This video does a really nice job of explaining it:
https://learnzillion.com/lessons/2596-subtract-within-20-...
But honestly, if your son doesn't get it, write the teacher a note and let her (or him) know that. His teacher NEEDS to know that he doesn't understand.
Many of the methods in schools are very foreign to adults, as this is not how we learned to add or subtract. But I encourage everyone to try not to get so upset and say, "Stupid Common Core." These methods really, really, really help the students understand numbers and what is going on.
It saddens me to see so many adults be so afraid of math. At least with Common Core this generation has a fighting chance.
ETA - I think I misspoke. Common Core is just a list of standards. It is not a teaching method. Schools/teachers can use many different methods to teach the concept. I'm not even sure what "new math" is, as parents were complaining about "new math" when I was in high school and I'm in my 40's.
I teach remedial math, so I work with the students who have never felt successful at math. Many of my students have no "number sense." They do not grasp the concept of what 3 + 5 means. Many of them cannot tell you that 3 + 5 = 8. They would have to use their calculators to get the answer.
The method in this post is designed to help kids understand how numbers work. If they understand why things work the way the work, they will be successful in math. If, instead, they rely on memorizing, then they will be memorizing until the cows come home. Math cannot be learned through memorization. There are just too many things that can factor into answering a question. Those who understand why things work the way they work are the ones who are successful at mathematics.
B, I feel unbelievably sad for you that you don't realize the best thing we can do for our kids is teach them many ways to do the same problem. It is through learning multiple methods that the kids gain true understanding. They can memorize 3 + 5 = 8, or in this case16 - 9 = 7. But if they use manipulatives or "10 frames" they will "see" if you have 16 jelly beans and eat 9 jelly beans you will have 7 jelly beans left.