The New York Times reports that the Bill & Melinda Gates Foundation and Facebook plans to hold two “hackathons” this month, bringing together software developers and educators to create new Facebook applications for teaching and learning. The first HackEd 2.0 event will take place at Facebook’s Menlo Park headquarters in California on Tuesday, when teams will build apps for “college-going, social learning, and out-of-school study,” a Facebook representative said by e-mail. Judges will award $5,000 for the best apps. There will also be several all-female teams from the Hackbright Academy, a 10-week programming training course for women. On April 24, another hackathon will take place at Facebook’s London office, where the top education app development teams will be given prizes of £1,000 — or $1,500 — £3,000 and £5,000…