Time dilation is mutual in special relativity, which means that the travelling twin does see the sedentary twin's clock running slow:

http://www.einstein-online.info/dict.../time-dilation
"Time dilation can be mutual: When two inertial observers speed past each other, each will find that the other's clocks go slower."

In other words, as judged from the travelling twin's system, the sedentary twin is younger - his clock is slower. However if a teacher wants to both prove and calculate the slowness of the sedentary twin's clock, he/she will have to consider a scenario in which that clock commutes between and is checked against two clocks belonging to the travelling twin's system:

http://www.amazon.com/Relativity-Its.../dp/0486406768
Relativity and Its Roots, Banesh Hoffmann, p. 105: "In one case your clock is checked against two of mine, while in the other case my clock is checked against two of yours, and this permits us each to find without contradiction that the other's clocks go more slowly than his own."

Here lies the secret of the twin paradox: Einsteiniana's teachers simply do not want to prove and calculate the slowness of the sedentary twin's clock, and accordingly do not consider scenarios in which that clock commutes between and is checked against two clocks belonging to the travelling twin's system. Such scenarios would be taught by antirelativists but they are successfully marginalized:

http://www.informaworld.com/smpp/con...ent=a909857880
Peter Hayes "The Ideology of Relativity: The Case of the Clock Paradox" : Social Epistemology, Volume 23, Issue 1 January 2009, pages 57-78: "The gatekeepers of professional physics in the universities and research institutes are disinclined to support or employ anyone who raises problems over the elementary inconsistencies of relativity. A winnowing out process has made it very difficult for critics of Einstein to achieve or maintain professional status. Relativists are then able to use the argument of authority to discredit these critics. Were relativists to admit that Einstein may have made a series of elementary logical errors, they would be faced with the embarrassing question of why this had not been noticed earlier. Under these circumstances the marginalisation of antirelativists, unjustified on scientific grounds, is eminently justifiable on grounds of realpolitik. Supporters of relativity theory have protected both the theory and their own reputations by shutting their opponents out of professional discourse."

Pentcho Valev