Saturday, July 28, 2012

Math Out-of-the-Ordinary


Math Out-of-the-Ordinary

In my home school memories - somehow - the day only felt like “school” after we completed a math lesson – even if I were to accomplish an impressive array of other subjects in one morning (on a good day.)  

We did math everyday.

This year I responded to a reader’s email with “Yes, I admit to being quiet on the subject of math in A Charlotte Mason Companion.” Therefore, seeking to be helpful, I cordially present a host of hints. They are woven within my descriptions of the materials. If your interest is in higher math, I supply a link at end of the post where Dean describes courses created by designers with an ardor for algebra. (I can’t resist alliteration when it suggests itself.)  


I recommend math lessons where young students can:

learn the language of mathematics,
use numbers with tangible objects,
take part in demonstrating how numbers work,
observe where numbers are found in the world around them. 

Math is a Language

Miss Charlotte Mason believed that in all subjects children gain knowledge (and retain it best) when it is “clothed in literary language” or, as she puts it another way, “conveyed through a literary medium.” She observed that there seemed “to be some inherent quality in [a student’s] mind which prepares it to respond to this form of appeal and no other.” Does she mean math, too?  Yes, she does. In Philosophy of Education, page 334, she says that possibly this is because, “when the mind becomes conversant with knowledge of a given type, it unconsciously translates the driest information into living speech . . .  Mathematics, like music, is a speech in itself, a speech irrefragibly logical, of exquisite clarity, meeting the requirements of mind.”

In the 1980s and then in the 1990s, when I wrote A Charlotte Mason Companion, we bounced around with math courses. Miquon was popular with home educators in the 1980s. It has a character of its own.


“How many ways can you write 12?” I’d ask. After my young student explored this on her own I’d give her a page like the one I’ve photographed. 


Miquon’s characteristic assignments make use of a young student’s inquisitiveness and preserve it. Maneuvering the rods, students find answers and come up with equations themselves. Miquon cleverly fosters mathematical reasoning and develops the language of math.








The Cuisenaire rods have been around for a long time and are still enjoyed by students today. My adult children would recognize the Cuisenaire rods and nod with a smile.












Each color and its length represent a number (up to ten) so that equations can be seen and felt. (For elementary ages.)


Making Math Meaningful by David Quine is another math course out-of-the-ordinary. We used some of Mr. Quine’s books, too. (Curriculum for K-12.)

To uncover the truths of math some children do fine with a conventional textbook. Some do not. That’s okay. There are different ways of becoming acquainted with math truths. A child really isn’t odd or unusual if he needs help other than a workbook to grasp concepts. There may be no reason to think, what’s wrong with my child? Many children “get it” only after tangible materials are at hand, demonstrating the kinds of things that numbers represent. This was true of my first child. It was a joy to witness her “I get it now.” I could see it in the brightening of her countenance and hear it in the inflection of her voice.  

“Children learn different concepts more thoroughly when ideas are presented many different times and in different ways.”   Peggy Kaye

Smoothing out a Math Snag

Games for Math by Peggy Kaye does more than take you through the steps on how to play her simply put-together math games. She shares her tutoring experience. She relates how certain children (she names them) with a math snag, responded to them.

Her activities correspond with the kinds of things children meet in their math books – but she offers tangible ways of understanding them and interesting ways of practicing them. A handful of strategy games get children thinking so do activities with codes, puzzles, tangrams, origami, a deck of cards, and more. 


When fact memorization was a goal, I’d set aside ten minutes of refresher just before supper. Memories would wane frustratingly without it. Review must be kept up. But the very nature of repetition can make a lesson taste stale. For this reason a young child may hit a snag with the memorization of his facts. Months of duplicate workbook pages turn him off. Boredom sets in. Frequently, all a child needs is the spark of a new idea.

Here’s one – math checkers.

Tape bits of paper to the black squares of the checkerboard. Each bit of paper has an addition or subtraction problem to be solved before making a move. You could place multiplication problems there later, I suppose. Such games are the kind to which you may find yourself saying, “Why didn’t I think of that?” They are nice and simple. But a busy mother doesn’t think of them because her attention is pulled in many directions.


A big pot of vegetable soup and a loaf of banana bread are two recipes for using math in the kitchen. By liters, milliliters, cups and spoonfuls a student is measuring capacity and making lunch at the same time. Did you know that 5 milliliters is a teaspoon? Two sewing projects demonstrate the necessity for accurate linear measurement with the making of a change purse and pillow.



A Math Imagination

Peggy Kaye’s book supplies a smidgen of math stories. It’s a pity there aren’t more. Creating fictional characters in fanciful plots (like her zebra who eats bags of yellow, buttery popcorn) can be used to get children willingly solving math problems in their heads. She quotes something unexpected from Einstein.

“When I examine myself and my methods of thought, I come to the conclusion that the gift of fantasy has meant more to me than my talent for absorbing positive knowledge.”

Imagination uses large mental muscles. It is a sign of strong intelligence. That’s why, in my home school story, Lessons of Blackberry Inn Carol’s children do mental arithmetic. They translate her math stories into equations. Carol takes care to think up situations that are adventurous like those found in Swiss Family Robinson - one of their read-alouds. Children like the challenge of making up their own math stories for their teacher to figure out. I invite you to give this a try. As I once did, Carol uses dominoes to review math facts. She would have welcomed Games for Math. Parents today will, too.

(Supplementary for Kindergarten – grade three.)


Math Clutter

Just when you cleared away the clutter out come the math manipulatives. But math clutter is the good kind of clutter. The 350-plus-piece kit, MathTacular will prove it.


