I've read it's important to demonstrate thinking aloud in math so students learn the thinking process behind solving math problems. This is something they teach instructors to do in certain reading programs but I've never learned to do it in math.
In math you pretty much assumed you would follow the steps your professor put on the board and not worry about your thinking. Now, its important because too many students reach high school without thinking how to approach a problem.
When students think aloud, it helps them talk through the details of the problem, the decisions made towards solving it, and their reasoning. One aspect of thinking aloud is that it makes students slow down and think about their problem solving choices so they have a chance of more fully comprehending the problem.
For students who struggle, thinking aloud can help clarify ideas, identify what they know or don't know, and learn from others when thinking is shared. This also helps teachers monitor student thinking.
There are a couple of key points to keep in mind when thinking aloud in math. First is to have students focus on one step at a time while taking their time to fully understand the problem before trying to arrive at an answer. Second is have students talk about what they notice, the decisions they make, and why they believe their choices are correct.
Some of the ways to encourage thinking aloud include:
1. Model it by explaining your choices, decisions, etc as you demonstrate solving the problem. Use technology to support note taking, and create visualizations of the bigger picture to help students develop understanding.
2. Provide students with a series of prompts such as I know......, One thing I can try........., or I want to try ........ because......... as a way of helping guide them through the think aloud process.
3. As students become more familiar with thinking aloud, have a peer listen to their thinking and comment on the content while the teacher listens to the strategies being used.
In addition, it is suggested teachers create webcasts which show how different students solved certain problems so students can see how peers solved the same problem. Furthermore, if a students think aloud is recorded, the teacher and student can listen to it and discuss the process to help the student improve their understanding of the processes used to solve problems.
This is just a scratching of the surface. I plan to revisit the topic in a few days but its a good start. Let me know what you think.