According to the 2011 Skills Gap Survey by the Manufacturing Institute, about 600,000 manufacturing jobs are unfilled nationally because employers can't find qualified workers. To help produce a new generation of welders, pipe-fitters, electricians, carpenters, machinists and other skilled tradesmen, high schools should introduce students to the pleasure and pride they can take in making and building things in shop class.

American employers are so yearning to motivate young people to work in manufacturing and the skilled trades that many are willing to pay to train and recruit future laborers. CEO Karen Wright of Ariel Corp. in Mount Vernon, Ohio, recently announced that the manufacturer of gas compressors is donating $1 million to the Knox County Career Center to update the center's computer-integrated manufacturing equipment, so students can train on the same machines used in Ariel's operations.

Examples of activities that fall into the “simple but hard” quadrant: Building a trench with a spoon (a military punishment that involves many small, repetitive tasks, akin to doing 100 two-digit addition problems on a typical worksheet, as Droujkova points out), or memorizing multiplication tables as individual facts rather than patterns.

Far better, she says, to start by creating rich and social mathematical experiences that are complex (allowing them to be taken in many different directions) yet easy (making them conducive to immediate play). Activities that fall into this quadrant: building a house with LEGO blocks, doing origami or snowflake cut-outs, or using a pretend “function box” that transforms objects (and can also be used in combination with a second machine to compose functions, or backwards to invert a function, and so on).

On March 12, a day after the tsunami, Mr. Yoshida ignored an order from Tepco headquarters to stop pumping seawater into a reactor to try and cool it because of concerns that ocean water would corrode the equipment.

Tepco initially said it would penalize Mr. Yoshida even though Sakae Muto, then a vice president at the utility, said it was a technically appropriate decision. Mr. Yoshida received no more than a verbal reprimand after then-Prime Minister Naoto Kan defended the plant chief, the Yomiuri newspaper reported.

“I bow in respect for his leadership and decision-making,” Kan said Tuesday in a message posted on his Twitter account.