I started by asking them questions like,

• What makes a body “proportional”? Why aren’t babies proportional? Why aren’t Barbies proportional?
• What is the standard of being proportional? What am I comparing with?
• Why is the Vitruvian Man so famous? Why does DaVinci have a “code”? =P

By the time they were done measuring themselves and finding all these different ratios, I told them that over the years, people have discovered one ratio that keeps coming up in nature, even in the human body. This ratio can also be found in the Fibonacci sequence.

The Fibonacci sequence is a nice place to have them discover the Golden Ratio and compare their measurements to it because it doesn’t depend on the accuracy of their measurements.

If there was time, we then went on to measuring the face and talking about how the ideal “beautiful” face is said to be  in the Golden Ratio, though this varies by greater amounts. Then we talked a bit about whether a standard can be set at all or not.

What I wish I did afterwards, however, is that I really wish I had them sketch out a Golden Body by setting up ratios equal to the Golden Ratio (proportions). That would have led quite nicely into my next lesson on similar polygons… which I will post possibly tomorrow…

For now, what I’ve got of the Golden Ratio is in the Box widget.

Anyways, a few quotes from the article to comment on:

Teacher effects are also much stronger than class-size effects. You’d have to cut the average class almost in half to get the same boost that you’d get if you switched from an average teacher to a teacher in the eighty-fifth percentile.

I have to agree. EXCEPT, teaching such huge classes year in and year out is exhausting and starts to create a bad teacher from a good one.

Teaching should be open to anyone with a pulse and a college degree—and teachers should be judged after they have started their jobs, not before. That means that the profession needs to start the equivalent of Ed Deutschlander’s training camp. It needs an apprenticeship system that allows candidates to be rigorously evaluated. Kane and Staiger have calculated that, given the enormous differences between the top and the bottom of the profession, you’d probably have to try out four candidates to find one good teacher. That means tenure can’t be routinely awarded, the way it is now. Currently, the salary structure of the teaching profession is highly rigid, and that would also have to change in a world where we want to rate teachers on their actual performance. An apprentice should get apprentice wages. But if we find eighty-fifth-percentile teachers who can teach a year and a half’s material in one year, we’re going to have to pay them a lot—both because we want them to stay and because the only way to get people to try out for what will suddenly be a high-risk profession is to offer those who survive the winnowing a healthy reward.

Teacher’s training camp?! That would be kind of awesome. But I already know I wouldn’t have made it back then because teaching brought out in me qualities I never really knew I had back when I had first started. The love for the students makes a person change, seek better, reach higher. The teacher I was my first year of teaching is so starkly different from who I am today. I know I’m not the best teacher out there, but I love my profession and I’m pretty good at what I do. I would hate to have not been given this amazing opportunity b/c of such a camp. Plus, how do you simulate a real classroom? Have you heard any teacher stories of late?!

I think Gladwell says it best in the end:

But there is nothing like being an N.F.L. quarterback except being an N.F.L. quarterback. A prediction, in a field where prediction is not possible, is no more than a prejudice.

I love that last line. In a field where prediction is not possible, there can be way too much prejudice.

Don’t judge me. I’m a teacher.  ;)

* UPDATE: I’ve added a Properties Summary Sheet to the Box widget that I should have given them after the properties checklist as reference. If I were to re-do this activity, I would give them all 3 handouts, but only have them do the parallelograms checklist–> summary sheet on parallelograms –> practice problems on Day 1. Day 2 would be trapezoids and kites –> summary sheet –> practice problems.

I just want to also point out here that the bullets match up for pg 1, the parallelograms page. For example, the 3 bullets under rhombus that are completely blank match in shape to the bullets in parallelograms. They just have to re-copy it in.

1. Actually attempt the work and show all work.
2. Correct their work in class
3. Learn from their mistakes

So how do you check and keep them accountable? Committing to one method always run dry after awhile and both students and myself slack off. I finally found a way that I’m happy with to get them to do this. A homework wheel!

When students walk in everyday, I put up the answers on the board and they all get green pens to make corrections, start the work, and/or work with their neighbors. I just walk around making sure no one is cheating and using pencil. After about 10 minutes of neighbor work or me doing the problems on the board, I spin the wheeeeel!!

• 2 problem check means I collect their work to give them credit for 2 problems that required work.
• Green pen logic  means I collect their work and I give them credit for their corrections done in green pen in the beginning of class. (They have to explain what their mistake was also.)
• Homework quiz, of course, is when I choose two exact problems from their homework and they get tested on it instead of me collecting the hw that night.

The binder check section is actually the initial reason why I even came up w/ this idea. I hate doing binder checks and I always forget to do them, though I believe in the value of teaching my kids organization. This way, I at least will check their binder about 2 out of 15 days (the fraction of that slice).

The FREE slice is just for fun. Though honestly speaking, I think it’s mostly for me. =)

{The wheel itself is just an Ikea Lazy Susan I bought a while ago for a trig activity I never did. I drilled holes onto the bottom and attached it to my wall. This is also only used for my Geometry class so far since it’s the only class with hw that I’m teaching right now.}

That second hindrance makes sense to me now in hindsight, but it really did take me this long to figure out that maybe I can give them a checklist alongside the quadrilaterals that I have started to create for them.

And it worked beautifully! I had them work in partners and work through together. They discussed, they asked questions (all the right ones), and they made their “discoveries.”

