More Thoughts on Geometry Proofs

What does a math teacher think about on the plane while she's traveling to see her dad in another state? Teaching, of course. I'm still working out how I want to start teaching proofs in geometry this coming year, and I had 2 extra ideas that I haven't quite fleshed out yet.

One idea came from a news article I saw the other day. It was something to the effect of school officials allowing nurses to hand out condoms to elementary school kids. The original article JUST stated that they're going to start making them available for K-5, and if my memory serves me correctly, that was ALL the article stated. Well, of course, it sounds so ridiculous and my 1st thought is, "crazy! why?", etc. Then I had to step back and think, what could be the real story behind this, and I came up with a few possibilities.

I discussed it with my friends, and sure enough, a few days later the WHOLE story came out. The school district was making condoms available to any student of ANY grade that asked for them, and I'm guessing that in their minds they were mostly thinking about high school kids. Then maybe the newspaper people got the story and JUST reported that the condoms were now available to elementary kids.

Anyway. What does this have to do with geometry? Here's my thinking. One reason to teach proof in geometry is to get kids to think logically and to think of all (groups of) events or statements that can lead to other events/statements. In this way, they won't be "victims" of people trying to sell them one version of a situation. So I thought this story would be a perfect example of just such a situation.

Somehow I'll begin the proof unit discussing why we learn them and just show them the 1st news story. Then I'll have them get with a partner or in a group and think of what events may have lead up to this article or that may have justified such a move by the school board. Then show them the 2nd article. Then maybe I'll find a provocative picture (in the sense of it may look like something bad or good is happening at 1st glance), and then have them think of things that may lead to this picture (or result from the picture scenario). Anyway, like I said, it's not fleshed out yet, but I think this will be a good start.

My 2nd idea has to do with Excel programming. I don't know if I can pull it off, but it seems like you can do some cool stuff with Excel if you learn a bit of VBA programming, and I'd like to create some sort of interactive proof-filler-outer that will be a quiz for them. If it's easy, then I can pop out several and have them online for the kids to practice with. I'm guessing that's a big if.

Anyhow, vacation with dad is over, and now I have a glorious week to do mathy stuff ... before my next vacation trip. WooHoo! Maui here I come (me and my fish-white belly). I'm guessing I'll look like a pale white tourist, but guess what? That's because I AM a tourist. Maybe I'll just have to drink a lot to be okay with it :).

Meeting Potential Students Outside of School

I started taking Lindy Hop Lessons a couple of months ago because I saw some people doing it, and it looked SO fun. The nice thing about it is that you don't have to be a couple to take lessons, and even if you come in as a couple, you rotate partners frequently in class, so it's not an issue.

Since the "leaders" (guys) and the "followers" (girls) are learning the same steps at the same time, and so we all know what step we'll be doing next, it's hard for me as a follower sometimes to "listen" to the pressure of the hand of the leader to determine what to do next, since I know what we're "supposed" to do, so I just do it (did that make ANY sense)??? Anyway, as with everything, there are good leaders and not-yet-perfected leaders (just as I'm a so-so follower). So, I always like when I rotate to a couple of particular guys because they have that leader thing down. They've got the hand pressure and rotation, and so I know to turn or move back or forward or whatever.

Last class, I was with a great leader, and we were learning a new step where I had to "turn outside". He had to lead this by doing a certain thing with his hand, which I had heard from ANOTHER dance class described as, "just like you're drinking a beer", since he sort of starts with his hand held high up and then tilts it in the same direction as if he's drinking a beer. So I turned to my "great leader" guy and felt I had to share this with him, and after the teacher showed the move, I softly said, "ah, just like you're drinking a beer." My partner looked at me and whispered, "I'm 16." Awkward. I amended it to "milk" and then had the scary thought, oh! he could be my son ... or student ...

Spring (or Decade) Cleaning

I'm not the best of housekeepers, and that's an understatement. Sure, the dishes are done and laundry done and trash put away, but there is dusting and vacuuming and clutter cleanup that only seems to get done when company is coming over - which is about twice a year or so. Ew, put that way, I'm gross.

Anyway, since my inclination is to sit around all summer and just read (this or this or this) or nap or do puzzles, I thought I'd give the house a once over this once.

Tons of old books will be donated to the library, usable clothes to charity, and our own personal landfill of electronics to Goodwill. We've just gotten in this complacent state of clutter all over the house, and I guess we don't see it any more. But now that I've cleaned 3 rooms (so far) of excess and unnecessary things we don't even use anymore, it looks so peaceful and inviting instead of this underlying current of unease and discontentedness.

Whew! I should have people over to celebrate.

Adding & Sutracting Integers

I talked with a math teacher friend today about how she teaches adding and subtracting integers to her 7th graders. She mentioned the following type of method, and I decided to put it to pictures. I'm going to try it next year with my high school kids who STILL mix things up. Maybe this will do the trick.

What's My Grade??

Probably like most teachers/schools, our grades are weighted for the grading period. Last year it was 45% homework and 55% tests/quizzes. Students always seem in such wide-eyed wonder as to how various pieces affect their grades. I think they're under the total points worth mentality, and this doesn't always translate into good grades.

