Summary
Learning to think and thinking to learn
I. Facilitating whole-group discussions
Addressing Diversity of thinking
When there is a discussion in the classroom, consider that is differences in the ways in which students process information called extroverts and introverts. Extroverts characterized as outgoing and gregarious and tend to process and think while they are talking or they able to think out aloud. Introverts characterized as shy and taciturn and they must think carefully before speaking. Every student is likely to process aspects of both introversion and extroversion. The way that can be used by the teacher to deal with diversity in processing information is to encourage the class to work collaboratively. Teachers suggest giving quieter students more time to process their thoughts for a whole group discussing. They are expected to share their solution method or idea.
Using incorrect solution
One of the most powerful ways to make an impact in young children’s thinking is by accepting incorrect answers or ideas as a natural part of doing mathematics and pursuing them in the same ways as correct solutions. The teacher began the discussion with an incorrect solution but did not indicate her own thought about it. Rather, she used the discussion to encourage students to think more deeply about problem’s meaning. Using incorrect solution allowed the teacher to begin a discussion that would deepen children’s understanding in ways that may not had been possible had she simply asked a student to share a correct solution.
Questioning one another’s solution
The most productive discussions around mathematical ideas seem to happen in classrooms where questioning is an almost spontaneous part of the way children talk to one another about their work. At the beginning of the year teacher should model behavior by questioning students each time they share a solution method. Then she asks other students if they have additional questions. She then discusses with them the value of this questioning and how it helps everyone more deeply understand one another’s methods. Gradually, students take over this responsibility and become questioner without much prompting.
II. Engaging with children a work
Suggesting a strategy
One of the challenges teachers face in engaging with students as they work is making those on-the-spot decision regarding students who seem to be struggling. Decisions about how to deal with students’ frustrations have lasting implications for setting a tone for doing mathematics. The teacher worked to determine what the students were thinking and encourage them to negotiate their different solutions themselves. She asked questions to solicit the students’ explanations and consistently reinforced her expectation that they must listen to one another.
Allowing time to develop understanding
When engaging with students while they work, how can teachers help students who are having difficulty in explaining their thinking or making sense of the task at hand? First, recognize that students will be working on similar problems throughout the entire year. Second, try to support children’s growing beliefs in their own ability to determine the correctness of solutions and ideas. Finally, allowing children time may suggest to them that many mathematical ideas take time to develop; they would not be problems if they did not, but not guiding students to a solution when they are struggling.
III. Concluding remarks
Maintaining a consistent focus on thinking is not easy; it requires formal, deliberate reflections on the impact of specific instructional moves. However, by combining such analyses with a commitment to learning to thinking, we can make major strides in creating classrooms where children are willing to take risks and think their way through whatever challenges they encounter.
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