Charlotte Mason Math | Atmosphere, Discipline, Life
A Charlotte Mason Math program that uses math rods? A debate arose from my last post on whether Gattegno truly exhibits the Charlotte Mason philosophy. I have been told by some that Charlotte Mason thought math rods were contrived. I think Gattegno would agree that in the wrong hands math rods are contrived.
I know that stuns you, but let me be clear, Gattegno would find counting beans and buttons contrived, too.
I want to examine Charlotte Mason’s view of education as an atmosphere, a discipline, and life in light of Gattegno's own views on education. I think you will find that they agree on a lot more than just contrived math objects. In fact, I don't think you could find a Charlotte Mason math curriculum that is more agreeable to all the best philosophies Charlotte Mason holds.
Charlotte Mason Math and Education as an Atmosphere
It stultifies a child to bring down his world to a 'child's' level.
Charlotte Mason Home Education Vol. 1 p 6
The reality is like all good things, manipulatives are quite abused in the wrong hands. When one thinks that the greatest use of rods is to teach calculating, well, there you have a contrived use of the math manipulative.
In fact, mathematics as a form of conveying how to calculate accurately is a low, vulgar form of mathematics. To present mathematics in such a form is to lower the atmosphere of the child.
A child forced to count beans and calling it mathematics is equivalent to serving a hot dog to a child and calling it food. Being handed algorithms and math facts on a plate is the same as chewing up a child’s food.
The delight of consuming math is all but removed. It becomes tasteless and bland. They have no idea what they are eating. The atmosphere is lost. Such attitudes conclude that the child is incapable of chewing and cannot handle a fork and therefore, must be spoon-fed processed math.
Then when a child, blinded by its demeaning atmosphere, gains no understanding of the algorithm you hand them pebbles, which is like handing them a fork. But now they are blinded and the fork provides them no benefit to perceiving the food.
Through the vulgar use of manipulatives, the child merely gets by with the lowest form of understanding, that is - if they even get by.
The Symbolic Nature of Atmosphere
The latter word is symbolic, it is true, but a symbol means more to us all than the name of the thing signified. We think of fresh air, pure, bracing, tonic,––of the definite act of breathing which must be fully accomplished; and we are incited to do more and mean more in the matter of our children's surroundings if we regard the whole as an atmosphere, than if we accept the more literal 'environment.'
Charlotte Mason Home Education vol 3 p 149
Atmosphere is everything. I think here Charlotte Mason hints more to its symbolic meaning. The fresh air, pure, bracing, and tonic breathing of mathematics isn’t found in processed and sterilized algorithms.
We do not present the most vulgar forms of art to a child to develop a keen eye for the beautiful. We do not bring in the leaves from outside and present them to the child in a sterile form to study.
In much same way, we must not sterilize mathematics by presenting math facts and algorithms in an isolated vacuum. The atmosphere of mathematics must be tangible enough to be perceived by the eye of a child, but rich enough to cultivate a genuine interest in the pursuit of mathematics. It must be a breath of fresh air.
Gattegno provides a methodology for the child to perceive mathematics and manipulate mathematics with understanding. A child's knowledge of algorithms are developed through experience with mathematics.
The child perceives the most efficient way to manipulate and create numbers because he has experienced the algebraic nature of numbers through simple handling of the rods. To use the rods to memorize math facts is a very contrived form of math rods. However, to use the rods to help students study the behavior of numbers is not contrived. It is very much like a nature study.
But maybe I am taking liberties with atmosphere, so let’s move on where Gattegno’s methodologies are even more harmonious.
Charlotte Mason Math and Education as a Discipline of Observation
This is all play to the children, but the mother is doing invaluable work; she is training their powers of observation and expression, increasing their vocabulary and their range of ideas by giving them the name and the uses of an object at the right moment,––when they ask, 'What is it?' and 'What is it for?' And she is training her children in truthful habits, by making them careful to see the fact and to state it exactly…”
Charlotte Mason Home Education Vol 1 p 47
Charlotte Mason rightly treasures the habit of observation. It is not a habit that manifests itself on its own as Charlotte Mason points out. It is one that requires the attentive parent to,ask questions of the child to improve upon observation. The parent also provides language to the child by which to express the observations more accurately.
In the same fashion, Gattegno says that all mathematics can be perceived with the eye just like nature is perceived by the eye. Gattegno walks harmoniously with Mason. The exercise is two fold.
First, Gattegno introduces clearer language to the student but only as the student is able to articulate the math they perceive. Second, Gattegno provides specific tasks and questions designed to heighten and develop the students' perception.
Cuisenaire rods are much like the field in nature. In them lies a depth of mathematical knowledge freely available to those willing and able to look. This requires a parent to have a some perception of math, but if we don't expect a child to develop the habit of observation alone, we shouldn’t expect it of parent.
