Billion to the Fourth Power

I don't know why, but I tend to teach math in the car. Which sometimes is really tricky when I'd like to be using my hands to draw an example or write down a list of numbers, and instead I've got them on the wheel (as I should!). Some of my kids appreciate this habit of mine, as they love math so much, it doesn't matter where we are or how I'm presenting it. Others of my kids have a harder time without a visual aid. Nonetheless, I found myself last week in the car with five youngsters, ranging in age from five to eleven years old, and we talked about all kinds of fun math.

I had recently been introduced to this website and at night had been working on some of its featured math puzzles. A few days later, the kids (including a nephew and a neighbor) and I were in the car longer than we thought we'd be, since an attempted outing came to naught. I decided to mention the puzzles to them so they could try finding some solutions. This led quickly to discussions about the Fibonacci sequence (which the 5-year-old could explain to us!!), Pascal's triangle, exponents, and how to multiply quickly by elevens.

I loved it. I loved that math could be so normal that we'd be discussing it the way we discuss movies or stories. I loved that every single kid in the car was engaged and interested. I loved that repeated, early exposures of 'difficult' concepts ends up making them easier down the road. I loved that everyone was actually being challenged to think in new ways, including myself!

The five-year-old was so interested in exponents that he asked me what a billion to the fourth power is. (Kids love to 'challenge' adults by asking them questions involving really big numbers.) I told him that I could show him a really fast way of solving that, but that it would have to wait until we got home so I could write on paper! When we got home, I showed him the fast way to write one billion (using 10^9) and then showed him how multiplying that by itself four times is easy as well, by multiplying the nine times four. He didn't know 9x4 off the top of his head, but he knew 9x2 and could double it to make the right answer. Smart cookie!

I hope that math can become even more fun and everyday for my kids and other children in my life. And I hope that when they think of me, they think of fun puzzles and discussions -- not dry lessons!

May 2014 in Status Updates

The beaches of North Carolina, May 31

5/1 Made a new dinner last night (Mexicana Veggie Bake) and it was a winner! Thankful for the friend who passed on her used cookbook to me (Speedy Suppers by Gooseberry Patch), and thankful for cheerful responses from my family. Music to a cook's ears!!

5/2 While weeding in our front garden (bordering on communal land, with no fence between), I came across a gold ring that has a fancy E engraved on it. I'm trying to figure out how to find its owner, but in the meantime, Ethan has gained much pleasure from wearing it (it says E after all) and pretending to be invisible. Can you tell he's currently reading Lord of the Rings?

5/5 Simultaneously proud of and happy for my husband Steve getting accepted into a funded PhD program in Islamic studies at Georgetown University, and wondering what the next few years will look like...

My heart's been breaking for those who loved the 2000+ people who died in Friday's landslides...  (in Afghanistan)

5/6 I have two new students today -- both in geometry -- yay! Thankful for Wyzant Tutoring connecting me with students who need help. Don't like giving away the commission, but at least I'm getting work! (later...) Wonderful students!!! Fun material!! What an awesome job I have!

5/7 Josiah discovered the 'voice recorder' function on my new cell phone today, and saw that I'd used it a month ago (while in IL) to record my piano dabbling. He got inspired and used it to record HIS piano playing (while I wasn't around) and even made it my new ringtone.

It just gets worse and worse. Possibly hundreds killed in another horrible attack by Boko Haram.   

5/9 My kids are thrilled with their consignment sale treasures ... stuffed animals, novels, and plastic soldiers all bought with their own money. I'm happy with my "new" books and games too, some of which will help me teach, and many of which will keep the kids happy while challenging their minds! They've already been playing Taboo Jr. this evening.

5/10 Coats, duvets and all winter apparel are now in the attic; windows have been open everyday; meals are being enjoyed on the back porch; guinea pigs are getting lots of outdoor time -- so are we I love Spring!! 

Hard to believe that my child who has struggled so much with speech difficulties is about to be in a short homeschool drama, which will include many individual lines for him to say ... I have the feeling that he might even outdo his brother and sister, since he has such a naturally loud and dramatic personality.

Scraping a deer hide in the Powhatan village at Historic Jamestown, May 11

Visiting Colonial Williamsburg, May 12

5/13 My kids just had the Best.Time.Ever. They got to take friends of theirs to the creek that they so love, AND it was hot enough (and the Moms were lenient enough) for all the kids to get to swim and enjoy natural water 'slides.' AND they found tadpoles, a frog, and a newt. Thankful!!!

5/15 The kids' drama teacher was so sweet to compliment each child individually at the end of today's final rehearsal for next week's skit. When she got to Ethan, she said she'd never heard him speak better and more clearly than today, and she and all the children clapped for him in particular. Made my mama heart proud and brought tears to my eyes.

