in this principality find themselves braced by effort and satisfied with truth.”

— Charlotte Mason, Ourselves

Charlotte Mason (1842-1923) was a British school reformer at the turn of the twentieth century, a contemporary of William James and John Dewey. She advocated strongly for poor children, arguing they were equally capable of learning a wide and liberal curriculum as were the children of privilege.

Mason believed that all children from the time they are born share a natural curiosity and hunger for learning, and the adult’s role is to spread a “wide and generous feast” of inspiring ideas.

She was also a homeschooling pioneer, and the homeschooling revival of the late twentieth century rediscovered and popularized her books. Many found her principles a refreshing balance to the dominant educational paradigm of pragmatism.

Continue reading Introduction to Charlotte Mason Math