Category: Math

Sloyd: Manual training for mind and soul

9/10/2014

“When is a child so happy as when he is doing-- or undoing—something with his hands?”

A portion of the term's work in sloyd.

If you've never heard about sloyd, you're not alone. I hadn't either, but I was inspired to dive in and learn more about this fascinating and nearly-lost-art of hand work. Now that we've spent an entire term working on sloyd at home and in our little homeschool community, I'm happy to share the treasure trove of learning we have encountered!

The root of the word sloyd (or slojd- in Swedish) can imply ‘artfully wrought’ and ‘wisdom and forethought.’ The basic definition is: a slow steady progression of working with ones hands to develop manual and mental skills and to develop character. It can be applied in metal, wood, paper, cardboard or other materials. We used cardstock and bristol board.

students doing wood sloyd

There's so much history and theory behind sloyd.

"it aims to make them [children] more fit to cope with the difficulties of life, and thus to make them useful and honorable members of the community."

It "...gives practical direction to mental activity. Man is not only born to think, but also to do. He is creative and must embody his ideas in form."

Charlotte Mason’s PNEU school program shows sloyd or carton work mainly from ages 6-12 during the handcraft period about 1 ½ - 3 hours per week. But sloyd had value also as an important addition to students' mathematical learning. At the same time children were doing sloyd, they were also learning elementary arithmetic, practical geometry and outdoor geography. Imagine the mental connections!

You can find a great book titled
Paper Sloyd: A Handbook for Primary Grades by Ednah Ann Erdich free online
which has instructions, ideas and models to take you through your first years with sloyd.
Our group did this handcraft with 6 year olds on up. As in the PNEU, when students finished making a model, they were encouraged to use their creativity to make up their own creations using the skills they learned and embellishing the models in some way.
You can also search AO and find some interesting Parent's Review articles
that discuss sloyd.

Sloyd is still being taught all over the globe, but particularly in the US at
North Bennet Street School in Boston,.
Click the link to see a short video on the benefits of sloyd and the value of hand skills training for today's society from the school's president.

We must “give children a respect and love for all honest hand-work and hand-workers and so save them from that blight of shame which still fastens on many a human being at the thought of working with their hands.” -Mason

"Let the youth once learn to take a straight shaving off a plank, or draw a fine curve without faltering, or lay a brick level in its mortar, and he has learned a multitude of other matters which no lips of man could ever teach him" --John Ruskin, "Time and Tide", 1883.

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One more snow & Easter-y things

4/23/2014

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growing our own Easter grass in the house, and watching dew! collect on it in the mornings

lettuce= fun to watch re-grow so quickly, but bitter as anything to taste!

brothers on a snow-dusted walk in the woods

Spring left an icy diamond caught in sprouted green

back in the warm for lunch, nap and lessons

on to the Easter traditions

little boys' plaid ties :)

Peter Cottontail popped out of the bushes while we were hunting eggs!

Another day... we watched eggs hatching!

some of the chicks were out and drying off

others found a happy home in the fresh air

and there were baby turkeys

baby ducks and geese

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The Rhythm of Year 1

11/18/2013

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"To push ourselves to work daily at education, to live, act, think and speak in front of children so that they'll be better every hour because of our example, is a lot harder than making a single enormous sacrifice."
--Charlotte Mason

It's November, and we're settling into a gentle rhythm for fitting school into our days here at home. It takes a little bit to get supplies organized and the posted routine turned into an actuality. It also takes some thought and preparation to take a child who at age four has free exploratory play taking up the majority of his day, to then, by age six, be able to sit down for a structured period of time and apply his mind to learning as well as telling back what he knows. I have found a slow, gentle introduction to one new subject at a time to be the most attainable in our home setting and much preferable to a throw-them-in-at-the-deep-end approach.

