This post is the first of our series of guest posts for Math Week here on Afterthoughts. You may want to read the preceding post first. Here is the series Table of Contents:
- Series Introduction
- Teaching Maths the CM Way {by Jeanne} <– you are here
- Five Strategies for Teaching Mathphobics {by Tammy}
- Teaching Euclid in the Homeschool, Part I {by Willa}
- Teaching Euclid in the Homeschool, Part II {by Willa}
The reason why mathematics are a great study is because there exists in the normal mind an affinity and capacity for this study; and too great an elaboration, whether of teaching or of preparation, has, I think, a tendency to take the edge off this manner of intellectual interest.
Charlotte Mason, Home Education {p. 264}
I am often surprised at the number of homeschools where Charlotte Mason’s philosophy, followed so diligently for the rest of the curriculum, is all but ignored when it comes to mathematics. Mothers spend hours, days, weeks – even sometimes years – in collecting the perfect literature books, arranging educational nature hikes, keeping Books of Centuries and Nature Notebooks, mastering dry brush painting and teaching three or even four languages and then they simply ‘add in a maths programme’. Any programme. Then later on these same mothers wonder why their dear children are dawdling over their maths worksheets and wondering quite what went wrong.
Sometimes at that point they begin to think about how to make maths more ‘fun’. They look at the so called ‘living maths’ books. They add in more manipulatives. They start reading maths biographies and dump the maths programme for another one that is based on literature, or uses an abacus or Cuisenaire rods or has the children collect stones for use as manipulatives. That one doesn’t work so they try another. Then a third. Maybe they decide to ditch the text altogether and write a curriculum themselves. Surely then the children will love maths, they say. But no, with each switch they become more and more confused and begin to dislike mathematics more and more. Just like Miss Mason says that they will.
Instead of going through all this angst, wouldn’t you think following Miss Mason’s words in the first place would be better?
Mason wrote about maths right through her six volumes, but particularly in the first and last, the two written some forty years apart. Reading the two side by side, it is apparent that Mason’s views change considerably with this passing of time, and so while it is good to have the practical information contained in Vol 1, particularly for young children, it is also important to know how she refines and improve things throughout her career. In the case of maths, this is somewhat surprising.
If I could take the anxious mother by the hand about now and sit with her over a rich frothy cappuccino and a peanut biscuit or two at my kitchen bench, I would offer her a few words of comforting advice. First, I would say this: Relax, elementary math is not so hard. {Actually, since I am an Australian, I would say primary maths is not so hard, but I am willing to compromise just a little for Brandy’s predominantly American audience.} Really, it’s not. Even if you found maths difficult yourself through high school, chances are that you did fine with maths at primary level. Most people do. Even if you’ve forgotten all you learned, you’ll have a chance to relearn it this time along with your kids. My long division is much stronger now than it ever was when I was the student.
Secondly I would say stop dithering over ‘living maths’ and choose a text book.
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, because there would seem to be some inherent quality in mind which prepares it to respond to this form of appeal and no other. I say in the initial stages, because possibly, when the mind becomes conversant with knowledge of a given type, it unconsciously translates the driest formulae into living speech; perhaps it is for some such reason that 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 mind.
Charlotte Mason, A Philosophy of Education {p. 333-334}
The first surprise in Volume 6 is that Miss Mason had come to the realisation after forty or so years that not all subjects are best conveyed through a literary medium, music and maths being cases in point. Mason saw that mathematics is a language of its own, always logical, always clear, one that meets the mind’s needs without embellishment.
Miss Mason’s students used basic mathematics text books available at the time. Despite always searching for the best text books, she did not request special literary texts to be written especially for her schools, and in the same way, we can use a basic text book too.
Next I would give my worried friend some very important advice. Once you’ve chosen a curriculum, stick with it. Regardless of the text book we choose, we should be chary of changing maths curricula too often. Every programme operates using a particular premise. Some are spiral; others are mastery based. Some build sequentially, some don’t. Some are visual and rely heavily on manipulatives – rods or an abacus. Some believe strongly in the mastery of maths facts. Some introduce algebra and negative numbers in grade one, others don’t. The only thing that you are sure to get when you change maths programmes is gaps.
Yep. Gaps.
Which brings us to the next point:
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.
Charlotte Mason, A Philosophy of Education {p. 233}
The reason the text doesn’t much matter is because mathematics depends upon the teacher, not the book. It is not which text book you choose, but how you use it that matters. Good teachers recognise the beauty inherent in mathematics and in the same way as they recognise the need to allow an author to reach the child without getting in the way, they ‘know that they must not drown their teaching in verbiage.’ {p. 51} When your student encounters a problem with maths – and odds are that at some stage he or she will – chances are that the problem lies not with the text book but the teacher. Spend some time going over the problem area. Try searching the Internet for different approaches. Slow down. Maths is not a race. Consider how important the problem concept is in the scheme of work. Is it foundational or supplementary material? Do you need to understand this work in order to move forward, or will it be covered again some time in the future? Perhaps you are under prepared and do not understand the information well enough yourself to teach it. Perhaps, alternatively, you have been like the teacher that Mason refers to, elaborating too much on either teaching or preparation resulting in the child losing intellectual interest. Perhaps you have been preventing the mathematics from speaking to the child.
And this is my last point. Teach mathematics the Charlotte Mason way. If you’ve been using her methods and philosophy in the rest of your school then use them in maths as well. Mason’s 20 Principles, her Educational Manifesto, and the Four Pillars of Education apply every bit as much in the mathematics class as in every other part of a child’s school day. Remember the hallmarks of a Charlotte Mason education – give short lessons {20 minutes a day in the early years, 30 minutes daily in grades 4-6}; expect accuracy of work; work on developing of good habits. Don’t give the child busywork, with pages and pages of equations that he can already do. Allow the mathematics itself to speak to the child, and quicken his imagination with Captain ideas. Teach maths in context. Use techniques that you use in the rest of your school – narrating, or telling back the method used to solve problems; keeping a mathematics notebook to record rules, theories, interesting historical ideas and examples. Use concrete examples before moving on to abstract ideas, demonstrating where possible with manipulatives. Make maths real. Use word problems and realistic scenarios that are relevant to the child.
There is much, much more that Miss Mason has to say about the philosophy and teaching of mathematics. As always, the only way to truly understand her methods is to study them. The more we understand about her reasons, the easier it will be to apply them in our homeschools.
Miss Mason believed about mathematics that there is no one subject in which good teaching effects more, as there is none in which slovenly teaching has more mischievous results. {p. 254} She also believed that mathematics are a great study and that an affinity and capacity for it exists in the normal mind if only the teacher does not get in the way. {p. 264} Let us, as teachers take these two phrases to heart and let us teach our children well. Let mathematics alone speak to our children with logic and clarity. Let us take time to give inspiring ideas. Let us teach mathematics the Charlotte Mason way.
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