Negative Numbers

We’ve been teaching Mark the set of Natural Numbers, as I suppose parents do the world over.  And, like parents do the world over, I tend to thing that my children are a bit above average when it comes to thinking.

The other day, I thought it’d be cool to ask him questions about the relative sizes of the numbers, so we started with simple questions like, “What is number is bigger than five?”  He said right away, “Six.”

“What number is between four and five?”

“Four and a half.”

“What number is less than zero.”  He thought for a while with a concerned look on his face, then tilted his head. “There’s no number less than zero daddy.”

“Well, actually there are a whole bunch of numbers less than zero.”  Now I had his attention.  “Negative one is less than zero.  And do you know how small it is?


“Negative one is so small that it’s less than nothing.  It’s less than zero..  As a matter of fact, it’s so small that if you have a negative number of something, you have so little that something that as soon as you get any of it, you have to give it away immediately, because it’s not even yours when you get it.”

“So, do you know what’s less than negative one?”

“No,” he said.

“Negative two, then comes negative three, and negative four. See, if you have negative four of something, you have so little that if you get one, you can’t keep it.  And if you get another one, you can’t keep it either, you have to give it back.  And even if you get two more, you still can’t keep them.  All you can do is give them back.  Then, all you have is zero again.  Then finally, after all that you can finally keep one.  Isnt’ that crazy? See if you can guess what number is less than negative four?”

He smiled and said really loudly, “Negative FIVE!”  Then we got out a pencil and paper and drew a number line and put a few numbers on it.

Which I thought was rather fun.

A couple days later, as we were going to bed, I asked him, “What number is right between one and negative one?”

He thought for a long time on that one.  He is just four right now, after all. Then tilted his little head and said, not too confidently, “Zero?”

Holly and I both that that was pretty fun (but I probably thought it was more fun).  We’re’ starting to work on skip counting the odds and evens next.

I suppose we ought to start working on the numbers higher than the days of the month a bit more (Holly does the monthly calendar with him most days).  Then after that we ought to start in on writing numbers with a crayon, or something similar, and then do some addition.

Actually, what I need to do is my taxes.

Teaching Mark to Count by halves

The other day while we were out on a drive to take some pictures up at the eagle preserve, I heard Mark counting: “one, one and a half, two, two and a half, three, three and a half, four… ” and on up he went to ten.

I said to Holly, “Are you hearing this?”

“Yeah.  He’s counting by halves. Isn’t that wild?”

Then I said, “Wow. When did you teach hiim that?”

“I didn’t teach him halves.  He must have picked it up somewhere else.”

So I asked him, “Mark, who taught you to count by halves?”

He said, “Lydia.”

‘Lydia,’ I thought, how could this be? “Lydia who?”

“Lydia Green.” He said. 

“Wow.  How’d she do that?”  Lydia, I know is can’t really talk yet very much, and I’m

pretty sure she can’t count.  Don’t get me wrong, she’s a great kid.
Holly said, “Oh, of course.  Lydia Green is one and a half years old.”

“Yeah, but how did she teach him how to count by halves?  Can she even talk?” I said.
“No, no, no.  Mark was wondering how Luke and Lydia could both be one year old, and yet Lydia could do so much more than Luke, and I explained that it was because one and a half but Luke was just one.”

“Cool”. I thought.  My boy can count by halves.

Conference in Anchorage

AMC Annual meeting at the Hampton in Anchorage

I’m at the annual meeting of the Alaska Math Consortium and there are many things that are real eye-openers.  I’m excited about some of the changes that will be made and how communication will be changing in the group soon.

I think it was an important to be here and have things to contribute and learn.
One things that’s wild is that the Hampton Hotel, here in Anchorage has a has a very fast Internet connection compared to home.  Which is nice because we’ll be working on our web-page and such. 

I’ve taken a few photos and will be trying to take some urban type shots today because one of the misconceptions people sometimes have about the math consortium is that it’s strictly for rural teachers.  That’s so far off base.  I want to take some photos today that we can put on our web-site to divest people of that notion.  The easiest way for them to know what size of schools we have in our membership is to look at our list of member schools, but today, people never look at long lists anymore when they aren’t personally involved in some way with it.  It has to do with the inundation of data in our society and how we are separated from the actual data by people and layers they create which automatically decipher it for us so that we will get something from it instead of skipping over it entirely.


Sunday, June 25, 2006

Often I tell stories to the kids in math class while I’m erasing the overhead scroll to make room for more class notes.  Usually the stories are short and not really stories but just little anecdotes or cautionary tales, snippets from my past.

With the senior Calculus math class this past year, I often didn’t know what story to tell, as they’d heard so many of my stories.  One day I came to the end of the blank space on the scroll, “Well, it looks like we’re out of space.  Normally, I have a story ready to go, but today I don’t.  Is there any story you want to hear?”

Most of the class didn’t have anything in mind.  But in the front row, Miss Holmes gave a big smile and said, “Tell us what it’s like when you put the boys to sleep.  What happens at bed time?”  Then she put her elbows on the desk and rested her chin on her hands and settled in for a story.

I thought to myself, that doesn’t sound like much to work from.  But I’ll give it a try.

“Well, here’s how it works at our house.” I said.

“Holly is all about patterns and routines for the boys.  She thinks it’s good for them to have daily verbal and musical cues for just about everything that happens.  There’s a song she sings before each meal is served that tells us all that it’s time to come to the table.

“Well, bedtime works like this:  First we read the boys a story.  We always have a very large pile of books from the library.  This week its stories with dogs in them.  I often read a story to Mark near bedtime, around 8:30 PM or so.  While I’m doing that, Holly goes and removes her contacts and puts on her glasses. Then while she’s brushing her teeth, Mark and I go in and brush teeth too.  I use one of the gadgety tooth brushes, Mark uses a dragon tooth brush.

“Then Holly goes to the piano room and starts playing the either an old folk tune from the big yellow book or an old church song or spiritual.  Mark runs in and sits on the piano bench with his mother.  Then eventually she starts playing, the final song of the evening, which is always the same, ‘Good night, Ma-ark, good night, Ma-ark, etc… using the tune from the Music Man, Goodnight Ladies.

“After that, Holly nurses Luke to sleep and I read one final story to Mark; usually a story from a bible story book or another book that Mark likes and has requested.

“Then comes the bed-time prayers, where Holly sticks her hand over and holds my hand and Mark’s hand.  Luke hasn’t learned to hold hands yet.  Usually I pray.”

“Then it’s time to go to sleep, but usually the boys can’t go to sleep, so Holly takes them out to the big black chair and sings them to sleep with songs out of the hold church hymnal my parents taught us to sing from.”

Then Miss Holmes smiled said, “That sounds rather idyllic.”

“Well,” I said, “sometimes it doesn’t work out so well.”  And I looked out the window kind of sadly,  “Sometimes, after Holly has sung and sung, then I have to take a turn.”