Math is more understandable when children can see and touch their mathematical world. Justin, the young man with the smiling face on the DVD, appears to love math. He says that math is everywhere. What a fabulously creative job of he does of showing us where to find it inside and outside the house. Rather than razz-ma-tazz, split-second film frames, punctuated by explosive sound effects, we watch Justin take the time and quiet he needs to demonstrate each lesson. He is a patient, likable, often funny teacher.

The DVD is comprised of 67 segments covering basic math concepts. It is easy to navigate to the lesson you want and repeat it for review. Justin uses the brightly colored manipulatives in the kit as well as props such as the cutting of apples into fractions. He plays hopscotch out on the pavement for reinforcing ordinal numbers – one of many ideas that children will find interesting. You can see the big chunk of pavement chalk in my photograph along with baby bears to count and arrange.



There are blue unit-cubes, ten-rods, and hundred-squares for learning place value, a die, a wooden ruler, a geared mini-clock, geometrical pattern blocks, a geo-board, and more. With the help of the succinct teacher’s guide your children can use all these items right along with Justin.



This kit is a home school gem. Those who take advantage of MathTacular will have a positive math experience. Use it to reinforce concepts in, Making Math Meaningful, Saxon, Singapore Math and others.

(For 1st and 2nd grade but Kindergarteners can take part, too.) 


Math for the Gardener

Can you think of a more pleasant place to demonstrate math concepts than in a garden? That is, once the weather cools a bit, closer to autumn perhaps, when lessons begin.  


If you like being outdoors planting flowers and vegetables, the lessons in Math in the Garden will be your good excuse for spending more time there. I don’t mean children doing math pages at the picnic table – although this is nice, too. I mean using math to better understand living things. 

This teacher’s guide offers ways to use math by: making and using a garden grid, finding the perimeter and area of leaves, the ratio of vegetable shoots to roots, volume in flowerpots, comparing angles of stems, making a circle garden for exercises in circumferences and radii, looking at symmetry in fruits and flowers, noticing patterns, and seeing geometry in trees, measuring weights and distance. 

The healthy bonus of students collecting data in their journal is in eating part of the research. 


Math in the Garden has cute watercolor drawings of child-investigators on every page, doing the activities. There is no need to attempt all the investigations in one growing season. Choose a few year-by-year and you will still be getting your money’s worth of practical and memorable learning outdoors. (To guide children ages 5-13)

I wish you a likable experience with math out-of-the-ordinary, full of interest and “conversant with knowledge” as Miss Mason says so elegantly.


NEWS


Sale     $5.00

Here are my new photographs of my CD talk on Mother Culture. Click CD below for details.

My great-grandmother crocheted the table doily. 



Happy for your visit,
Karen Andreola 



9 comments:

  1. I would have for sure added some of these in the earlier years if I had known about them. I think I will still check out that one for math in the garden though. We have a huge garden and want to get the two younger boys ( ages 12 and 14) in and applying their math skills. [o= Oh and Karen how do I order your CD? I forgot I wanted it and I want to get it while I can.

    Praying blessings on your week end.

    Blessings In Him<><
    -Mary

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  2. Mary,

    Please email me in regards to the CD. I have a plan.

    Yes, my children would have enjoyed Justin's DVD demonstrations and the kit's manipulatives.

    Karen A.

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  3. Refreshing and delightful post as usual...I never realized that somewhere in the back of my mind I felt that I had "cheated" my children because we skipped around with different math programs in the early years. And I don't give myself "credit" for all the hands-on math we did...so much cooking, baking. One of the best ways I found to teach fractions was to give the children candy and have them divide it evenly. Talk about having their complete attention! :)

    I was relieved when we found "the" one that was right for us- Math U See- many years ago. My oldest, who is graduating this year is still using it.
    Then we found Life of Fred, which I would classify as living math. The author is absolutely passionate about math, and the stories although very silly are so engaging! Math U See was not clicking for my now 13 yo ds with Aspergers. LOF is something that did and he loves and the three youngest children will use.

    I think we need to give ourselves to grace as homeschooling moms to say "it's okay to use a variety of things until you find what works" (although I know I myself have learned not to just switch because "I'm" bored with something.)

    Praise the Lord that there are so many programs out there to choose from and so many other real life practical ways to impart math knowledge.

    What is the game that is in the top picture with the dice? I've never seen that one before.

    Blessings,
    Nanci

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  4. Thanks so much for this post, Karen. I have struggling with how to present Math in a CM way. You have given me many options, and I'll be checking out these resources. :)
    I feel less stressed about it already! ;)
    Wishing you a blessed week,
    Lisa

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  5. Dear Karen,
    The search for the right elementary math program was a great struggle for me as we schooled our children. Other areas came naturally to me. I did finally realize that, for us, there was no right math program. Anything we used worked well as long as we were diligent to do it on a daily basis.

    We worship with several math professors. We found that their enthusiasm and interest was/is contagious, and we sought opportunities for our children to interact with them.

    Both of my children responded well to real life uses for math. One is studying Calculus I this summer in college, the other is studying Calculus III. They still talk with great delight about their professors' abilities to relate the subject to everyday realities.

    Susan

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  6. I'm happy you posted about math.

    I enjoy reading about your reccomendations and I will be adding math in the garden to our curriculum this year. what fun.

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  7. What a wealth of knowledge and JUST in time for my planning date with myself! ;) Thank you! :)

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  8. Wow - thank you for sharing all of this Karen. Even as an older mom with our first graduating home learner, it is always refreshing to be reminded of new approaches for the younger children.
    Blessings,
    Tonya

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  9. Thank you for this post. The comments above about Life of Fred was helpful as well.

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