Alphabet

Awhile back I made an alphabet book for my son, in which I tried to arranged the letters to highlight their symmetries.  At almost-three, he's just about ready to appreciate it...

Pentanonic awesomeness

I came across this simple but addictive music maker on M0ar, with no credit given:



It seemed that any possible pattern sounded good. I was reminded of this:

Quantifying student learning

A recent NBPTS report entitled Student Learning, Student Achievement: How Do Teachers Measure Up? included this diagram:



This struck me as quite accurate.

I reflected on an incident in class this morning.  My Math 1 students were learning to create a circle of a given area using a compass.  They each had an 8-cm circle on their paper when I asked them to draw a circle with half the area.  Inevitably, many students cut the radius in half and scribed a circle with 1/4 of the original area.

Student [skeptically]: Is this right?
Me: Does it look like it has half the area?
Student: No - so it's wrong?
Me: Can you find the area?
Student: So it's wrong?
Me: It's not wrong if you learn from it.
Student: So it's wrong [begins erasing].

Even at the time, I realized that the student was learning, even though he may not be able to solve the problem yet.  This type of learning falls in the bottom base level of the pyramid above - something identifiable but difficult or impossible to quantify.  (The student's preoccupation with having an answer deemed "right" or "wrong" is another topic altogether).

How have you come across unquantifiable learning?

Pi music controversy

Since I last posted it (since I showed it in third period, come to think of it), the "What Pi Sounds Like" video by Michael Blake has since been made unavailable due to a copyright claim by Lars Erickson.  Erickson had previously composed a symphony based largely on the same idea (using the first 32 digits of pi mapped to the tones of a major scale, etc.). The piece was recorded in Ruse, Bulgaria, late last year.


Do you think the claim is founded?

Tsunamis in the math classroom

Hearing about the earthquake and resulting tsunami in Japan this morning, I reformulated the warm-up activities in my classes. After news stories generate the interest, a few questions got the ball rolling:

• How fast do tsunamis move?


• How does the Richter scale work?


• How much energy does a wave carry?


• How accurate were the predictions for the tsunami's arrival at the West coast?

This Google gadget is helpful for putting earthquakes in context:



 

Software and services I use in teaching

aca capture pro

google earth

google maps

google calendar

wikispaces

wordpress

picasa

 

Pi slices

NCTM's Illuminations has some good pi-related lessons on a range of timelines. I'd like to build up to the Archimedean approximation in my classes some time, but usually I end up doing small activities and demonstrations on Pi Day. Here are a few.

• Buffon's Needle Experiment.  Simulates dropping thousands of needles onto lined paper.  The probability of a needle crossing a line is 2/pi, so we can estimate the value of pi through repeated trials.
  


• Multifactorials. Cool to show in conjunction with pi formulas from Ramanujan and others.
  


• Doomsday Algorithm. Not related to pi but fun to teach on Pi Day.
  


• What Pi sounds like. A cool new musical rendering of digits (there are a few other neat ones like this if you search).
  


• Pi10k. An experiment mapping notes to digits. Like the video about but not as good-sounding.
  


• Pi Rap Battle.  Near and dear to me.
  

 

Misleading area graph

This chart from the Freakonomics blog today gives us a horrific example of using linear proportions in an area (or "bubble") graph. The diameters, rather than the areas, are proportional to the values they represent...

And here's another nice examination of another misleading area model.

Making data exciting

There are two ways to make data exciting:

1. Have the data come from something exciting in the first place (see Pimpact on student learning)


2. Display it in an engaging way.

You can always make an argument for the former, but your students may care as little for your argument as for the data to begin with.  Here's one cool take on the latter:



Here's another, which I find myself showing in class frequently:

7 billion - challenge

Here's what I whipped up this morning, stemming from the ideas in the previous post.



I like the problem because we don't know what model the web site is using, so students can attack the problem in different ways and discuss the relative merits of each approach.  I also told them that I'd pay $20 if they end up predicting correctly (split between all the winners, of course).  I figure there's a good chance no one will.

 

7 Billion

Here's a nice lesson starter: predict when our population hits 7 billion.
This clip gives you the instant hook; follow it up with Worldometers.