The lessons

In progress

School is pretty high on the ‘fun’ list around here, for teacher and student. I mean that too! Really, who wouldn’t appreciate a guilt-free opportunity to ignore housework and laundry and go read a few really good books for a while each day. I hope and pray that the day I begin to find it turning to drudgery for either party, I would pause for a long hard look and make the necessary changes. How well can learning happen when the mind is overwhelmed or in a state of resistance?

From broken basement discard, to refurbished school-cupboard. A dream come true!

In an ideal world, where obedience reigns, nothing falls apart and fairies do the dirty dishes, this is what the school portion of our daily rhythm looks like.

I've heard it called gathering time and morning meeting and other lovely names; we begin our time after breakfast with the same concept. We've found which subjects work well while the little one is dashing between our feet and save the others for nap time. I'm still crossing lots of fingers praying he doesn't grow out of nap time for a long while. It's been an adjustment for me to give up my mid-afternoon time to get some work done around the house. I'm not a fan of change in general, but in this case, the rewards far outweigh any negatives.

During a morning we try to do the following subjects:
Bible Reading/Prayer
Recite our memory Verse
Calendar-Weather check
Listen to our composer
Spanish lesson
Sing our Hymn/Folksong
Read our daily poem

Chores and outdoor play fit into our morning, as well. Other times we run errands or have play-dates with mom friends and their little ones before lunch. I might remember to grab the cds and then we listen/sing/recite any of the above subjects in the car. We also love books on cd in the car!

Espanol

Using Ambleside Online Year 1 as our guide, our total time spent in focused learning during a given day is about an one and a half to two hours. I take my planning time (usually about 15 minutes) on Friday when school's over. Then my thoughts from the week we've just completed and where we're headed are still fresh in my mind. I find that it takes me much longer and is harder to get back into the mindset if I wait until Sunday night.

As soon as baby's down for the afternoon and the table is cleared, big brother and I pop onto the couch and begin with a book and narration, which one depends on the day and our reading schedule.

Viking Tales drawing narration

Short and varied lessons are the keys to keeping attention and interest. We do 5-20 minute lessons depending on the subject. When he asks, I let him choose which order the afternoon falls into, but, as I can sense that a certain predictability is a comfort to him, we generally follow his favorite order of things. Number comes next,

Making 8 with pennies and beans. "Which ones look alike?"

then copywork.

"Can I please write a letter to Auntie for copywork?"

Next he does his letters (aka learning to read),

Melt-mom's-heart-first-reading-lessons!

"...She gives me cream with all HER might, to eat with apple-tart."

and then another reading and narration.

Where did Shaka Zulu live?

"Mom, this is how Shaka did it."

Handcrafting, nature notebooks- a.k.a. science, drawing, outdoor geography, timeline, common placing, citizenship etc. fit in here depending on the day. We attempt to do each at least once a week.

Garter snakes have no ears, we discovered.

our time line

And Shakespeare comes last. Often baby wakes up and does Shakespeare with us. And that's it for school! We used to head out and pick eggs after this. I 'm already looking forward to resuming that part of our daily rhythm with new birds next year and listening to contented chicken noises and giggling at their antics once again.

Playing at The Globe Theatre. "I want to be Banquo."

Numbers in real life

The majority of the time the teacher role falls to me. Dad likes to be involved in school, more than just, "We did this or that today," but among his many bread-winner responsibilities he doesn't have much chance to dive too far in. It makes sense for me to help offer opportunities for him to connect to what we're doing.

Reading Peter Pan and dressing the parts

One evening I set out an 'assignment' for suppertime, a Picture Study narration that had already been assigned to us for our TBG community. It was very fun to sit back and listen to it happen. They looked quietly at a beautiful print from Vermeer. Afterwards, these are a few of the comments I heard.
"There was a box on the table."
"It was brown."
"No, Dad, it was blackish brown."
"She had a letter in her hand."
"Ya, it might have been a letter from her husband."
"There was some cloth."
"No, that's the table. It was blue."
"Like her dress!"
"Let's look at it again. Oh, I see what you were talking about that was a hook on her face. It's her hair, a curl."
"It's hard to see."
Another recommendation I've heard for dads is to keep a read aloud book going at all times, one they can pick up and read to the kids whenever it works. We're using the free reads on our list for some of our 'dad books.' It's an opportunity not to be missed!

