why does the mass of an electron increase as it approaches the speed of light?

Question: why does the mass of an electron increase as it approaches the speed of light?
- Keywords:
  electron,
  speed of light,
  subatomic
Asked by moyin to Jim on 15 Mar 2013.
- Jim O Doherty answered on 15 Mar 2013:
  
  It doesn’t – Einstein proved that the mass never changes and the mass is converted into energy. And its the same amount of energy each time.

moyin commented on 17 Mar 2013:

my physics teacher said that the mass of a particle increases as it approaches the speed of light-she didn’t tell us why though, that’s why you can ‘t use F=ma to calculate it

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Question: why does the mass of an electron increase as it approaches the speed of light?