Archived Information

State of the Art: Mathematics - July 1993

image omitted Mathematical discussion should be a daily part of classroom activity.

If a child asks you if this answer is right, and you say yes, you've robbed him of the real learning. It's a question of when you say good, not if you say it. Once you've probed for understanding, and you're sure that the child knows, then to say, `You've convinced me, that's terrific, what you said really made sense to me. Why don't you share it with the rest of the class?' But I'd wait until the last moment when I'm really sure that the child really knows it. 
                                        (Ball and Wilcox 1989, p. 15)
Mathematical discourse transforms student learning. In offering praise too quickly teachers sometimes lose the opportunity for productive mathematical discussions, a key ingredient for building mathematical power. The lecture mode of instruction also discourages mathematical discourse in the classroom. Recent research shows that classrooms where students engage in a rich mathematical dialog with their peers as well as with their teachers are effective learning environments. Students need to be actively involved in questioning, conjecturing, defining, and explaining.

Teachers can shape the classroom environment to encourage mathematical discussion. They can encourage the participation of all students by valuing each student's contribution, by reducing the risk of ridicule for being wrong, by encouraging honest disagreement, and by making sure that all students are included in the discussion. Mathematical discussion that is rigorous but open minded should be a regular and valued part of classroom activity.

When teachers openly discuss their own mathematical thinking and demonstrate the process by which they solved a problem, they encourage this active mathematical behavior in their students. Teachers cannot expect students to tackle difficult mathematical problems, to discuss, question, define, and conjecture if they do not do so themselves. They cannot expect students to be curious and excited about mathematics unless they are.
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[Students need to learn more and different types of mathematics.] [Table of Contents] [Teachers need to become "informed guides" to the learner.]