Thursday, March 24, 2011

Function Aerobics

I love how the Carnegie text has students working with linear functions from the very first chapter (even though students don't know that is what they are called at that point). Linear functions play a very large role in the Algebra 1 curriculum. Students work with linear equations on the cognitive tutor and in the text a lot! I've found, however, that students begin to think that everything they graph will be a line.


Last year when I started the chapter on quadratics many of my students thought they had done something wrong because their graph did not look like a line. So this year I decided to change things up a bit. Before starting the official work on linear functions we looked at all of the basic parent functions and a few of their transformations. So when students get to the quadratic chapters they know that if they see x^2 in an equation they should expect to see a parabola and when they see x in an equation they should expect a line and so on.


I had each student graph the parent function for six of the families of functions. After everyone successfully finished the parent graphs we did some "function aerobics". I ask (force) the whole class to stand and we make the parent graphs with our arms (and sometimes the rest of our body if needed). The principal at my school found out that the other Algebra 1 teacher and myself were doing this and even designed and ordered us function family t-shirts. We can now have "Function Fridays" were all 9th graders wear their shirts and we practice our functions aerobics. While my students whined at first about getting up and moving around, they all did extremely well on a quiz we had where they had to identify the parent equation and family give the basic graph. Our Algebra 2 teachers are thrilled that our students will know these basic functions when they get to their classes.


However, we didn't stop there. After finishing the basic graph each group of four students was assigned to a family of functions and became experts with the basic transformations. They made posters of the parent function and several transformations which now hang on my walls. An example of one of their poster is show below:

Wednesday, March 23, 2011

Go for GOLD!

The feature that students like most about Cognitive Tutor is the skillometer. What is a skillometer, you ask? As the word skill-o-meter implies, it is a meter that keeps track of your math skills in real time as you work through the problems. Now that’s what you call immediate feedback!

Look at the upper right corner of the web page. The skillometer is a row of green bars. Each bar represents a math skill that you are trying to master. The green bar increases for every question you answer correctly. On the down side, it also decreases for every question you answer incorrectly. Hint: the fewer mistakes you make, the less number of problems you have to work out! Slow down and don’t rush.

Eventually, the green bar should hit gold. This means that you have a 95% chance of correctly answering a similar question targeting that skill. You should see how excited these teenagers get when they see gold! It’s a great motivation to push the students to continue when sometimes they would rather quit. Once all the bars turn gold, you get promoted to the next unit.

If you click on the darker green upside down triangle, a list of the skills will appear. The more skills that are listed, that more dynamic the bars are. If there is only one or two skills, then students will have to work at least a dozen problems before the bar will even budge.

“Mrs. Park! Cognitive Tutor must be broken.”

“Why?”

“I’ve worked 100 problems and it won’t move me on!”

The English teacher will be happy to know that our students are great at coming up with hyperboles.

Friday, March 18, 2011

It’s Not Rocket Science

Deciding how you will grade your students on Cognitive Tutor is not an easy task. Do you base it on the time clocked in? Or how many problems solved? How about the number of errors they make? Above all you want to be consistent and fair. If I’m not, my students will definitely let me know about it.

Giving everyone a 100 for effort sort of makes the students loose respect for the software program, minimizing its effectiveness to engage students and push them to excel without frustrating and alienating them. (In my opinion.) But maybe effort grades work for you and your students. Every teacher has to decide for her/himself.

Cognitive Tutor Teacher’s Toolkit offers a wide array of reports that you can view and print out. My grading system for Cognitive Tutor is based on one or two of these reports. The only way to really familiarize yourself with the specifics of each report is to get your hands dirty, jump right in and browse through the different reports.

I believe Kasey and/or Brandy came up with some kind of formula putting into account the number of problems completed, the amount of time spent on the program, and the number of errors made. To be totally honest, I don’t have the time, or have made the time, to do this complicated, convoluted algorithm in order to assign a CT grade. Sure I can probably come up with some kind of excel program to make my life easier, but like I mentioned earlier, it’s not a priority at the moment.

My students receive weekly daily grades for Cognitive Tutor. At the beginning of this year, I gave students the goal of completing so many units or sections per week, however long it took them. As the fall semester went along, I noticed that a student one week would complete a unit in 30 minutes while this same student took five hours the next week. I felt guilty for having my diligent students work so hard to meet my haphazard goal. Over three hours on CT per week seemed a little obsessive for even me.

