This is something I picked up from a (brilliant) college teacher, Dr. Velez, in my abstract algebra class. One day for the third time in a row some student spotted an error in what he was writing, so he started a “typo tally” to keep count.

I do a modified form of the same thing with my students (my algebra 2 and pre-calculus — a bit fiddly to work into my lower level classes). These are the rules:

1. Every class period the typo tally resets; typos earlier in the week do not carry over.
2. If a student can spot a typo before me, the tally goes up. The typo must be mathematical in nature and not typographical, a slightly messy equals sign won’t cut it. If I spot the error and correct it myself there’s no score, even thought the students may yell “typo” while said typo is being erased.
3. If they catch three typos in one period, I bring them candy.

Last school year I got stuck 3 times, so it hasn’t been too bad on the wallet. It has the advantages that
a.) it keeps some students engaged with the simple act of writing something on the board
b.) it helps reduce situations where I find myself halfway through a problem before I realized I didn’t carry a 1 on the third step
c.) it broadcasts just how fallible I am even as an experienced teacher, and as students they shouldn’t feel bad for themselves that they make errors

(Addendum: Rules can be modified as you see fit. A teacher at my school heard about my method and kept a weekly count in his Algebra 1 class but without candy; the students still enjoyed attempting to make the counter go up as much as possible.)

So my summer program is officially done, and while I’m going on vacation next week with my wife (it’s been two years, we desparately need one) I should be able to get back to writing with more regularity.

I have a new class next year called AIMS Math. AIMS is the standardized test in Arizona that students must pass to graduate. The class is for seniors who have not passed the AIMS yet.

So, the skills vary wildly across the board, including some special education. There’s no real set curriculum since teachers are still experimenting, so I get to plan this out on my own.

The only directive: get students to pass the test and graduate.

How we can reach that is up to me. We’ll need to review some things not normally thought of by algebra teachers — i.e. the times tables — and simultaneously we need to cover (pretty much) all of algebra and geometry in an entire semester.

I figure it will help to write my thoughts out, so I’m going to write them out here where I hope to simultaneously pick the brains of all you smart people out there.

(To those out there who think I might be going through hell in a handbasket working on a standardized test class, well, it isn’t so bad. It’s just reviewing math, really. I have no plans to grind test questions à la The Wire.)

Link here

I admit (even though this is supposedly “much-anticipated“) I’m not sure what advantages this reference has over existing ones, like Mathworld.

Fun times to be had by all!

Commentary from the Guardian on a thinktank’s article on the decline of mathematics in the UK:

Unfortunately, in any case, even this aspect of their report may be marred by simple errors in applied arithmetic. The thinktank is worried that the loss of A-level mathematicians has resulted in lost earnings for the economy. If the number of maths candidates had remained constant, they say, there would have been an additional 430,700 over the period 1989 to 2007. In the adjacent table they say 430,031, but heck, that’s the least of our worries.

They reason thus: “Each of these students would have earned an additional £3,080 a year due to the market premium on A-level mathematics, equating to £136,000 over their lifetime. The total gain to the economy over the period would have been over £9bn.”

Now we’ll put aside the fact that the BBC said “a maths A-level puts on average an extra £10,000 a year on a salary [not £3,080], says Reform” because I can’t get £9bn for that period with those numbers (I get £12bn assuming a linear decline, although they may have access to more detailed data), and in any case Reform makes assumptions which are not, at face value, tenable, including the notion that the extra earn would have survived a widening group of people with maths A level.

Arguably this is a case of confused economics principles; more likely it is simply the thinktank taking the worst case scenario for a more sensationalized report. Certainly, there are shortages; certainly, people with mathematics skills can earn more; however, any exposition on such should hold itself to high mathematical standards.

So, I survived the first week of my summer program.

It’s called an Algebra Academy and it is for incoming 9th graders. (They still act like 8th graders.) It’s a mixture of mathematics, science, and engineering, culminating in a contest with several other schools using bottle rockets.

Today’s lesson I didn’t write myself, but it included a part that kicked everything up a notch, so I wanted to share.

Note that as run this lesson was more an engineering/design lesson, fairly light on the math, but it would be easy to ratchet up the geometry.

