No longer can we simply teach math procedurally. Students cannot build a solid number sense without thinking through an argument and articulating their mathematical conjectures. But how do teachers effectively support students in this process? This cannot be answered by purchasing the best textbook or investing in the latest technology. Teachers must engage their students in mathematical justifications; both written and oral. This blog post is devoted to mathematical discourse and argument.
Let’s begin at the high school level. Common Core Standard #3 for Mathematical Practice asks students to construct viable arguments and critique the reasoning of others. PBS' Making the Case includes 13 video clips that all address this very mathematical practice. Videos range from full class mathematical debates to structured group work discussions.
Being able to defend one’s reasoning is a skill that must be practiced on paper as well. Jawad Brown, a local 7th grade math teacher, highlights specific strategies that he uses to help develop students’ mathematical writing. The Evolution of Writing in a Math Classroom gives multiple examples of student work as well as varied approaches to teaching written justification.
Last but not least, we must address how argumentation can positively occur in the elementary math classroom. One of the best resources that I have come across since I began as the Regional Math Lead is Number Talks. The Facilitator's Guide and DVD include multiple discussion questions, strategies and video clips. It is absolutely amazing to see what mathematical discourse and critique can look like in the elementary classroom.