How does it fit?

At the beginning of the semester, I wrote a post about using the history of the LEGO company as a cautionary tale for innovation in education reform. The idea came from a Diane Rhem interview with the author of Brick by Brick. But there was another idea presented in book that also caught my attention - clutch power.

When a child snaps two bricks together, they stick with a satisfying click. And they stay stuck until the child uncouples them with a gratifying tug. And therein lies the LEGO brick's magic. Because bricks resists coming apart, kids could build from the bottom up, making their creations as simple or complicated as they wanted. … it is clutch power that makes LEGO such an endlessly expandable toy, one that lets kids build whatever they imagine. (page 20)

It was the last sentence that got me thinking. How might I design learning experiences that use clutch power - allowing learners to "build whatever they imagine?" In particular, I had one of our math courses for preservice teachers in mind. It explores a variety of mathematical topics that students often see as disconnected: algebra, geometry, measurement, and data.  Was there a way to treat concepts in that course as building blocks that learners could use across the domains to build new understandings instead of simply following the instructions I provide?

I am still working on that question, but I did start experimenting with simple problems that allow learners to add their own ideas while demonstrating their content competency. The following is one problem (modified) from the final I just gave. I would be interested in your feedback.

Plot the points (2, 2) and (2, 4) on the coordinate plane. Pick two other points that could combine with these first two to be used as the vertices of a trapezoid. Use this context to develop items that would align with the following targets (be sure to justify your alignment using the indicators):

• Graph points on the coordinate plane to solve real-world and mathematical problems (5GA1, 5GA2)
• Classify two-dimensional figures into categories based on their properties (5GB3, 5GB4)
• Solve real-world and mathematical problems involving area, surface area, and volume (6GA1-A4)
• Draw, construct, and describe geometrical figures and describe the relationships between them (7GA1, 7GA2, 7GA3)
• Solve real-life and mathematical problems involving angle measure, area, surface area, & volume (7GB4, 7GB5, 7GB6)

Because this was a new assessment for most of my students, this time around I offered some example items to pick from:

1. Define the term "trapezoid" and then use that definition to identify what other names apply to your shape.
2. Find the area and perimeter of your shape.
3. Extend each side (creating 16 angles) and find all the angle measures.
4. Write your own question for this context.

I still expected them to align the item with the targets, justify their alignment, and come up with a correct response.