Green Pen is the New High Five

Backstory #1:  I am trying a new bell work procedure this year. In short, I walk around the room with a handful of green fork pens. When someone finishes the bell work correctly, they get a green star and a green pen. Now they are qualified to coach and star papers for other students, and so on, until everyone is done.

Backstory #2:  I had an interesting conversation with a colleague recently. She mentioned that our German exchange student is used to finishing his work early. In Germany, he was always expected to help students who were still working. He observed that we don't do that much in our school. I rarely have students with nothing to do, but it made me think about how to more intentionally utilize students who "get it" to assist those who are struggling.

Fast forward to yesterday . . . My students were working on word problems.

I told students to do just one problem, and raise their hand to check it with me. In my mind, I was thinking that I wanted to make sure everyone was on the right track before moving on. But I had nothing else for them to do when they finished. Some were struggling away, and others were finished, twiddling thumbs, and otherwise disengaging.

In my head I was reminding myself . . . Always, ALWAYS, have something for next.

Then, light bulb! It occurs to me that my little green pen bell work procedure would be perfect for more than just bell work.

I picked up my supply of green fork pens and walked around the room answering questions as usual. When someone finished I gave them a green star and a green pen and the instructions -- "Now, look for someone (near you) who could use your help". They already knew what to do, since we've been doing this routine for bell work. Some of them amazed me with their ability to help someone else. I was helping one student when I saw another hand go up, so I directed someone with a green pen to head over there. I overheard the green pen student helping the other one find the mistake. I couldn't believe I was just going to have them sit there doing nothing for a few minutes while I ran around like a crazy person trying to answer all these questions and check all these papers.

I have tried to create a classroom culture of students coaching other students. I have my desks arranged in partners, and I talk about how everyone in the room is a teacher. Students are encouraged to ask their partner a question before me. Still, I have some students who are reluctant to request help from the person sitting next to them and other students who prefer not to be bothered.

I realized yesterday that I need to give students specific opportunities to coach someone else, and specific instructions on how to do so. What if completing a problem and checking in with your neighbor became the norm? I also discovered that my more advanced students are so much happier and more willing to help someone else AFTER they have had an opportunity to complete the problem on their own.

As an extra bonus, I also learned that the green pen has sort of become a status symbol of accomplishment in my classroom. Handing a student a green pen is a pat on the back, a passing of the baton, a rite of passage in the form of a writing utensil.

I hope to keep an eye out for students who never get a green pen in their hands and try to make it happen. I saw a struggling student light up yesterday when I handed him a green pen. "I've never gotten a green pen", he said. Sometimes it is the smallest things . . .

Factoring Woes

My students are doing okay with factoring overall, but it has been a struggle.

This is the graphic organizer I ended up using this year:

Students find it helpful, which is a good thing. I like/hate it.

I want them to be able to factor without it.

Here are some things I am thinking of changing for next year:

1.  Fewer methods:  Reduce the number of factoring strategies, so students have less to sort through. I am thinking I could teach trinomials with ax^2 first, and then apply that method to trinomials where a=1. Students should be able to adapt to the simpler situation, and they'll have one less method to remember.

2.  Figure out how to connect the type of polynomial with the name of the method and how that method is completed:  I am currently expecting students to see a trinomial, then identify that it has a leading coefficient, then recognize that they should use the "airplane" method, and then remember how to do the airplane method. So complicated! It is kind of amazing that any of them can do this at all.

One of my students pointed out that the arrows I am drawing for the "airplane" method resemble a trident. What if I renamed the "airplane" method the "trident" method? That seems like a better connection between the original expression and what you do with it. (Trinomial = Trident method?).

3.  School-wide consistency:  There are only three math teachers in our school. Why haven't we done this already? No idea. We definitely need to get together and agree on an approach to factoring so that students aren't seeing a completely new process from year to year.

4.  Find a hook:  I haven't figured out how to motivate factoring beyond, "You are going to need to use this all kinds of ways later this year and next year".

All things to keep in mind for next time . . .

Unless . . . Is there a magic factoring wand that I don't know about?

I Heart My Seating Chart

Due to a snow day right before break, I am spending the first day back watching my students take final exams. It stinks for them that they have to take exams after a two-week break, but I am enjoying a day of collecting my thoughts before our new semester begins tomorrow.

So what am I doing? I am making up seating charts. And I am sitting here thinking about how much I love my seating charts. (I know, I am such a nerd!)

I am sure that there is a more sophisticated way to do this . . . but I just can't stop myself from using sticky notes and multiple blank printouts of my seating layout.

You could use sticky flags, but I like to make my own by cutting off the bottom half of a small stack of sticky notes and then cutting them into fourths.

I use pink and blue so that I can see at a glance if I have a somewhat even gender distribution.

Best of all, it is super easy to manipulate your arrangement until you get it just right.

And it all fits in a nice folder.

Ok, time to start grading those final exams.  :(

Top 10 for 2011

After a year of blogging, I have one regret:  The length of my url. It is embarrassing. Seriously, what was I thinking? I thought it had to match the name of my blog. (I would make that shorter too, if I had a do-over). Oh well . . .

To celebrate the end of a year, I thought I would do a collection of most-read posts from 2011 (And one from 2010):

Scavenger Hunt:  Students partner up and pick a starting point. Then they search for the answer which leads to another problem. Great way to review.

