### Unschooling Homework Happens Unintentionally

The unschooling gang here gets a science lesson a week.  They learn about things like electricity, magnetism, waves, the Doppler effect, and water pressure.  They don’t do any homework or worksheets . The lessons are based on demonstration and play.  They watch the demonstration first, and then they get to play with it, (perhaps a more stern educational type than I might call it experimenting rather than playing).  There are no worksheets, no homework, and no books.

People might ask, “Can a kid really learn something without doing some type or rote homework to help them internalize it?”  As with most things unschooling, we’re discovering that the repetition that might be necessary to learn happens not at a desk or at our kitchen table, but instead in the outside world where the 7, 5, and 3 y.o. gang here spend most of their time.

Take water pressure for example.  The kids performed a water pressure experiment using milk jugs.  They filled two jugs with water, then punctured one of the jugs near the bottom and the other near its top, (but still below the waterline).  Measuring how far the water sprayed out of each hole, they could see that water pressure was created by the water itself.  When more water was piled up above a point—the bottom of the milk jug for example—there was more pressure—the water shooting out hit the ground a greater distance away.  That was it, the whole lesson.  There was plenty of elated squealing as water went everywhere, but then we moved onto other stuff, other activities.  Had they really retained the knowledge?  Did they need to work out a few problems?  We didn’t know, so we let it slide

Sure enough though, the world provided the opportunity.  A few weeks ago, on a camping trip, the gang reinforced their knowledge about water pressure when we stumbled upon an old water tank in a forest across the bay from San Francisco.

The gang wandered over to check out the wooden tank.  It was built of vertical planks held together with steel cables.  My partner took the time to point out to the kids that their were more cables binding the bottom of the tank than the top.  She reminded them what they’d learned about water pressure—that water stacked up on top of water built more and more pressure.  She pointed out how it took more cables to keep the tank from bursting at the bottom than it did at the top  Voila, scientific reinforcement in the real world!  The kids didn’t have to do homework, or memorization, we all just had to enjoy ourselves.  The real world provided reinforcement at no extra charge, because, that’s what the real world is happy to do for all of us.

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…

### Unschooling Math Jams: Squaring Numbers in their own Base

Some of the most fun I have working on math with seven year-old No. 1 is discovering new things about math myself.  Last week, we discovered that square of any number in its own base is 100!  Pretty cool!  As usual we figured it out by talking rather than by writing things down, and as usual it was sheer happenstance that we figured it out at all.  Here’s how it went.

I've really been looking forward to working through multiplication ala binary numbers with seven year-old No. 1.  She kind of beat me to the punch though: in the last few weeks she's been learning her multiplication tables in base 10 on her own.  This became apparent when five year-old No. 2 decided he wanted to do some 'schoolwork' a few days back.

"I can sing that song... about the letters? all by myself now!"  2 meant the alphabet song.  His attitude towards academics is the ultimate in not retaining unnecessary facts, not even the name of the song :)

After 2 had worked his way through the so…