Finding Memories in a 5 year old's Wonderings about
Numbers

*from
Susan Richman*

Recently during one of those icy days in
mid-January, when our electricity was out so none of us could use our
computers, we all put in lots of hours cleaning out the office in our home. You
know, the piles that accumulate in file drawers, on top of file cabinets, in
desk drawers, on overstuffed shelves, on desk tops, and under desks. Ours was
pretty bad, and by the end of the day I had literally 10 grocery bags full of
old useless papers and catalogs and files to take to the local recycler. To
inspire our day’s work, I read aloud from one of Don Aslett’s books on
de-junking and de-cluttering during breakfast and lunch. One thought stuck in
my mind as I read his list of funny reasons why you should take the needed time
to ream out your office shelves regularly— he pointed out that you just might
find some real treasures there. I want to share here about a few I found that
day.

I came across a stack of rather crumpled
large envelopes, with homemade stapled together booklets inside. I recognized
them right away as a very old record-keeping method of mine when our son Jesse
was quite young— these were from back in the dark ages before we ever had to
show such things to the school districts. My first impulse was to just pitch
the whole batch right into the trash can without even looking at them. But
thought I’d just check them out a little bit first... and I’m glad I did.
Before me the younger years of my two boys, Jesse now 21 and Jacob now 18, came alive for me again.

Turns out I took the time back then (I
fully admit I do *not* do this anymore) to really record little things the
boys said to me that showed what they were thinking. There were really cute
little things like a notation that Jacob was seen lying on his back on the sofa
kicking his feet rhythmically up in the air as a 3 year old, chanting aloud
happily over and over again, “I can’t walk with two feet in air, I can’t walk
with two feet in air....”, or funny conversations the boys had while playing
with little plastic dinosaurs or soldiers.

I especially found lots of math
wonderings, and reading them over made me realize again that this chance to
have informal conversations with a parent, who usually has much more time to
listen than a teacher with a whole busy class, is so important to young kids.
In fact, this chance to just talk and wonder about things like numbers is
probably more important than the time put into just going through the motions
of doing daily math work if it’s *not* accompanied by real thinking— or
better put, maybe the real purpose of math lesson times with our kids is the
opportunity they give us to have these sorts of focused conversations. Thought
you all might enjoy some of these wonderings— might help you value the
wonderings your own kids do related to math, or any other subject area. Shows
how much young kids can really work at trying to see the order to things....

*Here’s
one from when Jesse was 5 ½, in January of 1983*: In bed reading aloud more of *Farmer Boy*.
Somehow the idea of ‘ten’ came up and a light suddenly flashed for Jesse. “You
mean, ‘ten’ is ‘*2 fives’??” *Then on to 20 = 2 tens (here he asked, “Why
don’t they give it its *own* separate name?”). 2 four’s = 8, 2 three’s =
6, using hands and fingers. Suddenly seeing whole new relationships— exciting
moment!

*And
later that same month:* More
Cuisenaire Rod play [note— these are a terrific math manipulative, one of the
best]. As I washed dishes in the morning I asked Jesse which rods have even
halves. Jesse bounded off, worked with great energy, made guesses, tested ideas,
very excited. Also found quarters, thirds, etc. Has discovered for himself that
the black rod (representing 7 units) has *no* even dividers of anything.
Discussed idea of odd and even, and it seemed immediately clear.

*In
March, math came up informally as we ate orange slices*: “I think I’ll have two 4’s of slices,” says Jesse.
“Ah! but there are *two* oranges for you, so really you’ll have four 4’s,”
I say. Jesse thinks, “That makes ... two 8’s!! How many is that?” He tries
counting up to four several times, but that doesn’t help much. I suggest
Cuisenaire Rods can help. I get 4 purple rods [these stand for 4 units]. Jesse
understands why. Lay them end to end. “Now, to find the number total, find what
an orange rod [which equals 10 units] plus what other rod would equal 4
purples.” “A SIX!” Jesse sees. 6 + 10 = 16.

*Maple
syrup-making time meant lots of hands-on helping in the kitchen*: Jesse helping count out jars and lids and rings for
maple syrup batch. Got six quarts, found we actually needed one more. Full jars
set up in two rows on table, 3 + 4. Jesse counted, we talked about being able
to see that 7 didn’t have an equal half, then Jesse said: “But what’s one more
than 7? 8? I know 8 has an even half— two 4’s make 8. And one *less* than
7 is 6, and *it* has an even half, too!” Talk of how even and odd numbers
seemed to go every other number... Then Jesse asked, “Which do you think there
are *more* of, evens or odds?” He thought odds, I pondered!

*This
same month Jesse also came out with*
“I know that 12 is an even number— you know how? Because 12 is 2 more than 10,
and *10 *is even. If 12 were just *one *more than 10 it would be *un*even,
but since it’s two more, it *is* even.”

*He
also wondered aloud about big numbers that month:* Cuisenaire play— Jesse mused on sofa about what a
thousand 1000’s would be, then a million millions, etc., delighting in huge
names, and possibly *nameless* numbers. Then back to ten 100’s— what was
that. He wondered if he could make 1000 with Cuisenaire rods— and tried and did
it. Very methodical about it— first used all orange [10 units] rods for 100,
blue plus white [ 9 + 1] for 200, and on and on...

*Math
came up when building with blocks too*:
Jesse, while working on his five-story block building barn, says that there are
10 goats in his barn, and showed where they should be milked. He must have been
thinking about them coming out evenly in two milking stands, for he then said,
“Ten is an even number.” Then after a moment’s reflection he said, “It seems
that two *odd* numbers added together gives you an *even* number.”
Incredible. And just think— all without a math workbook.

*In
April Jesse wondered aloud*, “Could
camels with *two * humps live for *six*
days on their humps, since camels with *one* can live for *three*
with nothing to eat, and two 3’s equal 6?” A morning query from Jesse after we
read *The Camel’s Hump* yesterday on a car ride home from town.

*A
spontaneous musing from Jesse*: “Hey!
I bet that if you took out all the *odd* numbers from 1 to 100, that you’d
just have left a *half* of 100!”

*By
summer Jesse had developed a game of using Cuisenaire Rods for playing store*: Jesse was store keeper and set ‘prices’ in rods, and
I ‘paid’ in rods, always giving extra and so needing change. Jesse figured out
how to figure my change— variation was that he’d purposely fool me to see if
I’d ‘check.’

*By
September, Jesse was thinking easily about fractions*: Jesse figured out, in his head, how many hours Bev
had worked for us. 2 1/2 + 1 1/2 + 3 = 7 hours! He said, “The 2 and the 1 equal
3, and two 3’s is 6, and the two 1/2’s equal 1, so that makes 7!”

Finally I gathered up all the little
booklets, put them back in their envelopes, and filed them away on my shelves
again. It was fun to get an unexpected peek at the boys’ early years again, to
remember these early years of wondering and figuring and musing and playing.
Reminds me of how we all love to occasionally go back through early portfolios,
laughing over the funny spellings in early scrawled stories, the earnest
artwork, the memories of travels and trips and homeschooling get togethers with
friends. It’s worth it to keep these records of our kids’ growing up years. The
years do go by quickly, just like everyone says they do.

Wonder what I’ll find in the next room I
clean out... j