I think an earlier lesson on pronouns would be very helpful. All the pronouns were introduced in the basics lessons in nominative only, from what I remember, and until now, we've only used them in nominative. Now suddenly, without any explanation, we're getting accusative pronouns, and it's not intuitive what they mean, or how you can use them!
So from what I understand, I could make the following rule. Please correct me if i'm wrong :
1) 'ze' can mean a) 'She' or 'They' when used as a subject and b) 'Her' or 'Them' when used as an object (although haar and hen would be precise for the respective usages)
2) 'zij' can only be used as a subject. It means 'she' or 'they'