Since I went into a set of lessons with a half-baked plan and half-baked assessment and differentiation strategy, I should not be surprised that my results were very much mixed. 🙂

The objective of the lesson was to be able to explain that addition and subtraction move your location on a number line, and that they move in opposite directions (regardless of where you start!) – secondary objectives included being able to graph objects in four quadrants, and being able to visualize a number line where one is not explicitly drawn. To this end, I designed a task in which students would animate a little circle and make it move forward, backward, and diagonally.

During the first class, I delivered a huge chunk of instructions, gave kids a handout, told them to copy the code and then modify it. Almost no one knew what to do with the code and how to make it do anything meaningful. I felt frustrated that I wasted a class period, but it was important learning for me. Here is how I modified things during the next period and the things I wish I had remembered during first period.

1) CHUNK the information. As a whole class, I had the students type in a simple program all together, and we discussed what it did, line by line. We created a still shape, discussed how to position it in a place you wanted, and then added the code to make it move.

2) Check for understanding at every step. During a whole-class lesson, checking for understanding is often done by asking random students questions using my bucket-o-name-chips. You need to be sensitive about publicly embarrassing students, however. I also wander about the room and confer one-on-one. These fifteen-second conversations are really valuable for checking for understanding. I ask questions that get at the meat of the learning target: “What would be the coordinates here? Why is the shape moving to the left? How would you change it to move to the right?”

3) Assess the kids’ level of background knowledge and give them an appropriate task. I wish I had given the kids a pre-assessment before starting the lesson. I would have seen who understood variables and who didn’t, and who understood four-quadrant graphing and who didn’t.

4) Have a well-defined task and have more tasks than you think you need. Sometimes this isn’t a horrible way to differentiate… you ask students to accomplish A, B, and C, and oh, if you finish all of those and you’re up for a challenge, try D and E.

5) Keep the objective in mind – the understanding that addition and subtraction mean opposite motions on the extended number line. For an assessment, I ended up creating a little self-grading rubric for students to use at the end of the lesson, so they could judge their own level of understanding and reflect on it. It’s not a perfect assessment tool, but it helps them be a little metacognitive and keeps their focus on what they are learning from this imperfect process. I asked them to judge their own level of understanding on graphing and addition/subtraction, on a scale of 1-4.

I got a variety of responses. These students definitely seemed confident, and it seems I was reading them correctly.

It was interesting to see the rubrics of students who seemed to understand what they were doing, but may have been copying off the screen next to them. I appreciated their honesty.

Clearly some students were completely lost, but at least they knew they were lost. One power of the self-assessment is that the kids are more willing to accept help after they have filled it out.

This is the trajectory of so many math topics. Everyone ends up in wildly different places by the end, and the challenge before you is how to move the fast learners along on their trajectory while also getting the confused students out of the muck. I’m right there.

I decided to do a little cooperative learning next. We learned about subtraction of negative numbers in class, and what subtraction looks like on a number line. I planned a little programming exploration in groups, where students modified and analyzed a program together as they explored the mystery of subtraction. 🙂 It took about 20 minutes. The purpose was to solidify the meaning of subtraction on a number line, while also un-sticking the kids who were having difficulty programming. It was a little animation of a circle on a screen, nothing exciting, but demanding that the students analyze and explain, as a group, why the circle moved as it did when you added positive numbers to its coordinates, added negative numbers, subtracted positive numbers, and subtracted negative numbers.

As a treat, when the task was done and we had summarized, I showed them how you could make a circle “walk the plank” for Talk Like a Pirate Day. http://www.khanacademy.org/cs/walk-the-plank/1043148997 Super easy but a great hook for learning “if” statements.

Tomorrow we’ll do an individual programming task again, this time working on the “if” statement and starting to bring in multiplication of rational numbers.

Can I put in one more plug for how much I love the Khan Academy programming interface? I will, at some point, write a whole blog entry on why it’s amazing and what could even make it more so. It makes computer-based learning so accessible for me and for the kids.

Onward! Hoping for good assessment results on rational number operations as a result!!