Trusting the kids....

In order to be a facilitator in a mathematics classroom, a teacher needs to be willing to give up control in their classroom.  This does not mean that "anything goes".  Rather, there should be parameters for how classroom discussions will take place with a focus on respect for all participants.  The teacher also needs to be willing to let the students' conjectures and thinking drive the conversation.  While the teacher has an ultimate destination in mind, the path to that destination is determined by the students and their ideas.

A beautiful example of this occurred last week.  A fifth-grade class was working on the idea of how numbers change when multiplying by 10 (or 100 or 1,000).  The teacher had students explore the magnitude of 1, 10, and 100 using base-10 blocks.  Students then predicted what it would look like if they were to have a 2-D version of 1,000, 10,000, and 100,000.  Groups used paper to build these models.  After building their models, the class had a discussion about their observations.  They built the rule that when multiplying by 10, a digit moved one place to the left.  This conjecture was tested using calculators.  When students were confident in the rule, they wrote it on the chart paper.  Students were eager to explain their thinking and were engaged throughout the lesson.

Rather than teaching the students to "add 0 when multiplying" (I'll need another post to talk about why that is confusing language for students), this teacher build upon students' observations and reasoning to help them develop the mathematical rule.

In order to facilitate this lesson, the classroom teacher had to trust that the students would discover the rule - and they did!  :-)