Stations Review and Practice:  Students get a card with a couple of problems to work out. After a set time limit, they pass the card and receive another. New card has solutions to the previous one, and a new set of problems. Repeat. Also a great way to review.

Cake Day in Calculus:  Use cake to practice volumes of rotation.

The Loop for Logs:  A handy trick for switching log form to exponential.

8 weeks, 8 pencils . . . :  The end to your pencil-less, pen-less, and eraser-less student woes.

Crazy for Conic Cards (and a follow-up):  Cindy Johnson's conic cards changed my life. :)

A Fun Way to Start Class:  The truth, I want to do this soooo bad. But I'm not sure I can pull it off.

Logarithm Love:  Oh, if every unit went this well . . .

Color Coding: For Sketching Piecewise:  This trick helped my students sketch piecewise functions with ease. And they get to color.

Super Speedy Quiztastic Fun:  A fun way to practice short mental calculations.

Airplane Method for Factoring

I mentioned the "airplane" method for factoring in a recent post. Someone asked me what that was, so I thought I'd share.

I have seen a lot of methods for factoring a quadratic with a leading coefficient. Out of the ones I've tried, this is my favorite. The analogy to an airplane is a bit of a stretch, but students seem to remember it pretty well. So I'll take it.

I should also mention that, before I show this to students, I always spend some time letting them work on these by trial and error. I figure a process like this is worthless if they don't actually understand what they are doing. Once I feel like students understand the concept but they are still struggling to get every problem to work, I show them this. We treat it like a shortcut, and boy do they appreciate it!

Here is an example:

First, my students know they will need two binomials, so I start with two sets of parenthesis. Then I put the leading coefficient in each parenthesis. Hopefully, the students have a problem with this. We talk about why it is a problem, and I promise them that we will get rid of the extra 2 before we're all done.

Then, multiply a and c. (See the airplane wings? Use your imagination.)

Look for two numbers with product ac and sum b. (Propeller?  I know this is really a stretch.)

Put those numbers in the parenthesis.

Divide the extra 2. (The landing? Maybe.) It is pretty cheesy, but when students are having trouble I can say something like "you forgot the landing", and they know what I mean.

Done.

For something like this, you may need to divide both binomials. I point out how dividing by 3 and by 2 is the same as dividing by 6. We just choose the division that will keep integers.

Happy factoring!

Figuring Out Factoring

I have been thinking a lot about factoring lately. My algebra 2 students really struggle with it, and we have only factored quadratics (no sum/difference of cubes or grouping yet). I am worried because our first unit after winter break is rational expressions/equations. This unit is challenging when you CAN factor well, and almost impossible if you can't.

I am sure it will be necessary to take a few days to work on factoring before we start rationals. I need to review quadratics, teach cubes and grouping, and put them all together. I am working on how to structure that.

I have been doing some reading and searching for ideas. It seems that almost every method out there requires students to memorize some sort of process. (Except for this, and I am not sure my students are ready for that). As far as algorithms go, I am happy with what I've been using.

There are two issues that I want to address:

1. Helping students make a connection between what they SEE (trinomial, difference of squares, four terms, cubes, etc.) and what they DO (write two binomials using your preferred method, grouping, use a formula, or whatever).

2. Helping students get through problems where more than one method is required. (Like factoring out a GCF and then factoring the trinomial, or using grouping and then recognizing that one of the binomials is a difference of squares).

Here is a flow-chart I sketched out this morning:

I am picturing this on the white board, with an answer box next to it. You could 'drop' a polynomial into the top box and it comes out factored. If there was a GCF, you could put it in the answer box and then examine the remaining part and possibly drop it into another box. You could then take the pieces that come out of the second box and either add them to the answer box or drop them into another box. This all seems a little elementary, but I want it to be very obvious and very clear . . .

I am still refining this and hope to use it for the beginning of second semester. I will write about the final product. In the mean time, suggestions welcome. :)

Fraction Exponents. Easy.

Have you ever found yourself teaching a certain thing a certain way for years, and then one day you think about changing your explanation just a teeny tiny bit? And the new way makes infinite more sense to students, and the thing that used to be impossibly hard is now easy? And then you wonder what took you so long to find that more easy/obvious way of explaining something?

That happened to me today with fractions as exponents.

I won't bother to mention how I used to teach it. It was bad. Very bad.

Today, I started by showing them this, and they all shouted several people went "x squared!".

Then I asked them HOW they knew it was x squared. Somebody pointed out that three x-squareds multiply to equal x^6. Someone else said that you divide 6 by 3.

I made a big deal about writing x^(6/3) before writing the answer as x squared. And we did several more of these including some square roots, so they could see that you divide by two.

Then I showed them this, and gave some time to think about it and write down what they thought the answer should be.

Almost every single student wrote down x^(2/3)! And there were angels singing.

Then we worked on going backwards, which was no biggie at all.  Given x^(1/2), students could easily rewrite as square root of x and so on.

And then I didn't know what to do, because it used to take me a full class period to teach that. And some students would still be sitting there going, "Huh?". But today they just got it in, like, five minutes.

I realize that there is nothing earth-shattering about this method. The thing is, I've taught it this way before. Only I didn't lead with this part. I ended with this part. All I did today was change the order.

Oh, I love these moments of finding the tiniest little change that makes a huge difference.