Dear Jennifer,
Thanks for explaining your situation so clearly. It really helps me and others who are reading the post to understand your frustration. First of all, don't be so hard on yourself. Place value is one of the hardest concepts for children to grasp since it is so abstract. They need many, many experiences with the quantities before they grasp the concept fully. The best plan is to have him enter the numbers on the abacus every time until he can see it in his head. We often try to take it away too soon and move on to abstract thinking, but remember he is not at that stage of thinking yet.

Also, are you using the math way of counting? If you say 6-ten, nine plus 3-ten it should help him to see that 6-ten and 3-ten need to be added. Also, there can be some confusion with this problem only since 3-ten and 6-ten make 9-ten, which is the same number as the ones, which may be the reason for the confusion. Perhaps he does get it, but this extra 9 is the problem. What I would recommend is that you have him enter the numbers on the abacus to "check" his work, much like you would use a calculator to check your own adding and subtracting if checking over your checkbook. Let him see the numbers over and over to establish the quantities clearly in his mind.

Also, there are several good games that help with this. One is called Station Game N37, where you use the abacus, place value cards, and base ten cards. By seeing the same quantity three different ways it really helps cement the value. Another good game is N38 Can You find. Try playing some games for a week and then going back to the lesson. You are right in that you want to be sure he really gets this concept, but remember he is just in first grade. It will come. It takes many pleasant experiences to lock it into his long term memory. That is why games help so much.
Nancy