A common question uttered by instructors is, "Is this right?" Normally some student says yes or no, and then the instructor agrees and moves on. (This is a cousin of the questions, "Do you understand?" and "Are there any questions?") Unfortunately, it's overused now and its usefulness has declined. It's not that the question isn't earnest. The issue is that students hear this question all the time, and they sit back and wait for the bright kid to chime in and do the work on behalf of the class.
The goal when we ask, "Is this right?" is to check that students understand what is going on. Another more effective way to accomplish this is to ask students to discuss in pairs what their thoughts are. The instructor can say, "Work with your partner to determine if the presented solution is correct." Then all students are invited to engage in the validation, and the instructor is removed from being The Mathematical Authority.
Perhaps the main point of this is that it is important to develop students' ability to validate arguments. If the instructor and/or just a handful of students are the only one doing this, then the vast majority of the students are not engaged in validating arguments. Good teaching techniques can make a big difference, and help every student in the class be a participant in validation.
A quick rundown:
- Give a task
- Students work on task
- Student(s) presents solution
- *All students discuss presented solution. (Rather than ask, "Is it right?" you could state "Discuss the solution with your partner..."
- Instructor moderates the discussion
