Hi Jenny,
ASHR mean advance student honour roll. When a kid got bronze, silver and gold means he is in ASHR. Only those who got gold will get a trophy from the annual KUMON Ceremony. There is a chart to meansure how far a child had gone thru.
E.g like my son he is a gold awardee with 4 years advance in Maths learning, meaning he is 4 years ahead his peers in Maths, now he is primary 1 but doing fractions (Pri 4 level).
Feel free to communicate with the person in charge of the center, he/she will be able to give you a more indepth of what is ASHR. Not only that also to ask questions on your child progression. This is how I have been with KUmon since my son is 4, now he is in Pri 1.