Math Appreciation

Can you draw really well?  Well, none of us can.  We just don't have any gift or talent for it whatsoever.  So if I said to my kids that we were going to study art, and at the end of  6 weeks they would have to create a masterpiece painting on canvas.....   they would scream and run the other way.  It would be too intimidating, right?  Any of you non-artists can relate!  Yet they very much love learning about art and looking at it.  Well, we have a bunch of children in our family who dislike (ok, loathe) math, and think they're terrible at it (they aren't, they just expect perfection and immediate mastery).  So, my saying to them, "Let's do these math lessons, then we'll do some worksheets, and after a few weeks we'll do a test (aka masterpiece), well..... they scream, and run the other way.  It's too intimidating for people who have an inborn fear of math.


Of course, I want my children to love math and understand it.  I find it fascinating, though at times a bit frustrating and challenging.  The wonderful thing about homeschooling is how much there is available in the way of choice when approaching learning.    We've tried several different math curriculums  which I was very pleased with (Math U See with it's great DVDs and manipulatives and Life of Fred with it's quirkiness and humor), but the kids still aren't big fans.  


A homeschool coop project I'm helping with inspired me to do some math appreciation with my kids for now, rather than expect the masterpiece.  The coop math class only lasts five weeks, but  it's so great to see my kids do things with math they wouldn't at home by themselves.

They are more willing to make new rules to old games, experiment, and have fun when working with other kids.  They've collaborated really well in sharing ideas and solutions (which would be called cheating in school, but is actually  great  preparation for real life, don't you think?)


So,   I started searching and  found some wonderful resources that I hope will change my children's feelings about math along the way as we learn about math from a different angle for a while.

We really enjoy Joy Hakim's "A History of US". (I am aware we're talking about math....  stick with me.)  I'm reading it to the second set of children and I love it and so do they!  She has such a wonderful way of weaving history into the amazing STORY that it is, rather than a bunch of facts on a timeline.  She also does a remarkable job of integrating many topics into that story; economics, religion, ethics, science, art, poetry, etc.  So I was really ecstatic when a friend told me she has also started writing "The Story of Science".  YES!! ( My kids also think they don't like science much.  Silly kids.)  

Hakim  beautifully weaves a fascinating story  and integrates so many subjects, including math!  I've been trying to tell my kids that math is simply a language;  a foreign language to some of us, but one that the universe is based on.  In chapter 2 she quotes Galileo, 


"The universe cannot be read until we have learned the language and become familiar with the characters in which it is written.  It is written in mathematical language." 


Just what I've been trying to explain!   Did you know that Einstein gave a lecture at Moscow University in 1955 where he wrote something on a blackboard that has NEVER been erased?  


 "Physical laws should have mathematical beauty."


When in school did you ever learn about "mathematical beauty"?  Einstein seems to have thought  it exists.  I'm not going to argue with him, we're just going to try a little harder to find it.  ALL knowledge is one great whole.  I'm learning this on my own educational journey because my experience is from  public school which is all very compartmentalized.  I  found a group of books on Amazon and I ordered one to start with.  In "Mathematics  Appreciation" by Theoni Pappas he says he, "Introduces you to the fascinating interrelationship between mathematics and other subject areas, the evolution of mathematical thought, and the beauty of mathematics."  Right on.  He has many many books about math written for all ages.   I have a feeling we'll be getting more of them!  

I'm determined to help my children appreciate mathematics.  They may never be brilliant at it, or truly love computations and that's ok, but I want them to lose their fear of it and understand the beauty of it in our every day lives.  

Random Thoughts for Today

I wanted to post something profound; something deep and meaningful.  But my brain is like jello and I've drawn a blank, except for some strange and random thoughts (which I usually try and keep to myself).


1.  teenagers sometimes seem like God's way of getting back at us for past mistakes


2.  flies in late October!  it's like a plague or something


3.  strawberry marshmallows are surprisingly good


4.  Chloe is not old enough to be 3 years old tomorrow


5.  why is Thanksgiving "turkey day", but Halloween isn't "pumpkin day", or "candy day"?