And baby gets his share of stories too...

"...let us consider where and what the little being is who is entrusted to the care of human parents. A tablet to be written upon? a twig to be bent? Wax to be moulded? Very likely, but he is much more-- a being belonging to an altogether higher estate than ours; as it were, a prince committed to the fostering care of peasants."

Our favorite Poor Richard's Almanac quote: "Men and melons are hard to know." After we read this D'aulaire on Ben Franklin, DH and I watched the HBO miniseries John Adams bringing the famous revolutionary to life for me!!

"...mothers owe a thinking love to their children...
how shall this heart, this head, these hands, be employed?
to whose service shall they be dedicated?"

Oh, the stories we get to read!!!

Wishing we could step into this nature collection

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Immersed in Math

8/5/2013

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Math: A beautiful mountainous land. This is Volcan Irazu, Costa Rica -photo by my little sis!

Immersion is really the best way to learn something new. We do it with parenting (ha!) and also with forigen languages, like my sister who just returned from a college study trip to Costa Rica! (SO proud of her and a teensy bit jealous :) That volcano she visited (above) looks like it would be quite a glorious nature hike!

We do immersions at our Living Education Retreat. One subject. 45 minutes or so. One well-versed teacher. 10-20 'students' a.k.a. adults wanting to learn how to better teach that subject and so pretending to be the students. It's a rich experience in which to participate.

The ever-lovely Richelle immersed a group of us in the teaching of multiplication tables. Math is a subject that always made me cringe in school. Richelle says she was the same way. Love that we have that in common! She began schooling her sons, and in the process noticed some things happening in their learning process that catapulted her into loads of research on the best practices for teaching math. She then wrote a book on her findings. Its so interesting, and has been pivital for me.

Here's my narration on our immersion session:
We started out with oral questions like "John had 2 cents and was given 2 cents more. How many altogether?" Then we took out our manipulatives (coins and beans)and answered more questios by showing it with our items. We also constructed a multiplication table for 2's using our coins and worked with the table in a variety of ways while trading pennies for dimes etc.

We did 5 minuets of mental math questions at the end. Brain gym! I can see how doing this daily would exercise a child's mind into strong muscle, agile and adept.

Here's my brief narration from our first math plenary:
Basically, you introduce a child to numbers by working with each number starting wtih 1 so they understand all it's possible combinations while working with items around the room and manipulatives (beads etc.) Then you learn how to write that number before moving on to the next one. It is a gradual progression. Kindergartners should not be doing pre algebra, even if a worksheet makes it look like they understand it! After all, children take their brains to college not their papers. This early phase should not be skipped or rushed. And if you have an older child who missed it, go back and revisit it before moving on in where they are at. I'm going to do this for myself!

I learned that math teaching should be simple but not simplistic using methods that get right to the heart of each concept. I kept thinking the whole time how I wish I would have been introduced to math in this fashion. In the months leading up the the LER, math was one subject I was especialy looking forward to learning more about, because I will be further introducing my son to numbers this school year.

Richelle's encouragement that math is like a beautiful mountainous land, representing truth and inspiring awe made her session a joy to lean forward in my seat and listen to. She was quoting Charlotte Mason and others. Math is the language of art, science and nature. It tells about our Creator. Its order/laws give wholesome limits. Creation answers back to Him and upholds His laws. Galileo said, "Math is the alphabet with which God has written the universe."

Here are questions that relate to the principles that keep us on the right track with the atmosphere and life of our lessons in number. I want to revisit these throughout the year:

Are we having fun? Are the questions I'm asking engaging for my son and his unique peronality? Do I relate it to his life- nails, cousins, worms, legos, money, tractors? Is math drill a fun treat?

