September 23, 2014

Central Park

I'm still learning about my Fundamentals of Algebra 1 students. Some tasks I offer (operations on integers) they speed through with impressive skill. Other tasks (distributing with variables) stop them cold. I thought that Central Park would be a fun (re)introduction to variables but I was mistaken. It was a serious struggle. (Note: I think this is a great activity that I was ill prepared to support my students in achieving.)

We started off great: "We get to use laptops today?" "No, that cart has iPads." "IIIPPPPAAADDSS!!"

The estimation went pretty well. Students were a bit competitive but also helping each other out. One student got frustrated on the third one and I asked what would make it easier, then showed him how he could skip that step, no big deal.

Then there was a question (what measurements would be useful). There were many answers that didn't make sense, but some students asked for clarification. No one stressed about that part.

Next came some numbers. I was walking around the room rather than watching what happened at the teacher page so I didn't realize that most kids were guessing and checking. This is a valid strategy, they were using reasoning to increase or decrease the width. However, it meant that they were running straight toward a wall (writing an expression with a variable) rather than moving up a ramp that would get them over the wall (writing expressions with numbers). Kids' frustration levels built as they were guessing and checking successively more difficult problems and then they hit a breaking point when they couldn't figure out how to use variables (plural!) to represent all the situations. A good teacher would have re-gathered the entire class when most of them hit that point to have some conversation. I wasn't a very good teacher since I was focusing on being a good tutor (lame excuse- allergy season meant my ability to talk at whole class volume was limited). A couple students had the essentials and needed a small push. Many students were able to talk through a number situation with me and then (with a lot of prompting) generalize. Several students had already shut down and wouldn't talk to me or my co-teacher or anyone else.

After class I realized: students weren't writing anything down. I had to ask students to open their notebooks so I could draw pictures and write in numbers and show how multiple calculations looked the same. Apparently students expect that if they are using iPads they are only using the iPads - no paper, pencil or calculator required. I talked to some people on twitter that night (thanks team) and came up with a follow up plan.

We did spaces with lines between (partitions with no width). I walked around the room to check that every student had drawn a picture and labeled it. We did several with different numbers of spaces (clearly showing our work for each one - lots of repetition), then wrote an expression, then substituted into that expression several times. Spaces mastered. Next we did the same process for two spaces with varying size partitions. The only complaint I have about the original activity is how hard it is to see the partitions being divided by p+1. I wish it was easy to see something like half of each wall in each space. The two spaces situation is great because the partition is clearly split down the middle so you can either subtract then divide or divide both and then subtract (distribution of division over subtraction!). Finally we wrote an expression for the partition size and width of the lot varying. I learned that my students were able to complete the original process but they needed much more support than the original activity. Central Park is great and I would recommend using it. But if you teach kids who have struggled in math and/or aren't confident using variables, have some scaffolds in your back pocket ready to provide. And for goodness sake make them draw pictures and record their work!


  1. Thank you for sharing your challenges and your fantastic reflection on them. It's so helpful to see what other teachers (particularly ones that I really admire) respond to things not going as they hoped them to.

    Before I started in the classroom, my background was all in tutoring. I actually still own a fairly large tutoring company--at this point, most of the instruction is done by others and I have employees who take care of most of the administration. I also have a tendency to want to tutor rather than bring the group altogether. I want to learn more strategies for making full class discussions useful for more of the students. I know they're helpful for a handful, but having done so much tutoring, I think a lot about the students who get lost in most discussions. And knowing that I was often bored in math class myself, I want to ensure that the conversations are engaging for students who often get the content quickly. Oh, the joyful challenges of classroom teaching!

    1. It's also a question of timing for me. I like this activity because everyone can work at their own pace. When is the right time to pull the class together? When the first kid gets stuck? When half the class is there? When every student has reached the calculations section? It's a tricky question without a universal answer!