A colleague pointed out the following article to me: Put Understanding First, by Grant Wiggins and Jay McTighe. A sampling:
Unfortunately, the common methods of teaching and testing in high schools focus on acquisition at the expense of meaning and transfer. As a result, when confronted with unfamiliar questions or problems (even selected-response problems on standardized tests), many students flounder. Consider a high school algebra question that was included on state tests in New York and Massachusetts:
To get from his high school to his home, Jamal travels 5.0 miles east and then 4.0 miles north. When Sheila goes to her home from the same high school, she travels 8.0 miles east and 2.0 miles south. What is the measure of the shortest distance, to the nearest tenth of a mile, between Jamal’s home and Sheila’s home? (Students were provided with a grid they could use to plot the answer.)
Fewer than 40 percent of New York 10th graders correctly answered this item, despite the fact that the requisite knowledge is “covered” in every Algebra I class in North America. Test results such as these reveal not a failure of coverage but a failure of transfer.
Out-of-context learning of skills is arguably one of the greatest weaknesses of the secondary curriculum—the natural outgrowth of marching through the textbook instead of teaching with meaning and transfer in mind. Schools too often teach and test mathematics, writing, and world language skills in isolation rather than in the context of authentic demands requiring thoughtful application. If we don’t give students sufficient ongoing opportunities to puzzle over genuine problems, make meaning of their learning, and apply content in various contexts, then long-term retention and effective performance are unlikely, and high schools will have failed to achieve their purpose.
Mean Green Math 