Here is a quick tip that facilitates easily assigning readers, while making Gospel Doctrine class feel safe and comfortable for adults or teens who have reading difficulties, need glasses, are terrified of speaking out in class, or even have just a sore throat. Get a small item to represent the scripture "Thy word is a lamp unto my feet, and a light unto my path" (Psalms 119:105). I had a small clay Hebrew lamp I bought at a bookstore, but you could also use an ordinary (unlit) candle. Hand the candle or lamp to a class member when class begins, and explain to the class that if they would like to read out loud, they should hold it until you call for a scripture to be read; if they are uncomfortable reading out loud, they just pass it to the next person. After a scripture is read, the lamp or candle is passed to the next class member who either chooses to be the next reader or passes the candle on. This worked great in our class and made it so people didn't have to try to avoid eye contact with me when I wanted a scripture read and they didn't want to be chosen.
To get class members to read the lesson assignment--no joke, this works with adults--bring small treats and simply pass them around the class in a basket. They take one if they read the assignment. Several of my students said this was the first they had ever actually read Sunday School assignments. It just gave them a personal accounting each Sunday, and a mini reward.