Well, to be precise, it's not going up by 2. It's going down by 2. So, 3n minus 2 is the rule. You must mean 3-2. Your are adding 3.
Teacher notices that the rest of the students in the group are making the same kind of error.
We offered this vignette to the teachers during one of their class meetings at Marquette. The questioning plan that we inferred from this observation was that the teacher was very interested in asking questions about the meaning of the -2 in all three groups. Indeed, in this excerpt the questioning plan eclipses the teacher's listening. The listening that the teacher does seems to be expressly for the purpose of composing a sequence of questions that will lead the students to formulate a particular algebraic equation and to analyze it to understand the meaning of its parameters like the -2. In other words, this vignette illustrates a type of listening that is designed to evaluate whether the student responses are aligned with the teacher's plan rather than to interpret what the responses reveal about the students.