Yesterday, I looked at reteaching. While looking for ideas, I came across something from the San Francisco Unified School District Mathematics Department on reengaging students rather than reteaching.
Reengaging gives the feeling of having the students more involved in their learning while reteaching gives the impression the teacher is doing most of the work.
Re-engagement pushes the student to look at their own conceptual understanding of the topic so they can eliminate their misconceptions. It is said to be more effective because it engages students in a meta-cognitive way.
This method should be employed only after the student has had a chance to learn about the topic. At this point many students still have misconceptions and its important to clear them up. It is suggested the teacher give a short assessment to determine common misconceptions. The teacher should look at the misconceptions to determine what the student was thinking so as to help eliminate it.
Many of my students combine constants and coefficients so 3 + 4x = 7x. I realized the other day, they're previous teachers never took time to eliminate this particular misconception. They are used to adding numbers so they added the 3 and 4 without paying attention to the x.
Suggestions for helping students eliminate misconceptions are:
1. Math Talk - where students explain their thinking on a problem which contains a common error. Those who made the mistake are encouraged to explain their thinking while those who are correct are also encouraged to explain their thinking. This activity does need to have rules established so there is no name calling and it has to be done in a safe atmosphere so students want to talk.
2. Revision - Allow students time to revise their work if they have errors. When I was in school, we called it making corrections but revision sounds gentler and less intimidating. This goes a bit further than just correcting. If a student makes a mistake, they identify the mistake, explain why its a mistake and how they need to correct it before correcting it.
One way to prepare and use re-engagement is to have students answer a problem to determine their understanding and figure out where any common errors occur in the process. Next have students work in small groups to develop a strategy to help themselves find the errors in the problem. Students will share their strategies with the classroom.
Then students will analyze the problem looking for misconceptions and errors. During this process they will clarify their thinking by explaining where the mistake is and how to correct it. Finally, they revise their work before trying a similar problem.
For my students I think I have to use both reteaching and re-engagement because they need to learn the material and learn to determine their own misconceptions. I like some of the ideas I've read over the past two days.