If the answer is 'yes' then from 1st October 2018 you can travel at child fares - half the adult rate! So Goring to Wallingford is only £4 return (£2 each way child single)!
But the 09.15 Goring to Wallingford service, and the 13.15 Wallingford to Goring services can be a bit busy so this offer is not available on those services.
Any valid railcard can be used to get this offer, including Network Cards which anyone can buy - see the national rail website for details - it could save you a good deal on rail fares too.
Before 1st October ask for 'Pay One Way' and you'll be charged the single fare for a return journey.