My Wittle, Itty-bitty Baby...

No, sorry, not that one.  This one. The big one.

My wittle, itty-bitty, biggest baby boy looks so growed up.

We finally got this kid an eye exam and it turns out, sadly enough, that his eyesight is worse than mine.  And mine sure ain't great.   He's only 8.  Being a precocious reader plus genetics not in his favor are not a good combination.

So now he's stuck with "speck-TACKles" as he calls them (is that hilarious, or what?  I can't bring myself to correct him.).

His amazing discovery of clear sight has been fraught with hilarity.  When we walked out of the eye doctor's office, he stopped dead in his tracks to look at the landscaping rocks.  Driving home all I heard was, "Mom! Look at that!  Mom!  Did you SEE that?  Whoa!  That's amazing!"  We've realized why he lost interest in star-gazing and looking for wildlife, why baseball has been a struggle for him, and why he sits so close to the danged screen when we watch movies.

I try not to think about what comes next.  If he's anything like his Daddy (and he is), his eyesight may continue to deteriorate for awhile as he grows.  Nathan was coke-bottle-boy at 12.  And then there's the very strong likelihood of broken/lost glasses.  Jonah is only 8, and he's very distractable.

But.  I am so glad he can see again.  Sight is a gift.

(And I had this thought: maybe this is just a teensy bit like what it will be like getting to heaven.  It'll be like getting glasses and seeing everything so clearly for the first time and exclaiming in wonder at everything around.  Truly, a gift.)

Fair Day

We took the kids to the county fair on Sunday evening. 

Before that, it was very important to lounge around on the couch and take naps and all that to store up some energy for the massive undertaking that is navigating the fair with little kids.

Evidently, I was too busy having fun to take very many pictures.  The kids really loved seeing all the animals, even though we have lots of animals at home.  And Jonah and I looked through the exhibits and pipe-dreamed about what we want to enter next year.  Being at the fair always makes me miss entering things and I make all sorts of plans for next year, but when it comes around again, I'm just too busy to get to it.  BUT.  We totally could have won the "largest potato" contest, so next year, baby.  Next year.

And then we made a little parenting slip-up that I laughed about when I realized it at home.

"And now you can ride some rides, guys!" we said.

And they were like, "Uh.  Okay."

Evan and Andrew did not ask to ride rides.

They couldn't have cared less about riding rides.

They were quite happy to look at all the rides from the safety of our hand-holds.

In fact, they might have been a tad bit nervous.

Okay, so they rode two rides.  They were fine on the kiddy train, even if they completely couldn't have cared less.  Evan got a little upset about getting on the ferris wheel with Daddy, but was fine after a few minutes, though again, he really didn't see the point.

I think we've just gotten so used to the rides being a big deal for Jonah over the last few years, that we totally went on autopilot and didn't think about it for the little guys.  We just did it.  They're 2 and 3 years old for cryin' in a bucket.   We totally could have saved that four bucks.

Not a big deal, I guess, but I really laughed about it later.

And actually, Jonah wasn't that into rides this time around, either.   Last year he discovered the joys of riding rides with friends, and going alone just doesn't hold so much excitement for him now.

Corndogs, however.  

Now those were a pretty big hit all around.

I watched the 4-H kids milling around with their animals and projects, and it occurred to me that the day may not be far off when we'll be spending plenty of time at the fair every year.  For now, we'll enjoy our one afternoon each year.  It's probably a short-lived phenomenon.

Baby pictures will make you happy...

Okay, okaaaaaay.  I give in.  So much for philosophy.  Photos it is!

I know you all only love me for my good-looking babies, not my brains anyway.  It's okay.  I'm fine with this.

This.  This little miss is 4 months old today!  I don't think there's a more delightful baby in all the world.  I'm just sure there can't possibly be.

Nor a more handsome little boy sporting a highly sophisticaed hot-cocoa-mustache.  He's an old soul, is Evan.

And if that didn't lift your spirits, how about 9 jugs of hard cider bubbling away and looking so happy they could just float off with their yellow airlock-balloons.

But I know you really only come here for the baby pictures.

Math Buzzing

Blog?  I have a blog?  Oh yeah, I do have a blog.  And it's been a while, hasn't it?  And you're probably hoping I'm going to post some more photos of this sweet little lump of baby flesh that is wriggling in my lap right now, but alas, I have no intention of doing that today.  I have a bee buzzing in my bonnet and I'm going to work it out right here, right now, while my supper cooks and my boys play and my baby soaks me in drool.  You see, I have a marginal intellectual life that peaks out from under the laundry pile every now and then.

Okay, so I've been thinking a lot about math.  Teaching math, learning math, using math.  I've just completed a free online course from Stanford University called "How to Learn Math" and my mind = BLOWN. All I can say is sometimes a little inspiration goes a long ways.  It's taken me about two months to work through the class material and in that time I've done a lot of thinking and digesting and pondering.

