Monday, October 11, 2010

Thinking Mathematically: Chapters 2 and 3 Reflection

The three phases: Entry, Attack, and Review are a great way to break down any problem solving question.  Although these phases seem obvious to many of us, students often take these phases for granted.  Students often end up struggling to complete a question, forget everything about that question and move onto another question. 

The Entry phase emphasizes on the important information gathering questions to ask oneself: What do I KNOW? What do I WANT? What can I INTRODUCE? 
Careful reading is crucial when it comes to approaching any problem solving question, I found that the St Ives and the "hole" questions were very interesting and would probably ask my own future class similar questions that provoke their attention to catch the KEY words to solve the questions.

Important concepts of the Attack phase are: reaching the point of getting STUCK!, realizing what exactly you are STUCK! on, being calm and collected to see that being STUCK! is a good thing, thinking of how to resolve this STUCK! issue and reaching the AHA! result (or some KEY aspect that can lead to the AHA! result). 

I think the most valuable concept a student should learn is the Review phase.  Within the Review phase, the important concepts are to: CHECK the resolution, REFLECT on the key ideas and key moments, EXTEND to a wider context.  Students should be able to check and accept that their solution is correct and try to expand on what else they can apply the KEY points to, in order to solve other questions relating the one they have solved.

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