The Freebie Problem

I ran into my first real problem with Khan Academy the other night.

Both kids struggled a lot with the Rate Problems 2 section in Khan. These are problems that require multiple steps to solve, and a more complicated mental picture than the earlier word.

I really like these problems. They exercise our understanding of the relationships between rates and times and other factors. They compel us to think conceptually about the big picture instead of just crunching the numbers.

The kids might solve this by working out how long it takes 1 person to paint 3 walls, then how long it takes 1 person to paint 1 wall, then how long it takes 6 people to paint 1 wall, and finally how long it takes 6 people to paint 7 walls.

I urge the kids to make a chart, fill in what they know, and then figure out how they can fill in additional boxes on the chart until they have what they need.

Every now and then, however, Khan throws up a variant of the problem like this:

After Jessica carefully worked it out, I showed her how this one was actually easier. If the number of people and walls are the same in both cases, then the answer is also the same. 7 people take as long to paint 1 wall each as 1 person takes to paint 1 wall or as 11 people take to paint 1 wall each.

“It’s like a freebie,” I said. “You don’t even have to do the arithmetic.”

This Jessica remembered. As she continued to struggle through these exercises, every now and then she would proclaim, “A freebie!” and I would immediately hear the happy sound that Khan plays when you get one right. But she was otherwise struggling, and she didn't succeed in getting five in a row before we called it a night.

The next day she took a Mastery challenge. She aced it easily, and when the report came up at the end, it showed she had “Mastered” Rate Problems 2.

But she hadn’t come anywhere close to mastering it. She had just got lucky. The Mastery Challenge had served up a freebie.

Since I was watching, I promptly added more Rate Problems 2 exercises to her list and continued to work through these with her. Actually I first took her all the way back to the earlier Rate Problems topics. And eventually she really could do them all, and she knew it.

How We Started Reviewing with Khan

So far I’ve had the kids doing Khan in parallel. This is what that looks like.

They sit side-by-side, each at a laptop.

When there’s a video lesson that I think would benefit both, I make them both watch it. I actually launch the video on one computer so they can watch, then simultaneously launch it on the other with the sound off. That way both kids get “credit” for watching the video. I pause the videos occasionally to ask them to predict what’s coming, to reinforce a point, or to ask about a related topic. “Wait a minute,” I’ll say. “How is he doing 12 times 15 in his head?”

They do the exercises on a topic individually but simultaneously—each at a laptop. I monitor both from behind. Since Khan seems to serve exercises randomly, they’re working on similar, but different, problems. We have a strict rule that they can’t advance past a wrong answer ‘til Dad has a chance to ask about where it went wrong. I frequently ask them to narrate through problems even before getting them wrong, just to see their thought processes. I’m pretty adamant about letting them make mistakes, though. If I guide them to the right answer, then the “5 in a row” rule will fail to serve enough exercises.

Since the exercises keep coming until you get 5 consecutive problems right, it’s likely that one of them (generally Jessica) will finish before the other. I tell the one who finished first either to do Mastery Challenge quizzes or to repeat the exercise, getting another 5 in a row, if I think it needs further reinforcing. A couple of times I’ve let her call it a day while I’m still finishing up with Nathaniel.

I generally stop the lesson when I feel like they’ve had enough, after something between 30 and 75 minutes. Khan presents no more than a few Mastery Challenge quizzes, then introduces a 16-hour delay—we have to wait until tomorrow for the next Mastery Challenge. I usually stop when the kids have worked through exercises on one or more topics and no more Mastery Challenges are available to them.

As of August 1 they were both at about the 55% mark for pre-algebra. I hope they make it by Labor Day.

I Like 5 in a Row

I remember—too clearly!—what it felt like to open my math homework after coming home from school at 3:30. Or possibly from the school paper at 6:00. Or from the grocery store at 8:00. I was tired, math was the most tedious of all subjects, and there were so many exercises.

How many problems? 38? Turn the page. Heave a sigh. Whisper an expletive. 72! Pull the crushed spiral out of my backpack. Maybe we only have to do the odd-numbered ones tonight?... No such luck.

My son is the same way with math exercises. Filling out a worksheet holds no satisfaction for him. When he used to look at a page of math exercises, I saw my own dread in his face.

This is one area where Khan really shines. Last night I had the kids review both the distributive property and finding greatest common factors—areas in which they had missed problems on Khan’s Mastery quizzes. For each topic they watched a five minute video and did some exercises.

But Khan doesn’t make the kids do 38 or 72 exercises. It says Get 5 correct in a row.

That’s it. Just five problems. If you get them all right.

If you get four and flub the fifth, well, now you have to do five more. You could be stuck there all night, but you could be done in five or ten minutes. And that’s a powerful motivator.

Nathaniel, who has never, ever been careful about arithmetic, not since the first time he hastily filled in the space under 2 + 1 on a worksheet, never-once-careful Nathaniel, is being careful. When it comes to the last problem, I can see him sweating, checking his work.

Checking his work.