5/16 Steve's helping with Georgetown's graduation this morning ... I presume their outdoor ceremony will be moved into the gym due to rain. He can't figure out why their Plan B is a gym instead of their nice hall, but oh well. At least he won't be standing in the sun!

Oh my goodness. Josiah's just discovered Ursula Le Guin's Earthsea books and he is *tearing* through them!! So fun to see the kids get excited about good books! (I haven't read Le Guin myself, but she got raving reviews. I might just give her a try now!)

After torrential rain this morning, the beautiful sun has come out, allowing the kids to cheerfully look for worms and the guinea pigs to enjoy fresh grass. Think we'll take a creek walk to check out the water level and get some natural water for our tadpoles...      

5/18 Why did I decide to "Spring Clean" my closets and bookcases today? Bit off more than I could chew and now just want to collapse in bed early (like I did last night). Maybe the piles will just have to stay overnight... 

Progress made; job unfinished; going to bed anyway. Oh, and hoping that our troublesome guinea pig, who escapes every chance he gets and is currently 'missing' under our back deck, survives the night despite cool temps. I wouldn't miss him at all, but the kids would be heartbroken...

5/19 "I’m angry that some of the most genetically gifted women in the world – actresses and models – are still considered not good enough. I’m angry about what that means for the rest of us." Some good thoughts. I was just sitting in church yesterday looking at all the dyed hair of middle-aged women sitting next to their grey-haired husbands, thinking along similar lines. 

TIRED. Horrible night of sleep, followed by *long* day of errands and work. At least dinner was fun as we laughed over memories as we ate hamburgers at our picnic table. Love laughing with my family!!

Why do my children complain about going to library events? Today's program featured a local nature center, and despite Ethan's bellyaching all the way there, they had fun once it all started. They used nets to catch various pond creatures and then heard a naturalist share interesting facts about each critter. They saw a ghost shrimp, a pregnant mosquito fish, a baby snapping turtle, and baby clams, among others. Our world is an amazing place!

5/21 First day of "Couch to 5K" ... not totally successful, but anything active is more success than failure right now! Enlisting my daughter to be my partner, since we're equally out of shape. Now to hang on and keep going ... Jogging/walking the creek path was highly motivating!!     

So looking forward to seeing my mom's side of the family in just two days, as we gather for my cousin's wedding!! It will only be my second cousin wedding to attend despite the fact that I have 20 cousins.

5/22 Homeschool co-op end-of-the-year field games and picnic this morning, followed by final drama rehearsal and skit performance to a small audience of parents and friends. At home, trying to fit in teaching my neighbor how to care for our guinea pigs while also tutoring two students and packing for our trip. I'm tired Think I'll lie down 'til the next student comes...

My cousin Kelly and our grandma at Kelly's wedding May 24

Mom, cousin Alyssa, sister Saralynn, uncles Bob & Brian, me, in Georgia for my cousin's wedding, May 25

5/26 Getting mosquito bites INSIDE the condo (in Kitty Hawk, NC). Was only here 15-30 minutes and I had at least 5 or 6 new ones. My kids say that the mosquito is the one animal they'd be happy to see extinct.

5/27 Beach: best way to spend a vacation. Today saw dolphins, pelicans, a fish, and my three happy children, building in sand and trying a bogie board for the first time. Water was only 55*F -- so cold I could only take one-minute dips at a time -- but it was nice to cool us off on this warm day!

Josiah tries out a bogie board in Kitty Hawk, NC

5/28 Falling in love with the Outer Banks (North Carolina). So much less commercial than Myrtle Beach and Hilton Head. Spent a total of an hour in the freezing ocean yesterday -- perfect for me, who hates hot temps. Visited the beach in the dark, too, and saw big crabs scuttling across the sand in the light of someone else's flashlight. Went right out to buy my own flashlight so I can take the kids to see the crabs another night...  

Visited the Wright Brothers National Memorial today, and saw the spot where Orville and Wilbur made the first controlled engine-powered airplane flights. Interesting history!

Success today: getting all my family INTO the ocean! Naomi and Steve joined me in the chest-high cold water, and Josiah was out there too, but mostly on his bogie board. Ethan got as wet as he could, but didn't come out to the same depth. The cold water was totally refreshing, and the squeals of glee from my children made my week!

5/29 Josiah seems to have gotten sick, and Ethan might be ill too. Bummer way to spend a vacation...

