Saturday, February 23, 2019

CAST Reference Sheet: The Good, the Meh, the Bad, and the Wha?

With the NGSS-based California Science Test (CAST) set for its maiden administration this spring, a reference sheet has been prepared. Students have access to the reference sheet while they take the exam. Here's the reference sheet.

CAST High School Reference Sheet

Reference sheet development can awaken passions that physics instructors didn't know they harbored. So let's go through it. (It might be helpful to print the sheet or have it open on another screen. Blood pressure medication? A preemptive dose might save a life here.)

FORCES AND ENERGY
Good: Newton's Second Law, the weight equation, universal gravitation, Coulomb's law, gravitational potential energy, kinetic energy, work-energy theorem. All good.

Meh: Using w for weight. A little bit non-standard, but the judges will allow it.

MOTION
Good: Ft = mv, the use of ∆v in the equation for acceleration: the ∆ is critical here.

Meh: The use of ∆t rather than t. We never create problems involving isolated clock readings (t); intervals (∆t) are always given. The ∆ in front of the x in the equation for speed? I can take it or leave it.

Meh: The use of J for momentum. That's a rare one. I've seen it, but it is not common. I prefer ∆p, and I don't think I'm alone.

Bad: s for speed. I am reminded of a line from Star Trek: "A Vulcan would not cry out so." In this case, I will turn that phrase to "A physics teacher would never, ever use s to denote speed. Ever." I hope I'm not being ambiguous here. The very use of s for speed makes me wonder if anyone associated with physics instruction was involved in developing this reference sheet. A math teacher might make such a miscue, but not a physics teacher.

Wha?: Using the Greek letter, rho (ρ), for momentum. Why? Lowercase ρ is a symbol used to represent density in high school or college courses. It is also used to represent resistivity. Nobody ever uses ρ to represent momentum. Anywhere, ever! Momentum is represented with the letter p. Extra effort is required to insert the letter ρ. I am dumbfounded.

KEPLER'S LAWS
These are here for the benefit of items addressing Earth Science PE, HS-ESS1-4. I'll let them "Meh" or "Wha?" the notion that e = f/d is among Kepler's Laws.

WAVES
Good: The wave equation and the Planck-Einstein relation. I would have put them in that order, but okay.

Wha?: The reference sheet is set in a sans serif font. In high school, we use lowercase f for frequency. Someone at CAASPP seems to have found the special character, ƒ, which bears a striking resemblance to an italicized, lowercase f. If a pianist sees two of those in a row (ƒƒ), they'll hit the keys hard. The symbol, itself, is called "F with hook," or "florin symbol" and is used to denote the Dutch guilder, for example. This has been Sheldon Cooper's "Fun with Fonts" with your host, Sheldon Cooper.

EXPERIMENTAL DESIGN
Mostly good. It it's me, I'd use a cross (×) rather than a bullet (•) to indicate multiplication. The bullet really isn't a multiplication symbol. The dot (·) is, but the cross is more appropriate here.

At the risk of belaboring a point made in the post critiquing the practice items, I will point out to our gentle readers that no reference to index of refraction appears on the reference sheet. No n = c/v and (thankfully) no Snell's law. Recall that one of the practice items expected students to be familiar with the meaning of index of refraction.

CONSTANTS
If someone at CAASPP sees this, please explore the use of the dot symbol ·. On my Mac, I hold down  the shift and option keys while typing a 9. It's more professional than the big bullet • that you get with option+8. And drop the spaces in unit configurations.

I see N·m as better than N • m for newton-meters.

In all, the reference sheet is more good than meh, bad, or wha? But I wouldn't be keen to print it up and have students use it throughout the year. Replace the speed s with a v and the momentum rho with a p, and I can live with the remaining quirks.