Checking work reinforces math principles wonderfully. When he’s confirming that solving 9 X (5 + 4) is the same if he works it out as 45 + 36 as if he works it out as 9 X 9, he’s really learning what the distributive property means. I can remember worksheets and tests where my teachers used to write Check your work! optimistically across the top. Khan doesn’t, but doesn’t have to. It’s enough to say Get 5 correct in a row.

Trying to Master Pre-Algebra

I’m sort of evolving my teaching-with-Khan plans as I go.

My loose goal for the school year is to get both kids through the Algebra and Geometry curricula.

I’m not confident, however, that they’re ready to plunge into whatever topics are categorized under Algebra and Geometry. My aim for the balance of the summer is to get them to achieve “Mastery” in the Pre-Algebra topics.

Khan attempts to describe a student’s knowledge of each topic. A topic can be Mastered, Practiced to 2 or 3 different levels, or Unpracticed.

A quick way to advance through these divisions are Khan’s Mastery Challenges, very short quizzes on a variety of topics. Some tuning algorithm seems to refine the questions included in each Mastery Challenge. So the more Mastery Challenges a student attempts, the more relevant the questions become.

This seems as good a place to start as any, so we loaded up the Pre-Algebra curricula and started going through some Mastery Challenges.

The kids were delighted to ace some easy questions, and surprised at a few hard ones (or easy but utterly unfamiliar ones, like the Stem-and-Leaf Plots). They were maybe a little-disappointed to see that they were earning badges with names like Addition, Third Grade. They understand the direction they're going, though, and they can sense that they'll feel some satisfaction when they earn more advanced badges.

After the first week of doing this, it seems like the kids are each getting through one or two Mastery Challenges per day.

If we can maintain the pace, they should have the Pre-Algebra curriculum complete around Labor Day.

Trying Khan for Math

Nathaniel seems to have a knack for mathematical concepts. He can picture fractional quantities in his head, for example. He is impatient with memorization and drills, however.

He’s fifteen now. He knows math at a sort of B-student-in-pre-algebra-but-occasionally-horrifies-me-by-counting-on-his-fingers-to-add-seven-to-ninety-five level. I think he under-performs on tests, largely because of his impatience with the testing.

Jessica is nearly the opposite. She struggles with any sort of mathematical visualization and dreads story problems but takes real pleasure in knowing and repeating the process of an arithmetical operation. Drills of well-known material make her happy, and timed tests make her happier.

In both cases, I’d like to see the kids advancing faster than they are, and testing better. I suggested as much—and suggesting is always risky for a homeschool parent. So now I get to be teacher.

Really, though, I’m happy to try. I’ve always been a little envious of the teaching.

My first command decision was to re-abandon Saxon, this time for the Khan Academy.

I’m building a list of reasons why. So far it looks like this. 

I'm betting that Khan is better at...

• ...targeting lessons to what a kid needs to learn.
• ...building test-taking skills (critical to homeschooled kids who want the chance to go to college!)
• ...providing repeated drills when (and only when) necessary.
• ...reinforcing concepts already learned.

We’ll see how it goes.

A Week of Poems

A short list of what emerged while we wrote daily poems with The Poem Farm last week:

Attention to Description
Choosing the best word to capture something, the emotionally charged word, the word with the right sound
 

Efficiency of Expression
Words like turgid and cogent and concise came out while we talked about how a poem might express in one exact word what we might usually say in ten.

Meter
One of our kids hears meter easily. The other struggles to tell how many syllables are in the world struggle. But both could hear four strong beats in a line, and—at least some of the time—aimed for it.
 
Rhyme Schemes
The children did some rhyming instinctively. Then we looked at Amy's poems and old favorites from Shel Silverstein, and they experimented with trying to imitate more structured rhyme.
 
"Couplet"
A new word. And triplet and quatrain.
 
Voice
What it means to assume the voice of a hermit crab's shell.
 
Some Scientific Observation
Nathaniel did try to stay awake all night to watch his crabs. (Like me, he's an early-to-bed personality, and I don't think he lasted much past 10:00.)
 
A Little History
I'm not sure why Jessica is so interested in the first Fourth of July celebrations from Philadelphia in 1777, but we read about them together.

Editing
The satisfaction of seeing your work improve. Jessica was utterly pleased with herself when she sneaked references to red, white, and blue into her Saturday poem. "Isn't that clever?" 

Nathaniel, who invariably resists editing, worked hard to hide his pride after he changed "I'm only one out of a lot of shells" to "the sea of my kind blankets the sand."

What a delight this was. And how grateful we all are to Amy at The Poem Farm for sharing her own work and encouraging us.

Our Week with The Poem Farm: Sunday

I'm very grateful to Amy at The Poem Farm for sharing her own poems this week and for offering comments so generously to Nathaniel and Jessica on their poems. We've really enjoyed participating in this group effort. I hope we try something like this again.

