Thoughts from a reflective educator.
Here's the competition to an inquiry based classroom (via Christopher Danielson).
These students will clearly have memorized the order of operations by the end of the lesson. I don't think they'll have a clue what it's for, or why one would bother learning it.
David is a mathematics teacher and a learning specialist for technology at Stratford Hall in Vancouver, BC. He has been teaching since 2002, and has worked in Brooklyn, London, and Bangkok before moving back to Canada. 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.