No, we all need a guide who can develop our habit of seeing the mathematical ideas that are indeed perceivable to the trained eye. The value of Gattegno’s free textbook is not in the rods at all. It is in the method of disciplining the eye to observe the mathematical ideas that are inherent in the rods.
Charlotte Mason Math and Education as a Discipline of Thinking
Charlotte Mason often saw mathematics as the one true playground to develop the habit of thinking. When children perceive mathematical truth through the handling of the rods, they are also able to develop the skill of thinking and perceiving cause and effect.
With math rods, a child can perceive that the yellow plus the red is the same length of the black rod. They can also see that red plus yellow makes the same length as black. In such discovery, they can perceive that this continues to be true with the dark green and the white, the purple and the light green and so on.
With further observation of rod complements for tan, orange, yellow, etc., the child continues to observe this truth. Of course, only when we draw the child to observe these things, to search for the cause and effect, does the child become aware how things are the same and how they differ and what the cause is of their equality or inequality.
This is the sort of thing that the children should go through, more or less, in every lesson––a tracing of effect from cause, or of cause from effect; a comparing of things to find out wherein they are alike, and wherein they differ; a conclusion as to causes or consequences from certain premises.
Charlotte Mason Home Education Vol 1 p 151
It is asking a child to compare things. To ask what is different, what is the same, and to make conclusions based on their observation.
The child can then reason, without a doubt, that this is a certain property of numbers. The child has perceived with their own eyes and understanding the commutative property. This is a deep-seated experience that eventually translates over to a more streamlined memory of math facts.
I think that Charlotte Mason would agree that the habit of thinking doesn’t happen in a vacuum. It doesn’t happen from merely counting beans. Math is certainly not easily observable through beans. You can read why beans fail to develop number sense here. It doesn't mean it is wrong to use beans, but that beans compared to something like Cuisenaire Rods are an inferior tool.
Charlotte Mason Math and Education as a Life
This isn’t about the manipulatives though. This is about life, that is surrounding children with “living thoughts and ideas, not just dry facts.” This is about whether to teach mathematics as an art form of living ideas. Or is math more useful as facts for completing mundane calculating tasks of everyday living and making sure they are speedy and accurate.
Mathematics as Ideas vs Facts
Mathematics is the study of numbers. Within numbers are ideas of how numbers relate to one another and those ideas are expressed through generalizations.
Much like memorizing scientific facts, memorizing algorithms and math facts do not invite the child to study how numbers relate to each other. Facts make no appeal to connect with the child’s thinking or experience. Isolated facts derived from the studying math facts do not make it possible for a child to perceive the relational aspect of mathematics.
Education is the Science of Relations, appears to me to solve the question of curricula, as showing that the object of education is to put a child in living touch as much as may be of the life of Nature and of thought.
Charlotte Mason, Home Education Vol 3
For Charlotte, education is the science of relations. Nature is rich with mathematical properties and it is a worthy endeavor to develop the child's perception towards these relationships.
However, it is nearly impossible to perceive the relationships between addition, subtraction, multiplication, division, fractions, ratios, percents, polynomials, exponents, logarithms and everything else they might study in elementary mathematics. If you want your child to study those relations, you are going to need a set of graduated base-ten blocks like Cuisenaire Rods.
If living math is about ideas over facts, it should be presented in a way that invites the child to play and manipulate the ideas contained within it. Living mathematics must be tangible enough to be held by the eye, so as the child need not be told. However, it should not demean the child as an unthinking being in which to fill with facts like some vessel.
Through the cultivated habit of observation and provision of mathematical language, Gattegno provides the atmosphere by which math becomes a rich place of living ideas all while treating the child humanely and as a real individual person.
Let Math be Math and Nature be Nature
Much as nature should be the place to study that which is natural, so mathematics should be the place to study that which is numbers. We must not confuse the natural physical elements of the atmosphere of the child as its playground for math.
Mathematics is an endeavor of the mind, and Gattegno uses Cuisenaire rods only to provide a child with a ladder into their own mind by which to play and enjoy mathematics.
The question remains would Charlotte Mason approve of Gattegno? Gattegno’s methodologies for mathematics are a compliment to Charlotte Mason’s philosophy. You couldn't ask for a more Charlotte Mason math program. Gattegno provides parents with insight into the mathematical world, so that the parent may add to the rich feast that is laid before the child.
A worthy Charlotte Mason Math Curriculum
So for those who have made it this far, you may be wondering about Gattegno's methods. There is only one real way to know and that's experience it. Sonya from Arithmophobia No More offers free classes every week to help parents just like you develop their mathematical insight using Gattegno's methods. It is a very hands-on class with lots of opportunities to participate.