Chapters 2 and 3 from Thinking Mathematically by John Mason

In the first two chapters ("Phases of Work" and "Responses to being Stuck") of Thinking Mathematically, a model for approaching problems is presented.  The model has three main parts: Entry, Attack and Review.   The most important parts of the model are the Entry and the Review with the least importance on the Attack phase.

I find the phased approach very interesting, as the natural tendency is to jump into a problem and spend most of the time on the Attack phase.  The book really emphasizes that people/students should not rush into a problem.  The author also provides rubric words (or simple key words) to keep in mind during that phase.  I would use this in my teaching by spending more upfront time on really framing and understanding the problem.  We have done this within our 342 class and I have found it very useful.  Spending more time on the entry is critical to help students really get their head around a problem.  This includes identifying what they know and what they want.  This then leads to them introducing a possible solution at which time they are ready to attack.

In addition to spending more time and discussion on the entry, students should also relish in the “getting suck part”.  For until a student is really stuck and has given the problem lots of thought, s/he cannot truly appreciate the solution once found.  I like the idea of one must get stuck before they can learn.  I plan to emphasize this in the classroom.  The only difficult I see is that within a classroom of 30 students, each may go through these phases at different times.  I will need to pay extra attention to ensure that each phase is given the appropriate amount of time as needed by each student.  A difficult task!