Our general view of math is so warped.  Actually, not just warped, but limited and stunted.  How far would we get in music if we first had to spend years and hundreds of hours studying music notation before we could start to make music?  Dang that would be boring.  I would quit.  I'm guessing we'd have a lot less beautiful music in the world.  When you decide to build a pole barn or a house or a garden shed do you spend years learning the names of your tools and pounding hundreds of nails into boards?  No, you start your project, figure out what you need, and if you weren't very good at hitting a nail with your hammer in the beginning, well, you're gonna be improving that skill, aren't you.  If you fix a car, but it still won't start, do you write it off and go on to the next car?  No, you're going to back up and find your problem and keep going until it works.  Do we require extensive courses in parenting and all the things you'll need to know about children before having a baby and raising it into an adult?  Some might think that would be a good idea, but no, it's definitely a learn-as-you-go endeavor.

In no part of life do we think we need to have all the tools and understanding of them before we start.  It's not possible.  Our brains simply don't work that way.  We get bored, we can't keep track of information we don't use, and we simply don't have that kind of time.

And yet with math, we think the proper way to learn it is to spend years drilling, memorizing, and practicing, learning the tools in order, going through the steps before we use any math, if we actually ever do.  It's no wonder it's a classic, stereotypical question, whined by school children across the world:  "When are we ever gonna use this stuff?" 

And then of course, we're all well-drilled in the idea that mistakes are wrong! and bad! and must be purged out of our mathematical work.  If you make a mistake, you get a big red check mark and your grade goes down, and if that happens enough, you can't get into a good college and you'll be doomed to menial, minimum-wage jobs for the rest of your life.  Avoid those check marks!  No mistakes!  What about real life?  In real life when we make a mistake, we learn what not to do.  We learn what doesn't work, and we move on to find what does.  Are you getting this?  When we make mistakes, we learn.  Isn't that what school is supposed to be?  Learning?  But mistakes are not allowed in school.  That's a non sequitur if I've ever seen one.

I've come to the conclusion that we just have a very poor understanding of what math actually is.  I really like this quote by British mathematician Keith Devlin for describing what I (and most of the rest of the population, I gather) are not seeing:

"Mathematical notation is no more mathematics than musical notation is music.  A page of sheet music represents a piece of music, but the notation and the music are not the same; the music itself happens when the notes on the page are sung or performed on a musical instrument.  It is in it's performance that the music comes alive; it exists not on the page, but in our minds. The same is true of mathematics."

How beautiful and inspiring is a sheet of music?  Eh... meh.  But when we hear music?  Amazing!  I have to say that I honestly do not know what math "sounds like" or "looks like" or however else it can be beautiful. But I've been told that it is.   It's a way of expressing our experience of creation, but most of us don't "get it" even though we've spent many years learning math.

I recently read a portion of Plato's Republic and was astonished when Socrates said that math "leads naturally to reflection, but never [has] been rightly used; for the true use of it is simply to draw the soul towards being."  That may be a little esoteric, but this is Socrates we're talking about.  We know that math has lots of practical applications, but if kids are getting neither practical application nor beauty and meaning and excitement, then it is a dry subject indeed, and I can understand why so many kids love to hate math.

So.  This is all well and good, but where do we go with this idea?  Kids still have to learn math; can't get through life without it; it's useful in our society; need those shiny college credits... etc.  Well, that's what I'm trying to find out.  I want to learn to teach math to my kids without textbooks and worksheets.  And I'm no mathematician, so I think I'm gonna have to do some digging.

I saw an interview with Sarah Flannery, a young mathematician who has won awards for her work.  She said that she learned math because her father gave her math puzzles to work on.  As she worked on the puzzles, she discovered the tools she needed by asking questions and collaborating with her family and then she learned how to communicate the solutions.  I've also watched videos of classrooms situations where the students are all solving tangible problems together and learning together as they go. And then I've seen how my own  8 year old son lights up with real-life problems or entertaining math games and how he wilts at the prospect of a whole page of repetitious addition and subtraction combinations.

 I really think that the most important part of learning math like this lies in key #3 of the Seven Keys of Great Teaching: inspire, not require; and #7, you, not them. Sarah Flannery's father did puzzles with her.  The kids in the videos I saw had a teacher engaged in the problems with them.  Jonah loves to work out math problems or games that I am working on.  If I shudder at the thought of a math worksheet, why should I expect it of my child?  But if I'm learning to use a Japanese soroban abacus instead of a calculator, or Nathan and I talk about a math puzzle at the supper table, or I'm figuring out how many gallons of paint I need to buy for the room I want to paint, or I'm calculating the right amount of pectin and sugar to use in my quintuple batch of strawberry jam, you better believe my child will be wanting to use that math, too!  So my goal, for the time being, is rather than make them do math everyday, to show my kids math everyday and help them be excited about the solutions.

Cameo Appearances

Here she is, ready for her close-up.

Awwww...

Who is this?!?

He's ruining my shots!

Awwww... Pretty wittle pink tights!

What a beautiful dolly!

Work it, baby!

Hey!

Well, I never!

Can't you goofs be serious?

