Chanllenging Students, Challenging Educators

This summer Apple offered a number of short webinars for educators in their Apple Summer Semester Series.  One of the sessions focused on Mathematics and featured Dan Meyer, a high school math teacher who is attempting to turn mathematics education upside down.  His main focus is selling math to students in a way that is more engaging than the traditional mathematics text.  To do this he poses traditional math problems in non-traditional ways.  Typically by staging videos that get students questioning and inspiring them to look for answers on their own. He also proposes that this format for introducing problems increases the level of challenge for students.

As I think about what I want my future classroom to look like, a number of the themes Dan emphasizes keep coming up.  For example, I want students to learn to question and know what information is necessary to answer their question, and then know how to go about finding the answers to their questions.  I want students to feel confident in their answers, specifically, to recognize when their answers are reasonable and when they clearly are not reasonable.  I want students to understand that math is powerful and can really help them understand how the world works.

This style of teaching, however, I find very unsettling.  If the level of challenge for students is increased, by default, the level of challenge is also increased for teachers. I was not taught in this manner, as a student the instruction I received was overwhelmingly of the skill and drill variety.  I can write beautiful mathematical proofs, and I can solve equations, but I do not feel confident as I watch these videos that I would know how to start some of these problems.  If I don't know how to begin how can I help students see where to begin?  

With that concern in mind, I remembered reading about Thinking Mathematically by Mason, Burton and Stacy.  The intended purpose of this book is to help develop problem solving skills.  So I have ordered this book and in between my regular coursework, I am going to begin working through this book to strengthen these skills. Disclaimer: the problems in Thinking Mathematically are not presented in the raw way that Dan recommends for true exploration, however, I figure as long as I am interested that is more than can be said of high school students faced with a traditional mathematics textbook.  I am hoping that if I can learn to be more confident in approaching this type of problem then maybe I will be able to introduce these sorts of problems into my classroom successfully.