It follows from Einstein's 1905 postulates that time SPEEDS UP for the traveler (SYMMETRIC time dilation): as the traveler checks stationary clocks against spaceship's clocks, he finds that stationary clocks are slow and spaceship's clocks are FAST, which means that he sees himself aging FASTER than stationary people.

Some (very few) Einsteinians obey logic and teach the correct deduction:

David Morin, Introduction to Classical Mechanics With Problems and Solutions, Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [...] For the entire outward and return parts of the trip, B does observe A's clock running slow..." http://www.people.fas.harvard.edu/~djmorin/chap11.pdf

"The situation is that a man sets off in a rocket travelling at high speed away from Earth, whilst his twin brother stays on Earth. [...] ...the twin in the spaceship considers himself to be the stationary twin, and therefore as he looks back towards Earth he sees his brother ageing more slowly than himself." http://topquark.hubpages.com/hub/Twin-Paradox

High priests in the Einstein cult almost universally teach that time SLOWS DOWN for the traveler (ASYMMETRIC time dilation), which is non sequitur of course:

Brian Greene: "If you're moving relative to somebody else, time for you slows down." https://m.youtube.com/watch?v=QnmnLmwBmfE

Neil deGrasse Tyson: "...Einstein's special theory of relativity, which gives the precise prescription for how time would slow down for you if you are set into motion." http://abcnews.go.com/Entertainment/...ry?id=32191481

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