Sneeze at a Sparkler

by Jessica

On top of the fourth of July
All covered with fireworks
I lost my poor sparkler
When somebody sneezed

It rolled off my hand
And onto the grass
And then my poor sparkler
Exploded with pizazz

And then my poor sparkler
Rolled off of the hill
And there it grew into
A tree that grew sparklers

So here's a little tip:
When you're playing with a sparkler
Don't let anybody sneeze!

Watching My Crabs

by Nathaniel

Falcon-fast when in need of speed
These little critters don't need a lead

Sometimes hungry, sometimes not
Sometimes they leave their food to rot

Their constant love to explore
Is to the watcher sometimes a bore

Their tunnels are usually where they take their tour
If they meet, there might be some gore.

Scurry, scurry, scurry all day
They love to explore their life away.

Shakespeare in Our Kitchen

In sixth grade I thought I read Hamlet.

Shakespeare was a famous name to me, nothing more, and I think I saw some personal challenge in reading this most famous of grown-up writers.

When my book report came back, Mrs. Miller explained, very gently, that I hadn't read Hamlet at all.

I had found the wrong library shelf. My book was a historical study of the staging of Shakespeare. Seeing a title like Hamlet: A Performance History, I mistook it for the real thing. And there were bits of the real thing in there, but only bits, out of order, and buried among bits of other plays and lots of commentary.

A whole book about...another book? This was unexpected.

---

Skip ahead 30 years, and Camille and I have just read Macbeth aloud with our children, neither of them quite as old as I when I had attempted Hamlet.

Our kids are more familiar with how plays work, having seen many live dramas and musicals. (Homeschoolers buy tickets at the heavily discounted school rates.)

Initially wary, Nathaniel warmed enough to create costumes and two prop knives—a clean "before" and a blood-stained "after" version. Jessica embraced the role of Lady Macbeth a little too eagerly. Over the course of several nights we invited friends to read some of the parts, enlisted stuffed animals and dolls to stand in for characters, and compared notes from different editions while stumbling through the language.

We made delicious mistakes:

• Banquo's issue, referring to his descendants, was read as Banquo's tissue. Sneezing jokes ensued.

•  That business in your bosoms became the more intestinal business in your bottoms.

•  The blessings that hang about the king's throne were, about our kitchen table, no longer sundry but sun-dried.

•  When I asked for ideas about what a hurley burley might be, Jessica looked offended that I should ask, then hulked her lanky ten-year old body into a bicep-flexing pose and said, "You know, a hurley burley! A big tough guy with muscles."

And we were victorious! I don't pretend that any of us understood every word. But we got through it, followed the basic plot, and even discussed a handful of poetic images and plot parallels. Shakespeare migrated from the mysterious unknown into something recognizable. 

---

In college I was struggling to read Karl Marx when a biographical detail struck me. A fan of Shakespeare, Marx insisted that his children know all the plays.

Recalling my sixth-grade failure, I tried to imagine that. Were the whole family geniuses? Did other kids ridicule the young Marxes?

Above all, what sort of weird parents read Shakespeare with their children?

Now I have kids of my own, and the older they get, the more certain I am that homeschooling, well, weirdens them. I just hope it's in a wonderful way.

Our Week with The Poem Farm: Saturday

I've been delighted and surprised to see the different structures and forms our kids have tried during their collaboration with The Poem Farm this week. Most surprising of all, perhaps, was to see Nathaniel take on the voice of a crab's shell or to see Jessica speak to a firework. I admire their imagination.

Philadelphia, July 4, 1777

by Jessica

Thirteen ships a-sailing

Among the waters so blue

Thirteen cannons shot out

As many people who had shed

Red blood for our country

Watched the crew

Thirteen American flags fluttered

On white sails as our nation grew

Hooray! All thirteen states are free!

And so are you and me!

What Would I Do?

by Nathaniel

What would I do if my crabs grew three times their size every day?

What would I do if my crabs started spitting up clay?

What would I do if my crabs killed each other in a duel?

What would I do if my crabs tore up my sheets while I was at school?

What would I do if they fell down the loo?

What would I do? What would I do?

The King of Pop and Taylor Swift

On the way home from choir practice, the radio news played a report related to the investigation of Michael Jackson's death.

Jessica, still surfing the gregarious wave that an ocean of thirty girls roiling for two hours will kick up, started to prattle.

"Michael Jackson. I don't know much about Michael Jackson. He was a singer and he's dead now and he had five brothers and they were called the Jackson 5 and he had plastic surgery but I don't really know much about that and he looked kind of weird that is all I know I don't know very much about Michael Jackson."

Our kids really don't see much TV or Internet. I'm still amazed at what they absorb.

"And he kissed Mom," I added.

This is a fact. When Camille was a very young girl in an aisle seat, The Jackson 5 ran into the audience, and an almost-as-young Michael kissed her cheek. Camille's siblings validate the account.

"I KNOW! HE KISSED MOM! ISN'T THAT GREAT! He's like a sell-uh, what's that word, a sell-uh-britty or something, IT'S ALMOST LIKE MOM KISSED TAYLOR SWIFT!"