Am I letting the ideas strike him? Is he discovering the shortcuts on his own? Do I allow exploration before giving the corresponding math rule? In the books Mason used to teach math she skipped the pages that explained the math rule that corresponded to the lesson until after the students had discovered it themselves. She let them internalize it rather than the teacher feeding the information to them. This is a revolutionary way to teach!

Am I being content to go slowly?

Am I requiring the explanations for why he arrives to his answer?

Are the questions well within his grasp? Do I have the right tension? I loved this idea! To keep the proper tension for math learning means that I am pulling him along like a skiier behind a boat. I need to pull hard enough to keep his head above water so he's enjoying the challenge, but not so hard that he's being splashed in the face and sputtering. I also can't go so slow that we're not moving forward at all. Either extreme will cause problems. This will be a learning curve for me to recognize, but I'm sure I'll get the hang of it as long as I'm carefully aware.

Are we doing mostly oral work? Am I using written work very sparingly? We will use large graph paper in his own special math notebook- cool!

Am I using manipulatives when necessary, but when he's beyond them, do I take them away? This will also be something I will also have to learn to reconize. I imagine my friends with multiple children who have schooled for many years have a good feel for this kind of thing. I should ask them more about what that looks like.

Do I use one manipulative too heavily? Idea: use pennies but call them baseballs. Don't get hung up on one thing or make manipulatives the crutch:

2's Multiplication table

Here are few links, mentioned at the retreat, that I am further considering for our year 1:
Ray's New Primary Arithmetic and the corresponding teacher guide by Ruth Beechick (also availiable for free here. )

Richelle's Mathematics: An Instrument for Living Teaching book that gives the practical step-by-step for our daily lessons in number. I had my copy cut and rebound spirally for a few dollars at an office store. I can now have it laying flat in front of me leaving my hands free while I am working at the table or on the couch with my son.

I also looked at Olneys- free online math book, similar to Ray's but moving a bit faster.

Mathematics: Is God Silent? Looking forward to a peek at this book for mom to read.

Eventually we'll read Number Stories of Long Ago. I love that it tells how fathers and grandfathers used to tell these stories to the children around the campfire long ago. I imagined getting cozy with quilts and doing the very same thing with my boys on a crisp fall evening, hot cocoa in hand.

I won't need to buy many manipulatives because we already have them at home: beans, pennies, popsicle sticks etc.

I won't be buying stacks of 'kids' living math books' because in reality, this idea is a common misconception as it relates to a true living education. Having that clarification is freeing, though we'll probably check out a few at the library just for fun. (And yes, my son likes to make triangles with his arm on his hips thanks to The Greedy Triangle. We're just normal people here, okay! :)

"Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination." -W.W. Sawyer, "Mathematician’s Delight"

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Math in the Kitchen

3/27/2012

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Preschool math has been on my mind lately. Last week a friend borrowed me a little book. It's got me thinking more about how the brain learns math and what I can do with my son to foster his math learning as we go about our daily rhythm here at home.

In the book Beechick says there are a few modes of thinking that our brains move through as we learn math concepts. They are Manipulative (hands on), Mental Image (like a drawing on paper or in your head), and Symbolic (1+1=2).

"Piagetian theory says this [Manipulative Mode] thinking predominates up to about ages six or seven." She also says that we can't expect kids to do something in the next modes before they are ready to move on, and that they will let us know by certain things they do.

For example we can't expect kids to write and understand the meaning of 1+1=2 until they've had sufficient time to learn that one apple in this hand and another apple in the other hand makes two apples all together, and then they have to be able to imagine the apples in their head. Only after both of those are firmly in their minds, will they be able to understand the symbols with complete understanding.

I keep thinking of those kindergarten math workbook pages that have a picture of 3 apples, and the kids are supposed to circle 2 and then write the numeral 2 at the bottom. This shouldn't be. It's not really helping them learn. They need hands-on, real life examples of things to touch and manipulate in order to understand. And we need to allow them ample time in this stage not trying to rush them.

