Saturday, January 1, 2011

Supporting Instruction: Mathematics

The new Supporting Instruction monograph from the Gates Foundation describes the new "formative assessment lessons" being developed to help students learn and teachers teach the new Common Core mathematics standards for grades 7 through 10.  Those "FALs" are being designed by the Shell Centre in England and the University of California at Berkeley to support new and intensive attention to mathematical practice.

Each FAL starts with a rich math task and organizes a lesson that draws students into "a productive struggle with the mathematics essential for college readiness."
1) Students are given an easily administered initial assessment task. This provides teachers with a qualitative sense of their students’ grasp of the targeted mathematics.
2) Students are immersed in the mathematics of the initial assessment task through a set of collaborative activities. This part is designed as a guided inquiry. Students work in small groups, engage in discussion, take responsibility for their own learning, and learn from each other, often by examining each other’s work. Teachers provide feedback to move their students’ learning forward.
3) Students are engaged in a whole-class discussion. This is designed to pull the lesson together. Students get to strengthen their understanding while teachers get to deepen their insights into their students’ learning. It provides another opportunity to structure discussion, provide feedback, and allow students to learn from each other.
4) Students return to improve their response to the initial assessment. This gives students a look at what they’ve learned as well as more feedback, while providing teachers perspective on the effectiveness of their teaching.
Three samples of the FALs are available here.

The third sample, called "Solving Pentagons," is one I've tried: I was part of a June "class" of Kentucky educators and administrators who tried that task with guidance from one of the designers for this initiative.  I started with certainty that I'd be unable to do the work, found some starting points when I worked on my own, gained confidence as I puzzled with a team, and realized that when I went back to the task alone, I could indeed work through the challenge.

In writing about Rick Stiggins' call for balanced assessment, I've described the approach as working to create "a virtuous spiral in which students master one step, gain confidence, reach for another step, and cycle upward with growing knowledge, skill, and certainty that they can succeed."  My early taste of these mathematics FALs felt exactly like moving onto that virtuous spiral.  If they work as well for students still in school as the pentagon example did for me, they will make a difference in students' confidence and skill in using the math they will need for higher education and future careers.

(Have I mentioned that I'm excited?)

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