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Showing posts from February, 2020

Shifting and Zero Powers

9 y.o. Daize and I stumbled onto another math thing (I mentioned it briefly a few days back), and I’ve been aching to write about it so here goes.

Daize and I started talking about binary numbers years ago.  At the time Daize wanted to build her own phone, so we talked about how computers work—in binary.  From there, things just kind of kept rolling becasue everything is easier in binary for us.  When you want to talk about addition, of multi-digit numbers for example, and how to carry and all that good stuff, it’s simple to talk about binary where there are only two numbers you need to know: zero and one.  With memorization out of the way, Daize and I could talk about carrying and adding to our hearts’ delight.  Same deal for multiplication which then led us to raising numbers to powers, and here we are!



Raising numbers to powers—-for those who don’t mess with this stuff every day—iis usually illustrated by multiplying numbers by themselves.  So, 2 to the 2nd power is just 2 times 2,…

Talking Up

I did a new parenting “thing” this week, and it worked, and I’m so excited I’ve got to write something about it, and so here goes.  When I thought one of the kids—specifically 7 y.o. Towser—might have done something he shouldn’t have, I sat down on the ground before I talked to him.  I mean all the way down on the ground: my butt down, leaning back on my elbows, looking at the kid from below his line of site even when he sat down.



And then, we talked.  We actually talked.  To each other.  He was upset about the thing that had happened before, the thing that had caught my attention, but even relative to that he looked down at me, opened up about what was going on, and we talked calmly.

The calmness was the of the best aspects of the whole experience.  Towser and I talking didn’t add to the stress the kid was already holding inside.

Instead of trying to figure out what he should say, or what would keep him out of trouble, the kid spoke about his feelings.  He spoke about what had actual…

Homeschooling and Friends and Frustration

Playground day was huge yesterday!  The nearby homeschooling chess club was cancelled, and so everyone turned up at the playground!  There were all ages of kids from two to ten to mid-teens, and of course 9 y.o. Daize, 7 y.o. Towser, and 5 y.o. Tawnse, (aliases all). 



And before anyone asks, "Playground day?"  Allow me to jump out ahead.  Yup, we have one playground day a week, and it was yesterday.  But, it’s a bit of a misnomer.  Playgrounds are more of a daily thing.  This morning?  The kids were at a different playground where the youngest of the group is taking a cooking class through Parks & Rec.  Buddies who live near that playground often turn up to play some more.  This afternoon, another set of buddies will turn up at math group at a nearby public library.  And so it goes throughout the week.  There’s one day a week we call playground day because it’s set aside for kids and parents to meet at a different playground in different parts of the city.  But, that’s n…

Homeschooling Stereotypes; Also? We Voted Today!

Homeschooling Stereotypes

The 9, 7, and 5 y.o. unschooling gang, (also known by their aliases here as Daize, Towser, and Tawnse respectively), went to vote with me this morning.  We got to visit city hall which the kids love.  City Hall in San Francisco is a bit of a thing.  It’s ornate in the extreme, and then to top it all off, people get married there.  We haven’t ever been without seeing a variety of gorgeous wedding dresses.



We all took our time taking in all the wonder of the place for the umpteenth time—it actually never gets old, at least not for us—then we headed to the desks where we could pick up my ballot.

The people at the desk observed that it was odd to see three school aged kids at their polling place on a school day.  Before long they’d put together that the gang is homeschooled.  They asked the kids the usual questions.  How do they liked being homeschooled?  The gang’s used to this one by now.  They all responded that it was great!  Next a man asked if they ever get…

Tests for Teachers

"What!? Every teacher should be tested on the things they teach!" said the nine year-old unschooling kid this morning.

We were talking about our word game that had turned into a math conversation and back into a word game, but not before I figured out why any number to the zero power is 1. 

It turns out the answer isn't "Because I said so," as my 8th grade math teach would have had me believe.  There's a more intuitive answer that comes out right away if you talk about raising numbers to powers as shifting rather than multiplication or teacher-inspired mysticism.  It's simply that for the zero power of any number written in its own base, you just don't shift.  In other words you shift zero times.  The kid and I arrived on this purely by accident this morning because we had the time to play with numbers while we were talking about how many different words you could get out of a 26 letter alphabet for each size of word, (one characater, two character …