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}

**Jeanne**is an Aussie homeschooling mum to 10 year old Jemimah. She is passionate about the educator Charlotte Mason, the Ambleside Online curriculum, MEP maths, the Reformed Presbyterian Church of Australia, Japanese aesthetics, French language, Asian travel, children’s literature, her garden, and living a peaceful life in the country. She is honored to work alongside Brandy and other inspiring Christian women as part of the Ambleside Online Auxiliary. Jeanne writes about all of these things as well as whatever strikes her fancy at her blog, A Peaceful Day.

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.

Karen says

Thanks for this excellent post Jeanne!

Sarah says

Excellent grounding thoughts Jeanne in how to truly allow a CM education fill the atmosphere of our homes. Thank you.

walking says

I would suggest looking at the book she used which is available online, seeing if it suits your needs, or use it as a guide to find something more suitable.

Brandy @ Afterthoughts says

I just looked at it. It looks more like a *history* of math than what we think of as “living math” where the story is trying to teach mathematical concepts. I admit it is a fine line between the two, but still…I have been pondering teaching the Quadrivium using (not solely, but using) primary sources. That idea seems to fit more with this book than I would have expected.

Brandy @ Afterthoughts says

Okay. I just bought it. I think I’ll try using it during my morning Circle Time with all the children and see how it goes. Apparently, they used it in American schools for a time? The copy I found is from the 50s and it was printed by The National Council of Teachers of Mathematics in Washington, DC. Interesting. Someday I need to get a Kindle so I quit spending money on test-driving books like this, but I *do* so like a hard copy…

walking says

Jeanne, you wrote: ” I would say stop dithering over ‘living maths’ and choose a text book.”

It is hard to find the actual math texts Mason used as listed in her programmes. You can read one for free over at Google: A Shilling Arithmetic by Charles Pendlebury. Here is a link to the kind of “living math” book she recommended as a supplement to be read in leisure time (and she did not recommend many): Number Stories of Long Ago.

Brandy @ Afterthoughts says

Okay, so she recommended at least *one* “living math” book for leisure reading. Does this mean that we can or ought to do the same? I’m thinking of Life of Fred or the Sir Cumference books or something–are a few of these during leisure time a good idea? I haven’t done anything like that, but I am willing to…

...they call me mommy... says

This is SO helpful! Thanks Jeanne and Brandy!

Tammy Glaser says

Sticking to a program worked for our family too. I know it wasn’t perfect but jumping to another curriculum would have been far more confusing. That is where the good teacher comes in. If you have seriously looked at the books Mason used for math, you would be surprised. They are not at all living!

Michelle Downunder says

I agree with your thoughts wholeheartedly. I’ve been fairly consistent with Math programs but lost about a years worth of progress flipping around with diferent textbooks.

Jeanne says

Thanks, Michelle. It is lovely to see you visiting from Oz. 🙂

What have you ended up with for maths in your family?

Naomi says

Great points Jeanne! So true how we think of math as one of those ‘outside of CM’ areas. How do we go about getting those captain ideas ourselves? Brandy, thank you for hosting a topic few CMers would touch. Looking forward to the rest!

Jeanne says

I’m inspired right now by the idea of teaching a subject of fractals in nature next year, one period a week. I am so excited about this, I am even considering introducing them over the holidays! I am sure Miss Mason would have considered fractals captain ideas in maths!

lindafay says

Great article, Jeanne. I particularly like your advice to stick to one program instead of hopping around and:

“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…”

Jeanne says

I firmly believe that swapping curricula causes more problems than it cures. Working with your current curriculum and introducing more of Mason’s techniques seems the way to improve the teaching of maths in most homeschools, I think.

Jen says

Yes, I was so excited to see that you were doing a math series this week because it’s something I’ve been thinking about a lot too. It’s wonderful the way we can all learn from each other’s experiences.

Jen says

Wonderful timing for me to read this article! I’ve been dithering over whether or not to change math programs (maths programmes? I’m American but lived in PNG for 10 years and all of my children were born in Australia, so my spelling is now confused! But I digress..). I’ve been leaning towards sticking with what we’ve got and adjusting my teaching methods a bit…thank you for confirming that I’m heading in the right direction. =) I’ve found both of your blogs (Brandy and Jeanne) relatively recently via the AO forum and appreciate so much what both of you do and gleaning from your experience. =)

Jen

Brandy @ Afterthoughts says

The AO Forum is a great place to get confused about spelling. 🙂

Jeanne and Tammy have both had me thinking new thoughts about math lately and I am so grateful to them! I’m glad you’re here, Jen.

Jeanne says

Hi Jen, thanks for your nice words.

There are certainly times where a maths programme really does not suit student or teacher, and after persevering for a while then it is clear that changing in the only option. I understand that. I just think that all too often homeschool mums make this decision far too early, without recognising all the things they will need to relearn with the new curriculum. I am glad I have helped you reconsider!