Little Solutions

Before church this morning, I played through the hymns to prepare for the service.  Nathan was working in his office, Jonah was reading, Eleanor was lying on a blanket, happily kicking her feet and babbling to her hands.  The little boys were lining up all the hymnals on the pews, but I wasn't paying attention to them, so I didn't discover that until later.  For the time, all I knew is that they were quietly busy.

This is often a very meditative time for me.  As long as no one needs me presently, my mind is free to follow the music.

 Built on the Rock the Church doth stand,
Even when steeples are falling;

Crumbled have spires in every land,
Bells still are chiming and calling,
Calling the young and old to rest,
But above all the soul distrest,
Longing for rest everlasting.

As my fingers wandered over the keys, my mind wandered over the people in our church and other family and loved ones and some ongoing problems they and we have had.  I thought about apathy and sickness.  I thought about struggles and pain.  I thought about loneliness and isolation.

We are God's house of living stones,
Builded for His habitation;
He through baptismal grace us owns
Heirs of His wondrous salvation.
Were we but two His name to tell,
Yet He would deign with us to dwell,
With all His grace and His favor.

I thought about our country and the disturbing loss of freedom and difficulties of making a living in this world. I thought about blessing and abundance.  I thought about want and hardship.

I thought about all the things I've been praying about for so long.  The things that distress me.

 Now we may gather with our King

E'en in the lowliest dwelling;
Praises to Him we there may bring,
His wondrous mercy forthtelling.
Jesus His grace to us accords;
Spirit and life are all His words;
His truth doth hallow the temple.

These things all floated through my mind.  And then I thought about my children.  Sometimes I'm alarmed and frightened by the world they have to live in.  The task of raising them up to live here seems impossible, and I pray for wisdom in that job every day.

Still we our earthly temples rear

That we may herald His praises;

They are the homes where He draws near
And little children embraces.
Beautiful things in them are said;
God there with us His covenant made,
Making us heirs of His kingdom.

Then I remembered an article I read the other day.  This quote really struck me:

"I believe that when God sees the need for changes in the world, he does something really special. He sends down a baby. A little person with just the right talents, tendencies, interests, passions, and strength of will to change the world. And in times like ours, well, I’m pretty sure He’s been sending down a bunch of babies like that."

So here I've been, praying for changes and improvement in the things that bother and distress me.  Certain matters have been heavy on my heart for years.  And I'm not seeing any change.  But I know that God doesn't work on my limited time-table. So here I'm praying and praying for change, and God sends babies.  And a thought navigated through my mind as my fingers navigated the keyboard.

Maybe I'm raising the solutions I've been praying for.  Maybe they're right here, under my nose.  The change I was asking for is already in my home.

Lord, let me not ruin this opportunity.  Help me not loose this chance.  Because that's all I'll do if left to myself and my own means.

Here stands the font before our eyes

Telling how God did receive us;

The altar recalls Christ's sacrifice

And what His table doth give us;

Here sounds the Word that doth proclaim

Christ yesterday, today, the same,

Yea, and for aye our Redeemer.

 Grant then, O God, where'er men roam,

That, when the church-bells are ringing,

Many in saving faith may come

Where Christ His message is bringing:

"I know Mine own, Mine own know Me;

Ye, not the world, My face shall see.

My peace I leave with you." Amen.

(The Lutheran Hymnal  #467  Text: Eph. 2: 19-22 Author: Nicolai F.S. Grundtvig, 1837)

If You Carrot All For Me...

...My dear, we cantaloupe, lettuce marry!  

We are just having the most bountiful garden this year!

It's such a wonderful blessing, after a couple of dry, lean summers.  

But if I think about it too much, I verge on a panic attack.  There's just so much to do to get the harvest in AND take care of house and family.  So I try not to think about it, take it one task at a time, and keep refocusing on enjoying the summer and my sweet, funny, little people.  And fall into bed aching and well-tired at night.

I have to say, the garden is so much more enjoyable now that I have kids to enjoy it with.

They just love to be out with me in the garden.  They're happy to work along side me, however helpful or not helpful that may be.  It really is delightful (most of the time) to have them with me, so excited about everything they find.  And it's just so much less intense and more peaceful outside than inside.

They're even more happy to eat all our pickings.  The boys are just overjoyed at the nearly unlimited apples, carrots, cucumbers and green beans they get to eat these days.  The other night at supper, I actually heard Nathan tell Evan to stop eating so many cucumbers and eat some on his main dish.  What kind of crazy parents are we, anyway, that we have to tell our kids to STOP eating their vegetables?  They could happily make a meal of sweet corn and fresh milk.

As tempting as it is for me to let them live on green beans and dropped apples, I realize that they actually need some protein from time to time, thus the panic attack when we come in from the garden at 6:18 and there is no supper yet.

And then there's this sweet little apple dumpling whom I can pretty much characterize as "negative helpful" but that's okay, we love her an awful lot anyway!

And lest you should (for some strange reason) think that all is perfect in paradise, here is a picture of my herb bed.  Yeah, what herbs?  I weeded it quite soundly a month ago.  But then I got busy picking beans and making pickles, and when I turned around again, I couldn't find the herbs.  It's pretty disgusting, and I need to stop thinking about it now before I have to go find a paper bag to breath into.