Modeling Think-Alouds
“Teaching students how to make connections as they develop an understanding of mathematics concepts or apply their mathematics knowledge to problem solving can improve their comprehension and increase their overall interest in the study of mathematics.” – Laney Sammons
Our young mathematicians walk into our classrooms with a variety of experiences and diverse backgrounds. Some students make connections very easily and some need more guidance in how to draw upon what they know. Through teacher modeling and think-alouds, we can help our students make connections that build upon their prior knowledge and lead them to deeper conceptual understanding. Students need to hear your thinking and see you making relevant connections, so they can observe first hand how a mathematician solves a problem. The think-aloud is a time for you to do the talking and don’t forget to show your thinking too.
Here is an example:
The problem – Five children are ready for a snack. They have one dozen cookies. If they divide the cookies equally, how many will each child receive?
Teacher – “The first thing I need to do is remember how much a dozen is. I know that is 12 – like when I get a dozen donuts. Now, I think I am going to draw 5 plates. One for each child. ( Draw 5 plates on the board and count to double check.) I will give each child one cookie first. (Draw 1 cookie on each plate and count 1, 2, 3, 4, 5.) Next, I need to think, ‘How many do I have left?’ I will count on – I used 5, so I put the 5 in my head and add on – 6, 7, 8, 9, 10, 11, 12. I have 7 more left and I know that 5 + 7 = 12. Now I ask, ‘Do I have enough to go around again?’ Yes! I will give each child one more cookie. (Draw 1 more cookie on each plate.) I will count on from 5 – 6, 7, 8, 9, 10. Next, I need to see what I have left. I will count on from the 10 that I used– 11, 12.) I know that 10 + 2 = 12, so I only have 2 cookies left. Is that enough to go around again? No. So each child will get two cookies and there will be 2 left over. I am going to double check by counting the cookies on the plates and then add the 2 left over and see if I get a total of 12. I think I will count by 2’s. (Count 2, 4, 6, 8, 10 plus the 2 left over equals 12). That works!
You can also connect to a common classroom experience:
“Do you remember when we read, The Doorbell Rang? They had to divide their cookies into equal shares too. They had a dozen cookies. I remember that is 12 . . .”
Good teacher modeling helps our students see the mathematical behaviors and hear the mathematical vocabulary that we want our children to use. These opportunities help learners connect to their own life experiences, to experiences with prior mathematical concepts, and to math experiences in the world around them. When our children see how we use math every day, it becomes more relevant and more meaningful. Modeling doesn’t take much time, but does open the door to greater mathematical thinking, increased vocabulary, and deeper understanding.
Check out this link to the Math Coach’s Corner by Donna Boucher. It shares the modeling of thinking for attacking a 4th grade standardized test problem. http://www.mathcoachscorner.com/2015/01/modeling-mathematical-thinking-2/