6.  I get tired so much easier than when I was 23.... it isn't fair


7.  the Columbia Basin gets 300 days of sunshine a year...   why do we seem to get the 65 days of gloom all in a row?


8.  laundry is eternal


9.  a child of any age can say the word "mom" 34,394,182 times a day


10.  it's only 7:06, and I wish it was bedtime

Mark Twain said, “I’ve seen many troubles in my time, only half of which ever came true.“ 

Well, I was born a "glass half empty" girl.  Sad, but true.  If there was anything to worry over, fret about, or get down about, I was all over it.  But as I got older, I got tired.  All that worrying and seeing the ugly side of life takes effort!   I don't have the stamina anymore.  I've worked really hard to become a "glass half full" girl.  I'm getting there slowly.  Maybe it's one quarter full now.  Or maybe an eighth... being an optimist is a lifelong quest for me I'm afraid.  I'd rather get there sooner than later, but at least I'm traveling in the right direction!


Photography is the latest thing that's helped me focus on things differently.  It's amazing how the ugliest things, when captured just right, can make beautiful pictures.  It's just the angle it's viewed from, or the right light being shed, a certain composition, or sometimes it's in the eye of the beholder; just like with life.  If we change the angle we view it from, cast the right light on it, improve our perspective, or look hard to find the beauty and joy, we see it was all there to begin with.  

This is my ugly "garage"....   or shop...  or shed...  or whatever.  It's never had a car parked in it that I know of.  But it's supposed to be a garage.  Whatever it is, it's old and in need of help.  I decided to try and see it from a different perspective and see if I could find some beauty.

This is the side of the garage with a little different light, a different focus. 

This is our old corn crib.  It's kind of an eyesore.  Certainly not my idea of pretty.  

But this evokes a different feeling for me.  Like an image plucked right out of history.  You can almost hear the stories there are to tell. 

“When you reach the heart of life you shall find beauty in all things, even in the eyes that are blind to beauty.....we live only to discover beauty. All else is a form of waiting.” Kahlil Gibran

Dark Chocolate Pudding

I LOVE dark chocolate.  I know some people prefer milk chocolate (though I'm not sure why).  I made this dark chocolate pudding last week and it was SO good I had to share.  If you don't like dark chocolate, you can adapt it.  What's so great about this, is that it's homemade...  no artificial ingredients or chemical additives, not to mention a whole lot less sugar, and fat,  than the store varieties.  If you have a real sweet tooth, you can increase the sugar if you like, but the dark chocolate and slightly less sweetness makes this a more grown up and sophisticated dessert.

You'll need milk (I use 1% but you can use whatever you like), water, vanilla, beaten eggs, sugar, cornstarch, and Hershey's special dark cocoa powder (or regular if you don't like it so dark).  

You'll want to sift the cocoa powder through a small sieve to help it mix smoother later on.

Start by pouring the milk into a medium sized pan.

Then add the sugar,

and the cornstarch.

Whisk it all together really well and turn the heat on to medium.  

Let it simmer, but watch it carefully and whisk it often to make sure it stays well mixed and doesn't stick to the bottom where it can burn.  As it gets hot, the mixture will begin to thicken.

Meanwhile, you can add the sifted cocoa powder to the warm water and whisk well.

It's a little resistant to mixing at first, but just keep whisking....

and it'll all come together in a wonderful puddle of dark chocolate goodness.

It's time to add the beaten eggs....   but you can just dump them in or you'll have scrambled eggs, not pudding.  The eggs need to be tempered, which just means slowly warmed up.  Take about 1/2 a cup of the warm, thickened milk and add to the bowl of eggs.  

Whisk it together, then add another 1/2 cup of thickened milk.  Now, the eggs are warmed up.

Pour the egg mixture slowly into the pan and whisk well over medium low heat for just a minute or two.

When it starts to bubble, it will thicken even more to a nice, creamy texture....  like pudding.  Now add the vanilla, and you have boring vanilla pudding.....

Until you add the cocoa mixture and the magic begins!

Mix it all together until the chocolate is fully incorporated 

and it's a delicious pot full of dark chocolate pudding.


It's not done though!  I know, I know...   the temptation to take a big straw and just suck the hot pudding up like a milkshake is overwhelming.....   but it's HOT and I don't want you to burn your mouth.  So....

