### 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…

### The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

### Kids R Kapable

Just a little note to concerned ‘grownups’ everywhere.  If you look at a kid—and I mean really look—I don’t mean notice a person shorter than you, I mean make eye contact, notice their facial expression and observe their body language—If you look at a kid, don’t assume they need your help unless they’re obviously distressed, or ask for it.  You might think this is difficult call to make.  You might think, not having kids of your own, that you’re unable to make this determination.  You are.  You do in fact, already have the skills even if you’ve never been around kids  It’s a remarkably simple call to make, just use the exact same criteria you would for determining if an adult was in distress.  Because, guess what, kids and adults are in fact the same species of animal and communicate in the same way.  Honest.  If someone—adult or child—doesn’t need your help, feel free to say hello, give a wave, give a smile, but don’t—do not—try to force help on anyone that doesn’t want or need it.

Y…