Building a Tree House

Materials needed: Popsicle sticks (about 1000 for a large class), toothpicks (300-400 ought to do), tissue paper (substitute other colored paper type as needed), string, glue sticks (lots), scissors. (Also found out post-lesson sandpaper would have been handy.)

So, we told the students they were building a tree house with these restrictions: it needed a ladder to get up the tree, some sort of roof for shelter from weather, and given a 1 foot = 1 inch scale it had to hold at least 3 people.

They designed their tree house first using isometric paper, and they had to work out beforehand how much supplies they needed.

Then they “bought” their supplies. We kept expense accounts. We had

Popsicle sticks (aka large boards): $3 each
Toothpicks (aka small boards): 50 cents each
String (aka rope): 25 cents an inch
Colored paper (aka gallons of paint): $6 each
Glue sticks (aka nails): free

After the initial buying stage — here’s where the twist came in — all the prices doubled. We warned the students beforehand prices would go up after they got back from their break, but they all still boggled at the new price board.

This made the whole affair like a strategy game. First off it forced the students to plan well, and a couple even tried to use their math skills to help. Then students had a choice: do I buy what might be too much and risk wasted materials and money, or do I risk hitting the exact right amount when a shortfall could mean a much higher expense?

After it was all over, we judged. Cost came into play, but also design, stability, and practical ability to be used as a tree house.

Unfortunately I won’t be able to get any pictures. For some reason the students were keen on wrecking their creations after the whole thing was done. One tree house was intensely stable so they did an impromptu experiment of “how many textbooks can we stack on top before it collapses?” It lasted for 25 before it went down.

Apologies on being quiet lately, I’ve been busy prepping a summer program. To compensate, I bring you

Jearl’s Totally Subjective Biaxial Entertainingness Scatterplot

I imagine it might be difficult/entertaining to get students to understand the difference between “awesome” and “good”.

At some point in teaching logarithms students tend to hit a point of despair, at which point their usual line is “why would we need this for anything?”

One of my most vocal complainers didn’t care about math at all and wanted to be a photographer.

Results of Google book search on photography and logarithms

Each field has their own set of books that contain just the mathematics people in that career need to know. Such books are excellent sources of realistic problems, and if you happen to have the physical book at hand, you can make a student’s eyes go wide.

I ended up creating a lesson around f-stop sizes and the “zone” system of Ansel Adams. (Unfortunately, the student in question was absent that day!)

Fold It: Solve Puzzles for Science

And no, it isn’t researchers studying physiology in response to playing Tetris. This is a human-aided version of the protein folding research (previously being done by computers); it’s possible humans can do things better.

This left me wondering if there was some mathematical equivalent to this — solving open problems via posing them on a mass-intelligence page as puzzles. The best I could think of was an interactive version of this problem at Math Magic. It is possible some other recreational mathematics might work if modified, like a version of this card game Timothy Gowers recently wrote about.

I have discovered that word problems often contain nice activities if you let the students actually try them. Take this common one:

A tree that is 5 meters tall casts a shadow 7 meters long. At the same time of day, a building casts a shadow 20 meteres long. How tall is the building?

So, it’s certainly possible to just assign this on paper and have the students number crunch away. But why not have the students actually try it? Take them outside, get them to measure their height and the height of their shadow, then measure the shadows of some tall things that they’d normally have to climb. Voila, instant applied problem, and far more interesting to the students than the word problem.

Or take the ultimate stereotype in word problems:

Two towns A and B are five miles away. A train starts in town A heading towards town B going at 40 miles an hour. A train starts in town B heading towards town A going at 50 miles per hour. At what point do the trains meet?

This needs a little bit of a rewrite, but:

Let’s take these two Matchbox cars, wind them up, put them on opposite sides of this track, and run them into each other. At what point will they collide?

You see this is the exact same problem (especially if you make sure your cars have different top speeds) but it suggests an actual fun activity, rather than a classic Far Side cartoon about a math phobic’s nightmare.

Not on my final, fortunately, but it came up in a discussion. Without seeing the question, see if you can answer it.

Find the volume of ……
A. 5 cm³
B. 10 cm³
C. 12 cm³
D. 12 cm²

(sigh)