Put your pudding into a glass bowl, and put some plastic wrap directly on the surface of the pudding.  This will keep it from forming an icky looking "skin" on top as it cools.

Put it just like this into the fridge and wait a couple of hours (or as long as you can) for it to cool and thicken even more.

Then grab a dish and a BIG spoon and dig in!  There's nothing so comforting on a chilly fall night as a dish of dark chocolate pudding (still a tad warm because you couldn't wait any longer).




Dark Chocolate Pudding


6T sugar
4 cups milk
6T cornstarch
4 eggs, beaten
2 tsp vanilla
1/2 cup Hershey's dark cocoa powder
1/2 cup warm water


Sift cocoa powder and set aside. Pour milk, sugar, and cornstarch into a medium saucepan and heat on medium.  Stir often with a whisk.  Meanwhile, add cocoa powder to the hot water and whisk until smooth and creamy.  When the milk is thickened and bubbly, remove from heat.  Take 1/2 cup of hot milk mixture and blend into beaten eggs to temper.  Add another 1/2 cup of milk mixture and blend well.  Slowly pour warmed egg mixture into the pan and stir well.  Return to medium low heat and whisk until it bubbles and thickens more.  Remove from heat and add vanilla and cocoa and blend well.  


Pour pudding into glass bowl and place plastic wrap directly on the surface of the pudding.  Let cool in the fridge for until thickened and just slightly warm.  

By Small and Simple Things......

Do you see this little tree?  It's growing from under my front door.  Well, until later today when I rip it out before it brings my house down.    It started from a little seed as most plants do, and has grown into a little shoot.   

Here is a picture of it's older brother (or sister I suppose), that's growing in my front yard.  Still small, but growing towards its full potential.

This very tallest tree is  an impressive specimen of the same kind, grown up with nourishment, light,  and water.  It's quite tall now, and spreading its seeds. Literally.  EVERYWHERE.

And this is a swath of trees that show the scope in which they have grown, all from little seeds and shoots like the first little guy I showed you.   I hate these trees.  They're called Tree of Heaven, a SLIGHT misnomer.  Imported at one time from Asia and foolishly planted by someone before us on our property, they are exhaustingly invasive.  We have been battling them half-heartedly for years, and are on a search and destroy mission this fall.  


You're probably wondering what on earth my point is, except to complain about these stupid trees in my yard, or make you feel sorry for me (which hopefully you do).  My point is that it reminded me of a very true and important principle that I often lose sight of.   By  small and simple things, great things will come to pass.  These trees are the best physical example of that I could find.   The more important examples though, are those of a more spiritual or personal kind.  When people band together with small efforts, great things can happen.  When we exercise just a few minutes a day, worthwhile changes take place.  Reading something positive and enlightening for just a short time each day can greatly add to our depth and breadth of knowledge.  


I, who always want instant results to be sure something is successful, need to remember that taking one baby step at a time is often all that's required to reach our goals.   I want to be THERE.  Instantly.  Mission accomplished.   Well, sometimes success needs to marinate and develop slowly.   Developing skills and capabilities and  letting go of bad habits and hurtful baggage can take a while.  Sometimes, we deny our own genius and shy away from the great things we could do, because we let fear take hold or we listen to critical voices (even our own).  By small and simple things, great things CAN come to pass.  I'm going to move forward, one small step and effort at a time, and trust that my reward will be  something great.  

A Little Brag

Is there anyone out there that home schools their children, that doesn't worry and wonder if your kiddos are really learning everything they need to know? Do you panic thinking you've created massive craters in the fabric of their learning...   and they'll never get into college... or find a job... or a spouse... or be able to support themselves....   and they'll be living in your basement forever, because you FAILED?  Anyone else ever have those moments of terror?  


Of course, the "normal" thing to do is turn them over to the public school system where the experts in education can do a superior job teaching your children.  Every time I think I'm comfortable with what we're doing, one of the many traditional schoolers I know asks me or my children something (just for the record, I NEVER give public school kids pop quizzes...  I'm just sayin') and I find myself thinking, "I don't know!  Have we studied that?  Do they know that?  Obviously they're supposed to!"  And I'm taking a ride on the worry rocket again.  


