Saturday, January 24, 2015

Sometimes, it's enough just to be the bobble-head

We hear a lot about educational entrepreneurs these days. As a service to these bright young innovators, I have here a proposed product that can revolutionize the teaching of mathematics: the bobblehead instructor. Given a gentle nudge, the instructor will nod reassuringly and repeat one of the following phrases:

"Looks good."

"And now what do you do?"

"Let's try that."

"Um-hmm."


All kidding aside, when I was a high school math teacher, a substantial part of my day was spent doing just that. I generally reserved the last section of class for individual or in-pair work.  Kids would finish up their worksheets and start on their homework while I would walk around the room.

When a kid was stuck on a problem, it was usually enough just to stand there and, in an encouraging tone of voice, say some combination of the phrases listed above. The students basically needed someone to hold their hand.

Learning to be the bobblehead can be surprisingly difficult for new teachers. You have spent years preparing for this job, mastering your subject, learning to be an effective teacher. The natural impulse is to jump in and start instructing. Most of the time, however, that is not what the students need.

Students often attempt problems as if their desk were wired to deliver electrical shocks whenever they made a misstep. They have to learn to be patient with themselves and to relax a little bit. Having a teacher who stands there reassuringly is often the ideal form of assistance.

Monday, January 19, 2015

Monday Video -- Juggling and Geometry

[Every Monday for the next few months, we'll be posting a short video clip here at You Do the Math. All will have at least a tenuous connection to science, technology, engineering, or mathematics. Teachers can use these as writing prompts or as starting points for larger lesson plans (I'll try to include some hints now and then), but the main purpose is simply to have a little fun.]


Michael Moschen is the kind of juggler who wins  MacArthur Foundation Genius Grants. Not surprisingly, his routines are fascinating to watch and there's enough geometry and physics in this one to kick off an appropriate lesson or just to remind kids that you can have fun with these ideas.








Monday, January 12, 2015

Introducing Monday Videos

Introducing the video of the week

Every Monday for the next few months, we'll be posting a short video clip here at You Do the Math. All will have at least a tenuous connection to science, technology, engineering, or mathematics. Teachers can use these as writing prompts or as starting points for larger lesson plans (I'll try to include some hints now and then), but the main purpose is simply to have a little fun.

Our debut clip features one of my favorite pieces of cool technology, the rail gun. The following shows declassified footage of the test firings of the latest model.The soundtrack doesn't actually add that much so I would probably leave it off and either talk to the class or play music while the video was running.









Here are some of the highlights from the Wikipedia entry:
[The Navy] gave the project the Latin motto "Velocitas Eradico", Latin for "I, [who am] speed, eradicate".
...
In 1944, during World War II, Joachim Hänsler of Germany's Ordnance Office built the first working railgun, and an electric anti-aircraft gun was proposed. By late 1944 enough theory had been worked out to allow the Luftwaffe's Flak Command to issue a specification, which demanded a muzzle velocity of 2,000 m/s (6,600 ft/s) and a projectile containing 0.5 kg (1.1 lb) of explosive. The guns were to be mounted in batteries of six firing twelve rounds per minute, and it was to fit existing 12.8 cm FlaK 40 mounts. It was never built. When details were discovered after the war it aroused much interest and a more detailed study was done, culminating with a 1947 report which concluded that it was theoretically feasible, but that each gun would need enough power to illuminate half of Chicago.
...
In 2003, Ian McNab outlined a plan to turn this idea into a realized technology. The accelerations involved are significantly stronger than human beings can handle. This system would be used only to launch sturdy materials, such as food, water, and fuel. Note that escape velocity under ideal circumstances (equator, mountain, heading east) is 10.735 km/s. The system would cost $528/kg, compared with $20,000/kg on the space shuttle.


And here are some quick lesson ideas.

Writing prompts

This one is fairly easy.For younger kids, you could give them a scenario involving, for instance, a moon base. Have them talk about how railguns and other technologies might be used. You might also have them include an illustration. For older kids, the focus would be a bit more serious and realistic and might include potential problems with applying this technology.




Thursday, December 18, 2014

Rules of Kruzno -- updated



I've been alluded quite a bit to Kruzno, a game I developed a few years ago and which I am currently selling on Amazon, but I don't think I've ever posted the rules so here they are.

[Just to be clear, When you jump over a piece that you don't capture (for example, a white rook jumping a black rook), the piece that you jumped stays on the board.]











Sunday, December 14, 2014

Hexagonal chess

As mentioned before,I recently opened an Amazon store for the board game Kruzno. The game was configured to be suitable for a wide range of games. The best known of these was probably developed by Wladyslaw Glinksi in 1936. Glinski's Chess is one of the most popular chess variants with more than a half million players worldwide.

You can find rules many places online, but the following should be enough to get you started.





















Monday, December 8, 2014

Agon

[I recently opened an Amazon store for the board game Kruzno. One of the considerations when developing the game was to configure the so that it could serve as a good utility player, suitable for a wide range of games. My favorite of these non-Kruzno games is probably Agon. It's a challenging but easy to learn game that's deserves a much bigger following. Here is the write-up I did of the rules a few years ago. You can play it on a Kruzno board, of course, but any standard hex board will do.]

Agon may be the oldest abstract strategy game played on a 6 by 6 by 6 hexagonally tiled board, first appearing as early as the late Eighteenth Century in France. The game reached it greatest popularity a hundred years later when the Victorians embraced it for its combination of simple moves and complex strategy.

The Pieces: Each player has one queen and six pawns a.k.a. guards placed in the pattern indicated below
Agon Start

The Objective: To place your queen in the center hexagon and surround her with all six of her guards.(below)
win


concentric

Moves: Think of the Agon board as a series of concentric circles (see above). Pieces can move one space at a time either in the same ring or the ring closer to the center. In the figure on the left, a piece on a hexagon marked 4 could move to an adjacent hexagon marked either 4 or 3. Only the queen is allowed to move into the center hexagon. The figure below shows possible moves.

moves

Capturing: A piece is captured when there are two enemy pieces on either side of it. The player with the captured piece must use his or her next move to place the captured piece on the outside hexagon.
captures
If the captured piece is a guard, the player whose piece was captured can choose where on the outer hex to place the piece. If the piece is a queen, the player who made the capture decides where the queen should go.

If more than one piece is captured in one turn, the player whose pieces were captured must move them one turn at a time.

If a player surrounds the center hexagon with guards without getting the queen into position, that player forfeits the game.

Wednesday, November 26, 2014

Effort and Results

If we want to be serious about improving education, one of the first things we need to think about is the real and perceived relationship between effort and results. Take a look at the following three cases. To keep the discussion simple, I am using unrealistically idealized curves, but they should illustrate the main principles.





Let's say that the X axis in the graph above represents days in the semester and the Y axis represents some measure of mastery.

Which of these learning would we like to see?

It is easy enough to eliminate C. Obviously we don't want kids getting frustrated by going most of the semester without any progress .

Of the remaining two, most people would probably choose A, but I am going to strongly argue for B. I want to see B because I want the students to expect B in the future. I want them to go into every new topic believing that they probably won't see much if any progress at first but eventually they will see a more-or-less linear relationship between the work they put in and what they get out of it.

The great problem with A is that it reinforces students' most dangerous misconception: that math is something you get or you don't; that understanding either comes quickly or it doesn't come at all. You simply can't motivate people to work hard when  they believe that work is futile.