I love that this book does not presume we are all able to do all the problems and does not make us feel bad when we can't. Everyone is different and different people struggle with different problems regardless of their ability. If you don't at first appreciate the simplicity of the language I'm sure you will at some point come across a problem which stumps you at first and makes you realise how valuable and confidence inspiring this is.
I will definitely use the "how much dirt is there in the hole" problem. I think this would be very good for proving to students it is vital to READ the question! Extending problems is also something I wish to bring to the classroom, I want my students to be creative and extend problems they have worked on and I believe they should get marks for doing so. This will not only get them thinking further but will solidify in their minds what they have learnt from the original problem.
"What do you know? What do you want? What can you introduce?" is something that I frequently tell students to ask themselves when problem solving. Students tend to look at a problem and if they don't immediately know the answer or have seen a parallel problem solved get disheartened and find it difficult to continue. Breaking down the problem solving process into manageable steps is invaluable and often overlooked by students.
These chapters reinforce that it is OK to get stuck and that once there there are logical steps you can take, there is still progress that can be made.
Lovely, Deb! I agree with you -- one of the strengths of this book is that it acknowledges that everyone gets stuck, and that this is an important and inevitable part of the process. Too often people expect that only "math brains" can do problem solving, and that anyone who hits a snag ought to give up.
ReplyDeleteI'm glad to hear that the idea of extending problems is one you will use. It's a powerful way of offering variable entry points to any problem!