Why is it so easy to believe the principles, but such a  huge leap sometimes to trust the process?  First of all, I have to say, shame on me for not seeing those small, daily testaments.  I'm sure they're there, but I'm too busy worrying to stop and appreciate their simple beauty (note to self...   look for them!).   I do ADORE those times when it's made very clear to me that we're doing positively fine.  It confirms my faith in the process I SAY I believe in, but too often doubt.  


Over the years, we've tried on many home school methods, from your more traditional "school-at-home" textbook variety, to total unschooling where we just live and learn together without regard to much formal curriculum at all.   I can say honestly we've leaned much more towards the relaxed than rigid side.   

Taylor, who just turned 15, decided to go to public high school this year.  I know it wasn't meant as an offense (I like to think the best of people whenever possible), but the many exclamations of, "well good for you!" from friends and acquaintances upon hearing  this, seemed to imply that he had finally come to his senses and conquered over his ridiculous mother and her insane desire to teach her own and clawed his way free (am I a little sensitive do you think?).   Secretly I was worried that he was behind and not at all prepared for the rigors of high school.  Well, might I brag for just a moment?  He's handling football practice and games, plus all his classes and homework (including advanced English and science) just fine.  He's taking his MAP tests this last week or so and is scoring amazingly well (just like I always knew he would).  

Zachary is 18 and wants to start community college this winter. He took his entrance exams today...   and passed with NO problem.   Now, a cynic might say, that the "rigors" of public school aren't all they're cracked up to be so it's not such a triumph after all, and that our educational system has problems which need to be addressed.  In which I case I ask, why am I such a weirdo for teaching my own?  Seriously.  The other point of view is that textbooks and schools with their rigid time schedules, well prepared teachers, and thoughtfully crafted scope and sequence, are NOT the only or best way to learn.  Hmmmm...   ponder that for a minute.  Taylor's highest MAP score so far?  Science (and  let's just say that's never been a big focus of ours in the traditional sense).

Will I worry again?  Sigh.  Probably.  I need to work on that.  And  I'm starting right  now to watch  each day for that evidence that assures me we're ok.  I know I'll find it.  

Home School Rhythms

It seems that I'm always reading or hearing of a  home school family (especially with older children) who have the sort of daily routine I think I'd prefer.  You know, everyone up by 6:30, morning chores, breakfast, dressing and grooming, morning devotional (cord of wood chopped, animals fed, music practiced, barn roof fixed, etc) and all done before 8:00 am. Wow, what a beautiful start on the day!  By lunchtime, they're just plain finished, and mom is free to study, read, sew, bake, or follow any other hobbies or interests.  Yeah.....   well....   I've yet to find that nirvana.  


Here's the thing.  I'm a night owl by nature.  As a kid, no matter how early I was up, I could never go to sleep early; not even if I laid in a dark, quiet room for a LONG time.  Motherhood has forced me into living the lie (oops, Freudian slip...  I mean life) of a morning person.  Only one of my seven children seems to take after her father who is more of a morning person than anyone has a right to be  (the man doesn't need an alarm to get up at 4am...   how twisted is that?).  My bad luck it's my almost 3 year old, the one I desperately wish would sleep in!


I'm slowly discovering (I'm a little dense), that our personal family rhythms need to be honored;  tweaked perhaps, with some basic structure added to keep our slothful natures in check, but otherwise honored.  See, I enjoy some peace and quiet when I first wake up.  My brain is fuzzy and I don't respond well to needs and demands (which my kids so excel  at). I need time to read, or think, or to get myself organized while they're all blissfully sleeping.  So in spite of my best efforts, they're up later than I'd like.... because of me. 

And they are SO like me.  They also need that time to gather themselves and come to focus when they get up.  They want blankets (even in summer), hot cocoa (even in summer), and books, or crayons and paper.  Why is that a bad thing?  While I shower, meditate, pray, eat and dress, they have time to slowly bloom.  It's all good, right?  Then WHY do I feel so guilty?   It all comes down to comparing myself against other families...  those "ideal" home school families.  Any time I do that, I always compare my worst to others' best.  When will I learn this and just be content to do what feels right for us?  I'm working on relaxing about it this year and working with our natural rhythms.  When I do this,  I'm happier, they're happier.....   isn't that the goal?

