More on Making Thinking Visible.

  Many students find it difficult to explain their thinking when it comes to mathematics.  Often they can tell you what the next step almost by rote but they cannot always tell you why they need to do it.  This can be especially difficult for ELL students who may not be as fluent as other students.

Some students when you ask to explain their thinking often give you a look like "Why do I need to think about it?  I just need to follow the steps and I'll get a right answer!"

They don't seem to understand that thinking leads to better understanding.  There are ways to encourage and help students develop the ability to explain their understanding.

1.  Connect-Extend-Challenge which adds a layer to instructing students in a new concept or skill.  Instead of just teaching the skill, ask them how it connects to other problems they have solved because it requires them to access their prior knowledge.  Once they begin connecting the problem with other problems, ask them what is new before asking them to explain how this problem extends their knowledge and thinking.  The final step is to have them identify the challenges they faced learning the material.

2. Claim-Support-Question is designed to help students make a claim, recognize patterns, figure out generalizations, and learn to provide evidence to support the claim.  The teacher makes a claim such as "all multiples of four are also multiples of two".  Students gather in small groups to discuss if the claim is true or false.  They must provide evidence such as manipulatives, drawings, etc to support their position on the claim.  The last step is to have students list the questions that were raised during the discussion that have not been answered.

3.  See-Think-Wonder is for students to look at a visual pattern while explaining what they see.  They talk about it and then think about the next step in the pattern before discussing their choices.  The final step would be for student to express what they wonder about in regard to the pattern.  Do they wonder what the 100th step is or perhaps the 50th?  This is where they talk about it.

These are just three routines which can easily be implemented into your daily routine to help students learn to make their thinking visible and to help them increase their conceptual understanding of mathematics.

Let me know what you think, I'd love to hear.  Have a great day.