The definition of what effective mathematics teaching looks like very much depends on what purpose we assign to teaching mathematics. A classroom where the primary objective is to teach students a specific set of mathematical skills for them to use later will look much different than a classroom where the primary objective is to teach students how to think mathematically, although there is obviously overlap between those two classrooms. For a good description of the type of classroom which achieves the first goal but fails at the second goal, see When Good Teaching Leads to Bad Results by Alan Schoenfeld.
I will describe a classroom where the primary purpose of the classroom is to encourage mathematical reasoning, with a secondary benefit of students practicing mathematics skills they have developed.
What are the students doing?
What is the teacher doing?
What else would you add to this description of an effective mathematics classroom?
David is a Formative Assessment Specialist for Mathematics at New Visions for Public Schools in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his Masters degree in Educational Technology from UBC, and is the co-author of a mathematics textbook. He has been published in ISTE's Leading and Learning, Educational Technology Solutions, The Software Developers Journal, The Bangkok Post and Edutopia. He blogs with the Cooperative Catalyst, and is the Assessment group facilitator for Edutopia. He has also helped organize the first Edcamp in Canada, and TEDxKIDS@BC.