5/30 To prolong our beach vacation by one more day, we're camping tomorrow night -- for the first time in 3 years! Here's hoping we figure out our tents okay, that the boys feel better and that we stay warm enough to not be miserable. Oh, and it would be *really* nice if we spotted some wild horses -- would thrill Naomi's 11-year-old heart if we did! (6/1 Well, the only "wild horses" we saw in Ocracoke were the penned descendants of a wild herd. At least it was something! We also saw rabbits, something resembling a woodchuck, and a cool crab that buried itself in sand when frightened (Naomi even pet it!) (But the boys felt better and we were warm enough -- yay!) 

 Visited the location of the "lost colony" of Roanoke (1587) today ... not much to see but still fun to walk in their footsteps! Unfortunately the boys are still under the weather. You know when they choose a nap over swimming in the pool that something's not quite right!!      

We visit the first English (unsuccessful) colony in America.

6/1 Such a fun weekend!! It was the vacation we didn't want to ever end. Very hard to say goodbye to the ocean this afternoon, but we'll cherish the memories of falling asleep to crashing waves (while camping), star-gazing in a very black sky, seeing the sunrise over the shore today (though sand was blowing in our faces the whole time!!), and riding the kids' (and Steve's) first ferry (for cars). The boys have felt great and everyone liked camping (despite we adults not sleeping the greatest). Thankful!!

Love the lighthouses in North Carolina!

Highlights of today: waking up to melodic birdsong (we camped right next to a stand of bushes and trees to protect us from the strong winds), seeing the sunrise (which this night owl hardly *ever* gets to do), and eating Carolina BBQ (pulled pork sandwich) & fried okra -- DELICIOUS!!! Enjoyed every bite...  
 

The kids took their first ferry ride. May 31

We love the sand dunes of North Carolina! May 31

June 1

No Pencils in Math?

What if math education used no writing for the first few years? What if all sorting, arithmetic, geometry and algebra problems were done with movement and objects? Chocolate-bar fractions and M&M probability. Area and perimeter using square tiles and real rulers. Graphing using footsteps and string. "Solving equations" using a scale and bags of goodies.

I wonder how much of people's math difficulties and fears stem from premature writing, and too few hands-on activities. "Manipulatives" is a current buzz-word, but if they're only tossed in as an extra now and then, are they enough? When I tutor math students and they're struggling with a particular concept, I always try to show them in a hands-on manner what is going on. But why should I wait until they're struggling? Why can't math be kinesthetic all along?

My kids are (almost) 6 and 4 1/2 and they've both been doing kindergarten this year. I have done no worksheets about numbers and counting, but we talk about numbers all the time. We spent all Fall doing math activities concentrating on classifying, directions, and quantities. Numbers were something I brought up every now and then. Now my kids bring up numbers themselves and are continually telling me things like, "Mom, 2 and 3 make 5!" My older child has tried writing equations on her own because she's becoming enamored with writing in general. But I wonder if I wouldn't be better off saving the writing for later.

I think I would have more fun teaching and I know the kids would have more fun learning, if math were taught this way. And maybe, as a small side benefit, our next generation would not be so math illiterate.

Flexible Teaching

Homeschooling is going great. One of my frustrations when I taught public school (sixth grade) was that I had short amounts of time with each class and I had to cover exactly what the school district told me to. It made it pretty difficult to do anything creative or exploratory. And one of the few times that I did let the kids explore, I got yelled at by the vice-principal.

I had taken my class downstairs to the sidewalk and let them draw large circles using chalk and string. Then I had them measure the circumferences and diameters of their circles using string, and write down their figures on paper. We had quite a few pairs of numbers from all the various circles we’d drawn, and I asked them to use a calculator and find the ratio of circumference to diameter. Everyone had an answer very close to 3.

My 11- and 12-year-olds had just discovered “pi” for themselves. If I simply taught the formula “circumference = pi times diameter” everyone (remotely engaged) would ask “What’s pi? Where did it come from?” But by having them make their own circles and their own measurements and their own calculations, I (hopefully) showed them that pi is a number that just is. It is the beautiful true ratio occurring naturally in every circle.

Our vice-principal came outside just then, though, and was quite cross with me (in front of my class) for putting chalk on the sidewalk (we all know how horrible that is!) We spent the last rushed minutes of class-time ferrying water back and forth from the bathrooms to wash off our offensive circles.

Anyway, all to say that I love teaching at home, where I can be flexible and innovative without anyone’s permission. I can spend as much time as I like on a phonics game or a sawdust exploration time. We can learn measuring skills through real cooking instead of word problems in a mathbook. We can read “There’s an Alligator Under My Bed” five days in a row and make “alligator bait” (cookies) or jump around the room on pillows to keep safe from the “dangerous alligator in the water” (8-month-old Ethan). At least for kindergarten, this is the right choice for us!