So then the weekly goal was revised to say that students needed to put in a minimum of one and half hours per week. This worked well for most of my students. However, I had a handful of students that beat the system by putting in their required time but only completed a fourth of the six weeks curriculum. I added an additional requirement that students had to complete the curriculum by the end of the six weeks. This particular goal counted as four daily grades.

This system works for me. I might have to change it next year, depending on the students I have. What do you do?

Tuesday, March 15, 2011

Differentiating via the Cognitive Tutor

Last week I left the building to get Subway for lunch. During this time I had a chance meeting with a parent who sends their student to a local elementary school. He noticed my name badge and started asking me about the school where I teach. One of the questions he asked me was how I deal with some students understanding a topic while others still need more practice. I think this is something that every teacher struggles with (how do we differentiate our instruction). I think this is a great question for a parent to ask! Of course everyone wants to know how you can teach their child on their level!

Luckily for me I use the Cognitive Tutor! I told this concerned parent (who's child could be coming to me for Algebra 1 next year) about the Carnegie program. I explained how the Cognitive Tutor helps me to get students to master skills before moving on new ones. It gives my students that need it extra time with a topic while allowing other students to move forward at their own pace (I'm not holding them back waiting for others to catch up). I also told him about how in my class students work in groups. They help each other so that everyone is successful.

The parent was really excited about the idea of his child receiving individualized attention. His daughter (who happened to be with him) told me that she likes math and couldn't wait to be able to work on the computer! Although the Cognitive Tutor is not the only way I differentiate my instruction it is definitely the way I do it most often. Yet another reason to love the Cognitive Tutor software :)

Monday, March 14, 2011

Creating a Custom Curriculum for CT

When you first create classes in Cognitive Tutor and input your students’ names, you can assign them one of Carnegie Learning’s curriculums. In my case, I have access to Bridge to Algebra and Algebra I. Bridge to Algebra has 53 units with 1-7 sections per unit while Algebra I has 47 units with 1-7 sections per unit. The goal is to complete all the units in one curriculum within a school year’s time. With its artificial intelligence-like capabilities, CT keeps track of one’s mastery of specific concepts. Basically, the less errors that you make, the quicker you proceed through the curriculum.

One of the best features of Cognitive Tutor is that you are allowed to create custom curriculums. Let’s say that you district’s scope and sequence differs from that of Carnegie Learning. No problem! I create a custom curriculum per six weeks to mirror what my students are learning in class. Keep in mind you can only chunk together units. You cannot separate the sections under each unit.

If my students finish a Six Weeks curriculum before the six weeks is over, of course, I am going to want them to continue to work on Cognitive Tutor and not do anything for 2-3 weeks. So I will advance them to the next six weeks or assign them to CL’s curriculum.

At the beginning of the following school year, CL will ask you if you want to keep your custom curriculums or get rid of them and start over. Totally up to you. It’s nice to have some input. Creating a custom curriculum is not difficult at all. Give it a try.

I’m enjoying a week “off,” taking it easy and spending time with my family. Happy Spring Break to everyone in this part of Texas!

Tuesday, March 8, 2011

Pi Day

One of my favorite holidays is next week! What holiday is it you ask? No, It's not St. Partrick's Day. Monday, 3/14, is Pi day in my classroom (Pi is approximately 3.14 hence 3/14 is the day to celebrate everything Pi related!). When I was in high school my teachers always had fun activities for us on this day and I have continued the celebration with my own students (other teachers in my building have also started celebrating it too!)

So how does one celebrate Pi Day? While there are many options (just google Pi Day to find many suggestions), I start by reviewing parts of a circle. Then students get circular objects and measure there diameter and circumference to discover where Pi comes from. (Similar to a Carnegie lesson from the Geometry book). We make a scatter plot with the diameter on the x-axis and circumference on the y-axis and draw a line of best fit. Next to make it a little more Algebra related, we find the slope of our line of best fit. It usually ends up being close to 3 point something and leads to a discussion of error in measurement. I use a NCTM applet to show that if we could be 100% accurate we would always get the same number if we divide the circumference by the diameter and that we call that number Pi. I even wear I shirt that says "Math easy as Pi"(it has the symbol not the word).

Of course no Pi day celebration would be complete without eating Pi(e)! I bring in some pies and offer extra credit to the students who bring in a pie to share with the class. Two years ago I had a lot of pies left over and we donated them to a local shelter. It's a fun way to excite my students about math and give them a lesson they won't soon forget.

Happy Pi Day!