The Gratitude Game

Ever have one of those days, or weeks (or even months), where things just don't seem to be going your way?   Maybe the kids are out of control, or you get one flu bug after the next.  Maybe you lose someone close to you, or finances become a nightmare.  Maybe, in spite of all your great ideals and planning, life doesn't catch your vision and cooperate.  Unfortunately, adversity happens to everyone.  No one is immune...   money, education, and luck won't protect you.  How do you keep from getting down and feeling sorry for yourself (I really want to know....  tell me!)?


"The ungrateful heart...discovers no mercies; but let the thankful heart sweep through the day and, as the magnet finds the iron, so will it find, in every hour; some heavenly blessings."  Henry Ward Beecher


Yesterday, a very wise, gentle man, reminded me what I already know.  Gratitude is the key.  I believe all religious faiths teach the importance of gratitude.  So does every "success" book and personal development book I've read in the past 18mo (and I've read a LOT).  It's simply a true principle.  


Have you seen the movie Pollyanna?   Much to the initial annoyance of everyone around her, she's always playing the "Glad Game".  In any situation that seems terrible, she determines to find something to be glad about, no matter how small, and it makes her feel instantly better.   I'm going to play the Glad Game today (please feel free to join in).  I NEED it.  

I'm grateful for my children.  Aren't they amazing!  Who would I be without them (other than rested and relaxed)?  They are my reason for trying so hard, and never giving up.  (I wish I had a picture of them all together, but it's like herding cats).

I'm grateful for my faith and the foundation of belief I have.  It helps me in times of trial and reminds me "this too shall pass".  

"When the first baby laughed for the first time, its laugh broke into a thousand pieces, and they all went skipping about, and that was the beginning of fairies."  JM Barrie


I'm grateful for a child's laughter.

by Alyssa

For the great and varied beauty we have to see on this earth, which is never ending, I am truly grateful.

American Flags by woodleywonderworks

"Freedom is the last, best hope of earth."  Abraham Lincoln




I'm grateful for the freedom and strength of America.   I'm a first generation American on my Dad's side, and second generation on my mom's side.  I have a heritage of family who understood what it meant to live without freedom and came here to follow the American dream.  There may be problems that need fixing, but I firmly believe it is the most blessed place to live.  

And I'm grateful for chocolate.  I mean, really, isn't that something to be grateful for (my kids insisted I include the white chocolate in the photo but I think it's just wrong...   it's not really chocolate is it)? Just like when Harry Potter ate it to feel better after facing the dementors, it makes me feel better too (until I get on the scale).


I could go on and on (about what I'm grateful for, not just chocolate).  From time to time we all need to stop and count our blessings.  Please share some of the things you're grateful for.  It'll make us all smile!

Nothing says fall like.....

football and pumpkins.  Except chainsaws because I grew up in woodsy Virginia and people were cutting wood for winter all around us and the sound of one brings me back...... but I digress. 

 My dad loved football games, so the sound of one on TV instantly makes me feel autumnal.  I haven't followed football in many years, but now I have a Frosh football player and things have changed.  Two disclaimers; I am not a sports photographer, nor does my camera have the guts it needs.  Second, my 12 yo daughter Alyssa took most of the football pics and several on my blog yesterday.  She seems intent on proving herself a better photographer than me (she's a little competitive that way).

Number 82 belongs to me.  Taylor's a great kid!  Truth is when you have 39 players on a team, some are gonna stand on the sides.  He's loving every minute (and so are we).  Our team won, by the way,  14 to 13.

Ok, these are all mine.  I had to start October 1st with a pumpkin shoot.  What's says autumn like pumpkins? (except beautiful fall foliage which we aren't blessed with here)  We've got a crop of big, beautiful, orange globes this year.

Just a few more cool evenings, and these babies will lose all touches of green.  We can't wait!

 Bless it's heart, even though the vines are dying and pumpkins are ready to harvest, it's still trying to bloom and grow.  Maybe there's a lesson there.......


Happy first day of October!