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When does it work?

I have been sharing my experience teaching a group of fifth-graders how to problem-solve around fraction computation and using it as an opportunity to demonstrate the Teaching-Learning Cycle in action. Previously, I wrote about how I planned for a problem-solving lesson and then described my instruction during the following lesson. In this post, I want to discuss how I used assessment and evaluation to monitor the learners' progress and inform future planning and instruction.

We were using the clock model as a context for adding fractions and I wanted to gather data about whether or not the learners could determine when this model was an effective approach. I used an existing set of textbook items and asked the fifth-graders to: "Look at the expressions shown below - circle the ones that you think you could use the clock model to solve and place an 'X' through those you could not."
Once the kids had completed this task, I asked them to solve one of the problems they had circled. As they worked, I gathered data on whether or not they were able to determine when the clock model could work.

In analyzing my observations, I noticed what the fifth-graders could do and what they were trying to do. First, they all recognized that fractions involving ninths and sevenths were poor candidates for the clock model. Those who chose to solve #2, #9, and #10 were also fluent in applying prior experiences with the time context. Some learners thought eighths could work (circling #4) and others struggled to see that fifths could work ('X'ing out #3, #5, and #8). These last two areas of approximation gave me some ideas about what to focus on next.

The last assessment I gave was intended to gather data about how the fifth-graders might apply the idea of context to a problem that could not be easily solved using the clock model. As a ticket out the door, I asked, "Now what could you do to solve a problem you put an 'X' through?" Based on my evaluation of these assessments, I was prepared to plan for future lessons.

What would you do next?
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