Also, during the 1st day of school, I always have them do some math activity to get them thinking while I'm doing all my administrative stuff (roll call, seating chart, ...). So, VOILA, I decided next year to combine my 2 tasks into one. I have a draft of the "calculate your grade" assignment that I will hand out to all my students on the 1st day. Any suggestions on additions or revisions? I kind of hate to leave it at 3 pages since then I have a blank back page. Ideas?

Homework...

I've been thinking more lately about how I "do" homework. I'm still in the camp that wants to assign a completion grade only, so that they don't get penalized for making mistakes while they're learning. I see how many problems they attempt, and how many they grade in class as per my instructions, and I give them a grade accordingly. I still like to provide some kind of answer bank, so that they get immediate feedback and are more apt to persevere through a problem if it's wrong. And yet, I still understand that for some kids, this completion grade leads to laziness and lack of an honest effort and potentially to not grasping topics.

I have a thought rumbling around in my head of something I may want to add to the grade. I want there to be an EXTRA question group on EVERY homework that MUST be answered in order to get full credit (any credit?). Here it is:

1. What is a problem you had most trouble with?

2. What specifically is wrong, examples:
* I don't know how to start
* I don't understand some words
* I get stuck at the point ______
* I'm messing up with my calculations somewhere
* I ______

3. Write out which of the following you did:
* I looked through the book and found extra examples
* I went to our online book to see if there was a tutorial on this problem
* I went on Ms. Cookie's website to see if she had links that may help
* I looked through my notes to see if we did something like this in class
* I called/texted/e-mailed a friend and got help
* I did ______ and it helped
* I did nothing and waited until the next day in class to ask questions

4. Describe what progress you made after you did this, examples of what could happen:
* I didn't do anything, so I made no progress
* I solved the problem
* I understood more about what part confused me
* I made progress in the problem but still did not solve it (describe progress)

Maybe I'll print this out on pretty paper and have them tape it in their composition books as a reference. In this way, it'll cause the kids to reflect nightly (or the period before-ly) on their homework. My lists will hopefully also serve the purpose of prompting them to find other sources to persevere before giving up. And giving a grade for this portion will maybe be the incentive to do the reflection.

Which brings me to my next change next year. I'm a recent CONVERT of composition notebooks. Before I just let the kids buy whatever 3-ring binder or spiral notebook or whatever they wanted. At my not-so-new school they had a tradition of requiring composition notebooks for other classes, and the kids would tape pictures to the front that represented whatever class it was for, and the teacher would put packing tape over the cover to preserve it. Now all the notes are in the book and not easily lost and if there were handouts, the kids taped them to the appropriate dated page. I didn't do it this year, but ... Love it! I believe I'll require them to get the graph papered composition notebook. Then POOF! instant graph paper on demand.

Geometry Proofs

As I still have momentum from the previous year, I thought I'd get some ideas down for next year. I believe I'm teaching 2 levels of geometry (in addition to the PLTW IED course). I know how hard it is for kids to get up to speed with the flow proofs we teach, so I thought I'd scaffold it more this year, and potentially start with the following idea:



After a few (2?) of these, I'd try to incorporate a math story; then take away the "skeleton" at the bottom of the page for another story (but keep the statements), so they had to create the flow. Then start taking away more and more and finally bringing it to just a geometry problem statement. I'll have to flesh it out more, but that's the seed of my idea.

I like the flow proof style instead of the 2-column proof because there is a visual connection between what follows from what. I also like teaching proofs because it's a challenge for the kids and stretches their brains. It's also the first time (only time?) they see what it means to actually prove something instead of just give a convincing argument.

How to make a nice graph for tests and such

Someone requested a tutorial for making a usable graph for your worksheets, so here it is. (okay, the person nicely agreed to a tutorial after I was pushy and suggested one). Here's the 3 page download of my instructions.

And here's what it looks like:

A Surprising Finals Question (Apparently)

I gave the following 2 sets of questions on my algebra 1 final (click on it to enlarge):



For 13 & 14, they were given a line and were to draw a parallel line going through (4,1) then give me the equation in point-slope form. For these 2 questions, people generally did fine.

For 15 & 16, I had the same original line drawn, and they were supposed to draw the perpendicular line through (4,1) and then give the equation in point-slope form. This is the set of problems they had problems with.

I thought I was giving them a gentle teacher nudge by having them draw the picture before they wrote the equation. The original slope is -2/3. Holy Moly. So many students thought NOTHING of the fact that the line they drew was NOT perpendicular looking. They INSISTED the slope of the perpendicular line had to be 2/3, and by Golly, that's the line they drew. 90 degrees? eh!

Note to self, when I teach algebra 1 again, I have to do more of this type of problem before we get to finals. I never did do the drawing thing in conjunction with just the "what's the slope/equation/etc of the perpendicular line to ..." type of question. Apparently, I should have.

On a positive note, I'll be teaching them geometry next year, so guess what we'll be "reviewing".