Anyways, below is a quick snapshot of what it looked like.

• I did half of parallelograms with them because we had already covered these sections. They did the second half . We then went over all of it and I made the connection to what we had already learned before break.
• I have block periods. I gave them the whole packet to do in one period, which I shouldn’t have. I should have given them all the parallelograms first, then a bunch of practice problems. The next day should have been the   trapezoids and kites and a bunch of practice problems.
• Materials: rulers and protractors. One quadrilaterals packet per pair, but a copy of the checklist per person.

(My Word doc has a bunch of extra lines that need to be whited out. I’m not going to spend time doing it right now. If anyone does and want to send it back, that would be beautiful!)

Now you just have to type in the equation into the Google box and it’ll graph it for you, for FREE! It’s really basic, but kinda nice for that very reason. You can even type in multiple equations at once. =)

Rhombus

I used to hate introducing new vocabulary words.

I still swear by my Verbal Vocab for constantly reviewing vocab words throughout the school year, but oftentimes in Geometry, the lecture on the introduction of over a dozen new vocab words in one class can get so dull, dry, and just boring. Kids mostly tune me out by word three anyways.

But Geometry is all about definitions. Not just definitions, but properties that arise once these things are defined. It’s so nit-picky, but it can’t be ignored. I’ve tried having them create a portfolio, but the thing took me forever to grade and the students were not huge fans of them either.

So I had a scavenger hunt this week instead for classifying quadrilaterals. I normally do this at the end of the school year on a field trip and it becomes a monster project, but I find so much value in it that I keep trying to incorporate parts of that project into the school year.

Trapezoid

It’s two in part. The first part is a book scavenger hunt w/ fill in the blanks, a picture, and a non-example (which they are used to doing).

The second part is a photo scavenger hunt. I release them on to the campus in groups of 3 and have them search for the vocab words. They must email me the picture with their team name and an explanation of why that picture works.

It was fun. They had fun. Grading was easy (file after each period, search their name for all their emails) . I hung colored hall passes around their necks. I made them check in w/ me every 15 minutes. Book hunt took 15 minutes. Photo hunt took about 50 minutes.

Assignment is attached in Box widget as Intro to Quads Scavenger Hunt.

I saw this falling asleep last night and I had to share as soon as I had the chance. It’s a TED talk by Daniel Pink on motivation.

Basically, providing incentives to complete a certain task, like rewards and punishments, actually only get better results if the task is rote, mechanical, and very focused. 

If ever you need creativity or critical thinking, on the other hand, incentives actually produce significantly poorer results than not providing any incentive at all.

Interesting, isn’t it?! I’m a huge stickler for creating accountability in all my activities, ideally by motivation, but often by incentives. Even if part of me understood some of the ideas here, it really makes  motivation just that much more tangible to reproduce.

For example, activities that might be productive to use incentives for are times table drills, identifying a series of triangles as SSS, SAS, ASA, AAS, or HL, practicing solving equations, etc. I’d say most other activities should stray from using incentives.

So how do we build intrinsic motivation? That IS the big question, isn’t it. Well according to Dan Pink, there’s 3 main elements:

1. autonomy
2. mastery
3. purpose

Perhaps what we do most days is helping students build the first two. Purpose is the big challenge though. Helping students understand WHY these concepts are interesting and worthwhile. I think I’m going to try to focus on that once again. Maybe I’ll try an open-ended project in Geo.

Anyways, on a side-note, when people ask me what made the biggest difference for my Calculus Camp and those scores, it was definitely the motivation factor that camp gave them to pass. They had the know-how, the capability, just like all the classes before them, but why would they sweat over passing an AP Calc exam, when all of them only paid $10 for it and about half of them were thinking about community college anyways? Taking them up to camp changed that, but more importantly, it changed that for them together as a class. Those who never had competitive, college/univ. bound friends were not only mixed in w/ those who were, but they were all becoming friends.

If you teach/taught in a low-performing school (not that my LA school is low-performing anymore!! =)), one of things you would’ve quickly realized is that “they just don’t care.” Even the brilliant ones seem to take on this “C is still passing” attitude (not all, but most). What else can you expect when no one else, neither family or friends, expect any more of them?

Well, up at camp, we got away together as a class,  did team builders, played ridiculous games, got delirious at night together, ate Fear Factor-worthy things for punishment, and endured 15 hours of Calculus. When they got back, they were suddenly so bonded that they weren’t just trying to pass the test alone, but w/ their entire class. It was AMAZING. They suddenly wanted to pass this test because that was what we had spent the entire weekend focused on and even the weeks prior in getting it funded.

I only wish I had done all that on purpose. I had only taken them up b/c I remember having gone to Calc Camp when I was a student and finding it helpful. I also remember it being a bit boring so I added some flair. =) I guess I just need to figure out how to add motivational flair to math on a daily basis now.

http://www.math.harvard.edu/~knill/mathmovies/index.html

I use the Shrek clip as the introduction to inverses and contrapositives in Geometry.(This one was also on YouTube.) The PowerPoint I used is in the Box widget.

They have been combined into 2 PDFs in the Box widget, now moved to the left of the page.

These drills are to be used for the Timed Folders and all of them were created to be finished under 2 minutes. Time yourself to see how if you might want to vary the pass times.

Most of these (after the regular times tables) are new this year so PLEASE let me know what you think! =)