Megan Golding

Recently spotted on the Duarte Blog: Cheating by Charting. An excerpt from Spear’s Practical Charting Techniques. This stuff is genius.

Methinks this could be used in math class. “Hey kids, we’re going to play Corporate Spin today. You’ll hide a disappointing stat in a graph so the public doesn’t realize how much we’re polluting/raising prices/whatever.” (My, I didn’t realize I was feeling so cynical today…)

What time of day was this photo of the Washington Monument taken?

While writing this warm-up question, I came across the Sun or Moon Altitude/Azimuth Table page. Supply a location and a date and this page will tell you the angle of sun in the sky for any time of day. (Interesting side note: This photo of the Washington Monument could not have been taken between November and February because the sun never gets that high in the sky.)

I can already imagine all sorts of interesting extension problems based on this picture but for now I will keep it simple: my students need to practice the inverse trig functions.

(Props to my colleague Annie Sun for the idea for this game)

The goal is to get as close to 21 + 21i without going over.

Georgia Performance Standard MM2N1(b,c)

The math department at the high school where I teach is big into stations. If the concept is new to you, here’s the lowdown: On a station day, several learning centers are set up around the room and students circulate among them. Montgomery County schools in Maryland has published details.

From what I’ve seen, stations are particularly good at providing opportunities for reteaching and practice, in addition to acceleration.

The key here is that stations are useful as a differentiation tool. According to the MCPS folks, you should use assessment data to break students into groups. Not all students will visit all stations and time at the teacher station will differ based on the data.

I’ve applied stations a few times this year and have learned a few things:

• how incredibly important it is to model the concept to the class
• you must give explicit instructions in the stations where students work independently
• I like using assessment data to divide students
• give students their station assignments during warmup
• students need a way to check their work in the stations (I’ve posted solutions on the back of index cards taped to the wall)
• you need an assessment tool or record of students’ work in the stations — they need to turn something in. I’m thinking a culminating question at each station that has no solution posted makes a lot of sense.

Your time spent in planning stations is huge. Not only must you plan approximately three activities but you must also provide differentiation for each group. This could mean upwards of six times the work in advance. This time is so worth it! Do I even need to say it beats the heck out of lecture or drill-and-kill practice?

Long the premise of every lesson on probability, coin tosses are taking a beating (thanks Boing! Boing! for the share). Some interesting research (Diaconis, Holmes, and Montgomery) uncovered these biases:

1. If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was launched. (If it starts out as heads, there’s a 51% chance it will end as heads).
2. If the coin is spun, rather than tossed, it can have a much-larger-than-50% chance of ending with the heavier side down. Spun coins can exhibit “huge bias” (some spun coins will fall tails-up 80% of the time).
3. If the coin is tossed and allowed to clatter to the floor, this probably adds randomness.
4. If the coin is tossed and allowed to clatter to the floor where it spins, as will sometimes happen, the above spinning bias probably comes into play.
5. A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity.
6. The same initial coin-flipping conditions produce the same coin flip result. That is, there’s a certain amount of determinism to the coin flip.
7. A more robust coin toss (more revolutions) decreases the bias.

Always the hacker, I suggest following the link for strategies to winning a coin toss.

Is there a place for this research in my math classes?

Filed under: spherical cows-and-Other-Oversimplifications.