Friday, November 30, 2012

My Centroids Lesson Keeps Stalling Out Right Here

and I don't know how to fix it.

The kids and I literally stared at each other for ten minutes over this. I wanted to take them all outside and drown them in the pool. (I know it's not their fault, though, obviously.)


I don't have any other good way to come at this, though. Other options for asking relevant questions seem too ambiguous for this age group. Applications of triangle centroid are thin on the ground, or at least I haven't thought of any yet.

Ideas?

Thursday, November 8, 2012

Benefit from My Hours of Frustration

HERE.

There are some questions below to go with it that don't suck. No further comment. I am so sick of this lesson.


Open the Geogebra File Triangle Inequalities.ggb. (Follow the link from Edmodo, or go directly to http://www.geogebratube.org/student/m21418) You can use the sliders to change the lengths of two of the sides. You can also change the position of two of the segment endpoints. Side AB will always measure 10. Use the sliders to generate four different sets of side lengths: two that can form a triangle (you will know for sure if it turns purple,) and two that can not form a triangle.
AB
BC
AC
Can a triangle be formed?
10



10



10



10





1 Using the given lengths of AB and BC below, find the shortest possible integer length of AC, and the longest possible length of BC.


AB
BC
Shortest possible AC
Longest possible AC


10
3




10
5




10
1




10
14

(conjecture)


x
y




Answer this question without using Geogebra. I have three pieces of wood. The pieces measure 4 cm, 9 cm, and 11 cm. My friend has three other pieces that measure 5 inches, 8 inches, and 2 inches. Will we each be able to create a triangle? Why or why not?

Monday, November 5, 2012

Tablets

So, one of my Geometry sections has 1:1 tablets. We have a set of twenty we are piloting this year, and I believe the intention is to go school-wide next year. I got chosen for this because, you know, I have a reputation.

I had become accustomed to the capabilities and limitations of the classroom tech available at old school. We regularly used a set of Dell notebooks on a mobile cart, and the TI-Nspire Navigator system. So I was at expert ninja level with those tools. I could use them inside and out, I had smooth ways of getting kids proficient with them pretty quickly, I was well-versed in what I could expect kids to figure out vs what I had to demonstrate carefully and repeatedly, and I could use them to actually you know make instruction better than it would be without them.

Starting with new-to-me hardware (Acer Iconia Tablets) and software (Windows 8) has been a frustrating exercise in back-to-novice levels of crippling ignorance. It's back to the first days with the Nspires, where it's impossible to anticipate where the tech will say "no," and no lesson plan survives first contact with the students. The simplest thing, "Take a picture of one of the proofs you just wrote and email it to me." turns into twenty minutes of troubleshooting cameras that don't work, and picture files we can't find in order to attach them, and how to login to your school email account. Meanwhile, my favorite smartass has already sent me an email with the subject GREETINGS FROM DEH OTER SIDE O DEH ROOM, and has spent the intervening twenty minutes taking selfies and is starting to get disruptive because I haven't given her something else to do.

But, shoot, I guess we just all have more things to learn here, che? I have been very consciously modeling what I like to think are productive behaviors, for example Cheerful Curiosity in the face of unexpected technology hiccups and also Not Throwing Any Tablets Out the Window nor Any Children Either for That Matter.

Having one section with tablets and two without, though, are some nice built-in experimental and control groups, don't you think? We're starting triangle centers this week, in conjunction with which I normally teach compass and straight-edge constructions. So, I'm thinking the tablet section will learn the constructions Geogebra-only, and the other two sections will learn them compass-ruler-pencil-paper-only, and we will see what we get. It begs the question if I can possibly fairly assess them all the same way, and if not, can I really draw any conclusions from this little mini-experiment. And I know it's not a real experiment, it's just like preliminary poking at experimentation. But whatever. I make my own fun.