http://tinyurl.com/394yl6

And, yes, I know that poster. I used to have it in my classroom but it makes some jobs look so difficult that I have to wonder if it unintentionally scares people away from those professions.

Student: “Mr. Elias? When will we ever use the law of sines?”

Me: “The law of sines? Well, Gertrude, I’m glad you asked! If I consult my handy ‘When-Will-I-Ever-Use-This’ chart, look for ‘Law of Sines’ on the horizontal axis and follow down the column, I can tell you that you’ll use it in your job as a mechanical engineer, astronaut, or restaurant owner!”

Desired student response by the poster-making company: “Wow – I can’t believe all those jobs require me to apply the law of sines! Can we do another example so I really understand the concept?”

More likely student response: “Good. Then I’m never going to be any of THOSE things…”

The bit about increasing depth along the same topics while enduring greater time and content restraints — that used to terrify me. You’ve got a first year teacher handed a stack of Algebra standards, expected to pull through all of them by April + keep the peace + make it Quadrant D meaningful.

Given how most textbooks are built ground-up from the standards nowadays, your solution that (grossly paraphrased) “we can cut this superfluous section there to free up time for more depth over here,” feels wobbly to me. Maybe I haven’t compared the situation side-by-side closely enough but the course outline is pretty lean.

From my perspective, the solution is both a beauty and a beast, so difficult and so simple at the same time.

I have to manage my class well in order to free up hours on the month. Then I put my pen to lesson planner and bleed. (Apologies to that other metaphor.) It’s kind of agonizing but you only have to be brilliant once per concept and then you’ve got it for a career.

Case in point, Scott: Linears were absolutely whomping me. I spent two weeks essentially going in circles between abstract formulizing and concrete data sets. It was miserable.

So I sat and just agonized for a little while and 18 hours of hard work later, I was teaching linears like never before, a beautiful lesson which compressed several topics into one, hitting Quadrant D a few days faster than usual.

My hat’s off to teachers who accomplish the same by merely shuffling the order of instruction or who can somehow bypass the agony. Unfortunately for me, hard work’s the only solution I’ve got right now to accomplish the goals of your post.