She gives a good list of ideas how parents can foster this kind of learning (playing games, at the grocery store, in the dining area, yard, garage, workshop, kitchen, car or even by the TV.)

I can't help but ponder my Math Methods courses in college. I never considered myself a math whiz, and maybe I missed something, but this book has laid it out most clearly for me. I now have more confidence in teaching my son math and am excited about learning alongside him!

I invited him to help me make supper the other night. We peeled 8 tomatoes for our soup. As I put them in the sink I'd say, "Here's one more. How many are in the sink now?" I tried very hard to keep it fun and not get too preachy. For a while I just kept quiet and watched him concentrate and work. I don't think he's ever peeled tomatoes before.

As he set the table he said, "When Daddy gets home there will be four people, and if Grandma comes it would be five. That's my whole hand!"

I am trying to make a mental habit to be conscious of the little opportunities throughout our days to inject some simple mathematical thinking.

Here's our recipe. Mmmmmm.......
Fresh Tomato Soup (from this cookbook, which I love!)
8 medium tomatoes, peeled and seeded, if desired
4 cloves of garlic, minced
Combine in saucepan and cook over medium heat, stirring occasionally, until tomatoes are soft.
3 c. water or vegetable stock
2 chicken boullion cubes
1 tsp. sugar
2 sprigs of fresh basil, chopped
Add, bring to boil, simmer 5 minutes. Run through a blender, if desired.

I served ours with Ultimate Grilled Cheese Sandwiches (with bacon and 3 cheeses), tall glasses of milk, and homemade Granola Bars.

One more thing, I'm also excited about this Pre Math-It program/game my friend borrowed us too. Dominoes are always a hit here.

Got any fun math ideas you'd care to share?

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Intentional Counting

1/2/2012

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We're working on learning numbers...

We started a kid calendar this year. We'll take a picture next to our favorite tree each month to put on here, and we'll talk about the changes in seasons. We'll also put a sticker on each day as we count down to family members birthdays and holidays each month.

We've been playing Slap Jack a lot too. We say the number as we flip it over. I found this cute mini card deck at the thrift store. We also have a GIANT set of cards that I used to use in the classroom. Both are more fun than normal sized cards. :)

Counting on the ruler is fun too.

I sewed a set of felt numbers from a pattern in Meg McElwee's book Growing Up Sew Liberated. I love all Meg's ideas! Fabric is so much more durable then those paper types that get torn in a hurry.

Oh, and we started a chart/graph to count our eggs each day. I'd use chicken stickers instead of the little turkeys if I had some.

Here are a few other ideas for learning our numbers this year.

- Playing games- Uno, Connect Four, Chutes and Ladders
- Numbering the stairs and counting as we climb
- Sing a counting song
- Mother Goose rhymes that have counting
- Magnetic shapes- count the sides
- Baking together and using measurments
- Grocery shopping has lots of opportunities for counting

What are your ideas?

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Welcome!

"I am recording this so that future generations will also praise the Lord for all He has done." -Psalm 102:18

I am a mama to 2 sweet brothers who aspires to a "thinking love" toward my children.

Take a peek into our journey towards a living education inspired by the writings of Charlotte Mason.

Be sure to leave me a comment if you're inspired!

I prefer to keep my text and images right here. Please don't copy without permission. Thanks!

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Previously...

Our Story

Our Year 1 Rhythm

Cloth Diapering

Century Chart

Learning to Read

Wool Felting

Nature with Little Ones

Playful Learning ABC

Living Math

Raising Tadpoles

Homemade Cleaning Recipes

From Caterpillar to Butterfly

Beginning a Foreign Language

Animal Tracking with Kids

Beginning Preschool

First History Lessons

Maple Sugaring with Kids

Children in the Garden

Sloyd handwork

Monarch Miracle

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"In this field small efforts are honoured with great rewards, and we perceive that the education we are giving exceeds all that we intended or imagined.”
- Mason