Its well known we need to build metacognition in math to help students learn the material better. Often students do not think well of math due to the idea that mastering math in the classroom is learning a bunch of formulas, rather than understanding math can be meaningful.
Metacognition can help increase the meaningfulness of instruction so math makes more sense. We know students can do the calculational part of the problem but fall short on applying meaning to the problem.
If a student is given a problem where they have to determine the number of buses to order for a field trip where they have the number of people going on the trip and the number of passengers in each bus, students will carry out the algorithm correctly. Their downfall comes when they have a remainder. They often give the number of buses with a remainder, or they do not round up to include the remainder.
There are three ways to look at metacognition in math.
1. Beliefs and intuition - This is one based on the ideas people bring to the classroom and how do they shape the way we do math? One big belief which has developed is that the classroom math is just formulas that do not relate to the real world. Students find math boring because of this.
2. Knowledge about your own thought processes. - It is important for students to know how they think because problem solving requires you use what you know efficiently. Student understanding of a task and their ability to solve it are effected by what they think they can learn.
3. Self awareness or self regulation - How well does a student keep track of what they are doing when they solve problems? How well do they use observations to guide their problem solving? In other words students need to develop an awareness of their thinking and their progress as they are solving problems.
As teachers we need to model our thinking for students so they learn how to think about thinking. It is recommended we use the words "I think,,," when attempting to show students your thinking and so they see the process.
Providing graphic organizers also help create a visual representation of that thinking. Graphic organizers help the mind focus on the important parts of our thinking and we can look at it when we are done.
Finally, teachers should plan the behaviors they are trying to model by creating a script or a plan ahead of time which includes possible misconceptions so they can be addressed a head of time. One misconception my students have is they do not need a zero place holder when dividing. They always leave it out.
Let me know what you think about this. I love hearing from others.