Yeah...my family is also big on the Wad O'Cash, which can occasionally be very fun, don't misunderstand, but it's not, like, special. Like I thought about what you would like and picked this.

And I've already been collecting gift ideas for weeks even though we haven't even drawn names yet. I already had an idea of what I would get for them if I drew my Dad, my brother and one of my sisters.

I'm kinda starting to feel like the strong family ties that helped me rationalize staying in California were mostly in my head.

I'm in the middle of grading the first part of a big project I've been doing with my class. This project is really cool - it's based on the Towers of Hanoi game, and has them looking for the pattern that determines the minimum number of moves to win the game for any number of rings.

Looking over the projects, there are very few cases where I'm thinking "Wow, this student really has no idea what's going on." Almost all of the students, with the guidance I allowed myself to give them, were able to come up with some good thinking. I just know that with application of problems like this, over the course of the entire year, I could get some serious problem-solving and mathematical communication out of the students. Not to mention, they'd actually like it. The problem? I'd cover less than a third of what I'm supposed to cover in terms of the actual curriculum, and they would generally do terribly on the Algebra State Exam.

Which leads to the question: is it really so important that EVERY student learn to factor ALL factorable quadratic equations? Or is it better to allow those with that bent to learn such things, but provide ALL students with rigorous problem-solving projects that encourage thinking? The answer seems to obviously be the last one. If I didn't have a state test, I honestly think I'd plan my next unit, over Thanksgiving, around the idea of having 4-5 different problem-solving projects that students could choose from, everything from "Use classroom textbooks and the internet to learn how to solve quadratic equations in several different ways. Explain each of the methods in your own words, choosing one example from each of the following options" to "Imagine that Bob has a free-throw percentage of 50% after the third game of the season. At the end of the season, Bob has a free-throw percentage of 90%. Did Bob HAVE to have a free-throw percentage of 60% somewhere in the middle? What about 75%? 80%?"

The problem? Only those that chose the first project would be able to pass the Regents. And therein lies the problem with high-stakes testing around a particular curriculum.

ETA: Sorry for the rant. Feel free to ignore. I know this isn't really the Teacher Thread.

{{{LAGA}}} No honey, not in your head, they are in your heart, where love should come from.

I know this isn't really the Teacher Thread.

It isn't? Aw, heck.

Last week, I used sine and cosine to figure out the angles of a drawing my students were supposed to make, and in the process MAYBE made a couple of them think trigonometry might be a worthwhile class to take! Also, I learned that kids today are learning a very different mnemonic than Soh-cah-toa. Something like "Some old hippie ... totally on acid"?

And I totally feel you. Boy do I feel you. I mean, we all agree that project-based, conceptual learning in depth is much better in the long run than lightning-fast skimming over every topic in the math book every single year, but... ah, the lovely test.

I learned both SOH-CAH-TOA and "Some old hippy caught another hippy tripping on acid" from my ancient Algebra teacher. I think they're both older than the hills.

Soh-cah-toa

What dos this stand for? Sin something cos something tan something?

I think I must have made up my own mnemonic for whatever it is....

SOH=Sine=oposite over hypotenuse CAH=Cosine=adjacent over hypotenuse TOA=Tangent=opposite over adjacent

I think? Geometry has been....16 years ago.

Oh, that makes sense.

I would just picture the triangle in the unit circle in my head. And remember that tan(π/2) was undefined, so cos(π/2) had to be zero. So then sin was the vertical one and cos the horizontal one.