I am a Ph.D student in computer science. I am TAing one course this semester, which requires the basics of abstract algebra like rings, fields, ideals, and basic theorems about them. I have done two courses in the mathematics department related to algebra (abstract algebra and commutative algebra).
Working as a TA, once a week I have to teach some basic algebra objects and their theorems to these students. This is the first time I am teaching things related to algebra. I feel like it is hard to explain this things to students. This is how I teach them: I first write the definition and then give them one or two examples. Many times I find out that these student say that they have understood the definition, but when I ask them the next day, they are blank. I want to simplify things, but I don't know if this will be a good way to teach algebra.
Question: How do I teach algebra for the first time?