September 30, 2012

Living Math Reflections


Since I first heard about the idea of 'living math" I loved it! I loved the idea of including stories about mathematicians into our discovery of arithmetic. Reading about other people's passions often ignites passion in us and I wanted my boys to know other people in history have had a passion for numbers. I want them to wonder why and perhaps catch the passion for themselves.  I love doing math incrementally line upon line working towards mastery of a concept before moving on. I love going at their pace. I loved not having to give them a text book. Mostly I just did not want my kids to hate math. I want them to get it and master it however deep they go in it.

"Living math" is a kind of vague idea to many, and though Charlotte Mason did say a fair bit about it in her writing I found myself stabbing in the dark, adding pieces of her method here and there in our home education but never having a solid feeling I really know what I was doing. Maybe I am not alone here. So this week when I found in my inbox the weekly post from Simply Charlotte Mason announcing they were putting out a manual about living math I was on it. I have had some rich afternoons since then and now pouring over all the quotes and helpful practical tips of how to do it.

Basically as I read  through the e-book pages I have felt affirmed that my thinking about math, not to mention those little gut decisions that I made not knowing were right along with Charlotte! yeah! I also have found little things to add, tweak or wish I could redo because ahhh here is the answer I needed two years ago! If you have ever wondered about living math and wanted to know just what it is and how to do it or if you have wanted a scope a sequence to help you plan your own journey into arithmetic then you might want to read this e-book: Mathematics: an Instrument for living Teaching


One of the very first things which intrigued me was the title. How is mathematics a tool for living teaching? It comes from this quote from Charlotte's writings:
“I need not touch upon the subject of Mathematics. It is receiving ample attention, and is rapidly becoming an instrument for living teaching in our schools” (Vol. 3, p. 236).
How is mathematics a tool for living teaching? The answer is very cool. Charlotte used math to build mental and moral habits. Habits like accuracy, reasoning powers and intellectual truthfulness. Though she did not discount that it had usefulness for everyday life her focus was on the habits it established. This was a refreshing idea for me and a new way of answering to myself why do we do math?
"The practical value of arithmetic to persons in every class of life goes without remark. But the use of the study in practical life is the least of its uses. The chief value of arithmetic, like that of the higher mathematics, lies in the training it affords to the reasoning powers, and in the habits of insight, readiness, accuracy, intellectual truthfulness it engenders” (Vol. 1, p. 254). 
So, inspired now with a new reason for doing math I began to understand better what living math is and how to go about it. I felt affirmed in my gut desire for certain ways of doing our math assignments, like my desire to have a neat math page was not picky it was important. It had a purpose to build something of value beyond that simple act. And getting the right answer was no longer just me being tough on them it was right and building in them a good habit of accuracy and intellectual truthfulness. Charlotte helped me see why I valued these things and gave me permission and a framework to continue in them.

"In my reading of Charlotte Mason’s Original Homeschooling Series, I noticed Charlotte used words I had never applied to the study of mathematics—words like joy, beauty, truth, and awe." -Richele Baburina 
To build these mental and moral habits Charlotte recommended using a curriculum which had these following characteristics: (from Mathematics: An Instrument for living teaching page 97-98)
  • Provide for careful progression. We want a gradual unfolding of ideas, not
    simply a “getting through” of a course of study.
  • Work well with a number of manipulatives in the introduction of concepts
    but not be shackled to them for the entire course of study.

  • Not require expensive or complicated apparatus or work with only one type of manipulative. The child should be able to separate the facts from the objects used, so being able to utilize a variety of everyday objects is best.
  • Not drown the subject in too much verbiage. 
  • Give examples that are interesting and aimed at reality; money sums and
    those involving the familiar are best.
  • Give examples that, while interesting, are not too difficult.

  • Give examples that work well with oral work. Children’s work in Charlotte’s
    classrooms was largely oral in the earlier years, and continuous oral practice
    was still given in later years.
  • Assist the child in arriving at the method of solving problems or making
    discoveries himself.

  • Facilitate reasoning powers not just mechanical ability.
  • Allow for short lessons, no longer than 20 minutes in the earlier years and
    30 minutes in the junior high or high school years.
  • Allow you to adjust the pace for your child. 
  • Allow for mastery of concepts. Securing your child’s understanding is a
    must before proceeding to the next concept.
  • Allow for adequate review. Once a concept is mastered it will still need a
    sufficient review, and having examples of varying difficulty is best if your child progresses rapidly or for review the following term or year. 

"If you don’t have a strong grasp of mathematics, please do not despair. Don’t be surprised if, as you begin applying Charlotte’s methods in mathematics, you also start seeing the reason behind the facts, discovering new relationships, and experiencing joy and delight while obtaining more mathematical understanding yourself. " -Richele author of Mathematic:A Tool for Living Teaching
Last summer I fell in love with a wonderful turn of the century math book written by Emma Serl who also authored Primary Language Lesson, a grammar study I think Charlotte would have loved. She may have loved Everyday Number Stories too for as I read through the e-book and the list above it kept occurring to me how well that this little free book fits into living math education she was writing about like a hand into a glove. By working through this math book with the boys I found real joy in math for the first time, for I saw the relationships between multiplication, division, addition, subtraction and fractions. Really fun! But more than that the real life problems and stories were easily made practical by using ordinary things around the house to explain and bring alive the abstract math. They enveloped measuring, turning problem inside out and upside down looking at an addition problem and making it into a fractions problem. Best of all it made us all think circumspectly about math in its beautiful rudiments.

