Sunday, February 27, 2011

Confessions of a Scatter-Brained Teacher

Ask my students or anyone who knows me, and they will tell you that I am extremely organized.  Unless you ask someone who has lived with me, like my husband or my college roommate.  And they will tell you that I am as absent-minded as they come.  I lose misplace things constantly.  I forget to complete tasks that I haven't written down.  If I bring my laptop home from school, I have to attach my keys to the laptop bag in order to avoid leaving without it the next morning.  Even then, I could end up at school with an empty laptop bag.  I forget names of people I know.  The list goes on.  It is a really unfortunate problem.

My hyper-organization is actually my attempt to compensate for my lack of proper brain activity. So here are a few things that help me function like a regular person:

A binder (or two) for each prep:  All the materials I have ever used and could possibly need are here, tabbed by unit.  This is an absolute essential, even if you have a regular brain.

Summaries:  At the end of each day, I type a quick summary of that day's lessons.  This information could be as little as a sentence or as much as a paragraph.  I tell what I did that day, and include a short reflection of what went well and what did not.  I summarize at the end of the unit as well, telling myself whether the unit was perfection or a gut remodel.  If you think you don't have enough time to do this yourself, I encourage you to try it for one unit.  It literally takes me about five minutes a day, and having the information available saves me ten times that when I teach the same unit the next year.  I teach three preps in the fall and add a fourth in the spring, so I do not have time to re-invent the wheel.  I'd love to start from scratch each year, but that just isn't feasible.  Having this information at my fingertips helps me isolate the areas to focus on for improvement in the future.

Folders:  Current -- holds everything from the binder for the unit we are currently working on. Next -- holds everything from the binder for the next unit.  That way, I can go ahead and read the summary and do some tweaking as I have time.  File -- at the end of each day, the materials for that day go in here.  Everything from this folder will go back in the binder at the end of the unit.  I have one set of these three folders for each course, and I keep them on my desk for easy access.

And all this is just the beginning . . .

Sunday, February 20, 2011

Planting Seeds

I've been thinking about something cool (yet, a tiny bit disturbing) that happened a while ago in my Calculus class:

My students were solving a problem and encountered a quadratic equation that could not be factored. They freaked a little. (As their algebra 2 teacher, so did I). I gave them a chance to think about it, and someone suggested the quadratic formula. Then someone remembered the song that I had taught them. And, be still my heart, someone else noticed that since a = 1 and b = even number -- it would be super easy to complete the square. And they started discussing how to do that. I was proud.

With that problem completed and about ten minutes left in class, I wrote "ax^2 + bx + c = 0" on the board. I asked them if they thought they could complete the square with that. Working as a class (there are only ten of them), they figured out that they needed to divide by a . . . and et cetera et cetera.

I could not believe their reaction when the quadratic formula showed up. They were blown away! They were actually LAUGHING and saying how awesome that was. At this point, I should have reveled in the beauty of their mathematical discovery. Instead, I started thinking about what a rotten Algebra 2 teacher I must be. This should not have been brand new information.

So, I asked them if they remembered that I had shown them this same thing two years ago in Algebra 2. Someone said "Yeah, but this time it makes sense!". I am not sure if that comment made me feel worse or better. Then I realized that they did remember how to use the quadratic formula and how to complete the square, and when to apply those methods. The only piece that was missing was the connection between the two.

I thought about it for awhile and I decided that connections just take time. The more we learn, the more the pieces start to fit together in different ways. I remember that when I took Calc 1, I really didn't understand what I was doing. I think I was halfway through Calc 2 before the light bulb went on. Then it kind of all made sense to me at once.

I guess I don't need to be so hard on myself if the students don't get 100% of everything the first time they see it. I am planting the seeds that will lead to discoveries and connections down the road. Sometimes this will happen in the future without my knowing. This time, I was lucky enough to be there to watch it happen.

Friday, February 18, 2011

Super Speedy Quiztastic Fun

A couple weeks ago, I did a trial run of Kate Nowak's speed dating. It was a great way to set students up for coaching each other, and students love the social aspect of the activity.

That got me thinking of a faster version, for practice of basic skills at "lightning speed". I am thinking it could work for identifying properties, factoring a quadratic where a = 1, or anything that is not so paper-and-pencil problem solve-y and more flash card-y. I tried it with converting logs to exponential form, and for evaluating logs.

For the fast version, students stand in two rows facing each other. Everybody has a flash card with the answer on the back. Students quiz the person facing them, and provide coaching as needed. We talked about what appropriate coaching (helpful hints) looks like vs. inappropriate coaching (name-calling, answer telling, etc.). Then, students trade cards and one row moves so that everyone has a new partner and a new question.  I ended up rotating every 15-20 seconds. It worked great, students got reinforcement on these concepts, and the whole activity took less than five minutes.

As a warm-up, I used one set of cards (the 1st and 3rd pages front/back from the document below) for converting logs to exponential form. I made them so that if you copy them front-to-back, then the right answer is on the back of the right card. At least, that was the goal. (I wish I had included some with negative exponents). Then we moved on to another set of cards (2nd and 4th pages), where they had to identify what number goes in place of the '?'.

log flash cards

And, I have to mention, the beauty of the moment when I had this on my board as part of that same lesson:  (When will my brand new fantabulous technology cart function properly??)

No one asked me who had too much time on their hands and thought this stuff up.  No one asked me why they have to learn this stuff.  They just got it.  And they came to class the next day asking if today's math would be as easy as yesterday's.

Thanks (AGAIN!) to Kate for suggesting the use of the word "power" before "log".

Monday, February 14, 2011

Thursday, February 10, 2011

Quick and Dirty Review

Let me set the scene: We have had 7 snow days since the beginning of January (I know we're not alone!). I am more than a week behind schedule. Today's plan: Review the unit so that we can take the test tomorrow. Almost four weeks have passed since the first day of the unit, and student memory is sketchy. To make matters worse, we are on short schedule with a 1:00 release for parent/teacher conferences.

I needed to review in the most efficient way possible.  I had a sheet of review problems ready.  I wanted each student to focus on his/her weakness because there wasn't time to do them all in class.

I ended up instructing the students to skim the review problems and start on the hardest problems. I literally told them to find the problem that scares them the most and start with that. Better to do those in class where they could ask questions and save the easier ones to finish at home. And, since I knew those instructions would result in 10 hands raised simultaneously, I also used my planning period to write out the solutions on post-it notes and put them on the board like this:

Students could raise their hand to get help from me. Or, they could discuss a problem with their partner. Or, they could go grab the sticky note for the problem they were working on. I put the number of the problem under each post-it, so that students could tell at a glance which notes were already in use.

The whole day was less thorough and more chaotic than what I would normally plan. But my goal was accomplished: Everyone left the room having completed the problems they viewed as most challenging. All in under 35 minutes.

And they are going to go home tonight and take a second look at every problem they completed with assistance and try it again without assistance. Okay, probably not, but I did tell them to do that.

Monday, February 7, 2011

The Loop for Logs

A few years ago, when I was introducing logs, I drew some arrows like this:

I wanted to show that this base here goes with this exponent over there which goes with this answer over here . . .

Then I noticed one of my students drawing a loop on all of his papers, like this:

He said it helped him remember the order, especially for when one of the terms was a variable.  This has turned out to be a pretty helpful mnemonic device for changing logs to exponential form.

This year, when my calc students (who were also in my algebra 2 class) encountered a log, I just reminded them of the loop and they were like "Oh yeah, the loop."