I have more to read, more to implement and if this subject will be like any other Charlotte Mason methods I have implemented they will be a success.

Happy figuring!


15 comments:

  1. I am so thrilled to come upon your review. I just ordered this new SCM book ... they continue to inspire. Beautiful post. Thank you! I am eager to seek out Serl's math book ... we love PLL!

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    1. I hope you enjoy it as much as we did!!!

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  2. Sarah, this is such a helpful post! Thanks for sharing. I will have to check out Everyday Number Stories.

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  3. Reading this post made me think of this series of math books...Practical Arithmetics. They are just so gentle and lovely with great examples.

    http://www.christianbook.com/practical-arithmetics-book-1/george-strayer/pd/545009?event=WL&item_code=WW

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  4. Thanks for the link Sheryll...there are also more turn of the century math books that are good out there. Don Potter's site has a huge list of them on his site and I think Practical Arithmetics is there, most are free. I have also been using Ray's Arithmetic oft and on because I like the basic line upon line approach and the good story problems.

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    1. Here is Don Potter's URL: http://www.donpotter.net/education_pages/math.html

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  5. What grades would you say Serl's Everyday Number Stories is geared toward? K-3ish? I'm going to print and bind a copy this week. Thank you, again!

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    1. Good Question Kate. I assume your estimate is right but I have little experience beyond my three boys to say. It really depends on what they know and how much you want to teach for the concepts range from addition on to division very soon in the book. In addition she asks the student to give answers like what is 1/3 of 12. Though her approach makes this doable at points where a concept is new you may slow down, give additional instructions etc before doing the practice exercises. My 6 and 7 1/2 year old found it challenging but they have never had any instruction on multiplication or division before. It gave them a keen understand however of the need for learning the multiplication tables something you may want to add to the teaching of the book. Have fun!!!

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  6. This was a very thoughtful and inspiring post. Thanks, Sarah!
    ~Debbie

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  7. I am trying to decide whether to purchase "An Instrument for Living Teaching." My 8 yr. old son keeps teaching me to continue to use Charlotte Mason methods of teaching. He is a very hands-n child. I am currently supposed to be using Saxon. It is very hands-on, but in a different way as I am even board with it. Instead of him using the booklet and counting to 100 each day to use a different hands-on approach. So my question is would I be able to use this as a curriculum where yes he is writing but not too much. He has trouble with a lot of writing. I want him to learn, but in a more fun way. I suspect sensory with him. He tells me each day Math is boring, so I am thinking about using this book with him. Since you mentioned other books I was unsure if I could just use this book as a curriculum per say. Any help would be great! Thank-you for this post!!!

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  8. Hi Kelly,
    My boys also don't do well having to write alot, but they will do hundreds of math problems if they are put into a game format or a hands-on project where they are doing something. They also do well doing the problems orally. Mathematics: An instrument for living teaching give great guides of how to teach with CM principles but it is not a curriculum so much as a scope and sequence. It does suggest a few curriculums in back pages that will work with CM. I also recommend Emma Serl's Everyday number stories. However, even though it is CM friendly I adjusted the lessons to they fit the skill level of my boys. Using Everyday Number Stories I may have them write in 10-15 answers, do some orally and some hands on. That would be three different lessons. In everyday number stories you can DO so many of the lessons hands on and orally but you will have to not follow the book per say but use the book to help you. For instance, I have Ray's Arithmetic which is very dry, just rows of problems one after another, but when I use those problems with a game like Storm the Castle where they are going for a goal and doing the problems orally they do five pages not 10 problems. With boys I have learned to do a lot of our lessons orally so their mind can show its stuff and continue with the handwriting at their pace but to not limit their schooling because of it. Every day number stories is FREE no harm in trying it. Storm the castle is also FREE just google it and you will find it on Ellen's website. Please write again if you still have questions.

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  9. I have not really had my son write at all except for the answers with math on the wipe-off board as last year was such a battle to home-school. I am not really looking for a curriculum per say. I guess seeing how CM taught is a curriculum right in the book I asked about before? I did look at the sample page on Simply Charlotte Mason. It mentioned how not to move on until for example they know how to add 1 first, so not to go from 7+7 for example. I am hoping it has more of these suggestions or hands-on suggestions. Does it? My 8 yr. old is so hands-on unlike my older daughter and my older son. My 8 yr. old has taught me to look into CM. I am seeing the boredom with even my 6 yr. old whom loves worksheets!! I have been using Saxon which seems to be just way too much!!

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    1. Yes there are a more of that kind of examples for Multilication etc. Predominately the SCM manual is a conglomeration of what CM says about mathematics presented in a organized fashion and with more explanation so her ideas are clear. If you read the sample you have a good idea what is in the book. Youmay really like it.
      What I gather form the SCM manual is that CM basically used manipulatives (things around the house) and did much of the math orally. I suppose you could still continue with Saxon if you have time to break up the lessons and make them more hands on and oral and only takes 5-15 minutes a lesson. I have done that with Everyday number stories and I too plan to use Saxon in the same way. Perhaps you would like the SCM manual for math as then you would have a good grasp of the method and be able to apply it how it fits your kid.
      Let me know if I have answered your question better this time around. :)

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  10. I think I best just order the book huh? lol It does sound like I would like it, but I keep second-guessing myself. Last night, I was looking at her Phonics as well. Hmmm...do I need to look at that one too?

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