Messy Thinking

The image to the right is a photo of my desk.  I keep a stack of large sheets of paper on it that I scrawl a whole lot of stuff on, this one just happens to be mostly some maths  questions I have been working on recently.  This messy thinking I feel is really important.

There is a bit of everything here, some measurement, algebra, arithmetic and some random problem solving tasks.  None of the problems on here were particularly big problems, they were in fact quite small, none of them were also particularly important, but they were just questions that had my interest at the time.  None of the stuff on the paper is particularly neat or well set out, but it served its purpose, it allowed me to organise and test my thinking at the time, it help me to process the question I was working on,  That is the point of messy thinking and I think that this type of thinking is under-represented in most classes.

Most people's view of doing mathematics is looking at a question and carefully setting out a well articulated set of steps to solve the problem and being able to do that straight away.  Yes of course it is possible to do this, but only when the question you are doing is well known to you and well practiced.  It does not happen in this way when the problem is unfamiliar or challenging.  on these questions you have to try your ideas somewhere, you are going to make mistakes, you are going to have several shots at it, it is only when you have tried and made sense of the problem that you can begin to see how to turn it into that nice neatly articulated solution that so many are used to.

The problem with this is that most students do not want that messy thinking in their books, they don't want any mistakes in there, they only want those perfect solutions.  If they make a mistake quite often they will rip the page out to make sure that no-one can ever know that the mistake was made.  This year I wanted students to feel safe to do the messy thinking.  This has been achieved in two ways. 

1. They are currently running with two maths books. their normal one that they can write their perfect work into because that is safe for them, they also have a messy thinking book.  This second book is where they can record all those thoughts, all those ideas they want to try.  They can use this book to document any of their thinking but it has some very clear rules
   1. They must use pen. I don't want them to have the temptation to erase anything, in that book we value mistakes and what we learn from them
   2. They cannot rip pages out or used liquid paper for similar reasons to above
   3. If it is work that is being assessed, they need to formalise the thinking in their other book.  The messy thinking is good in developing the solution, but clearly writing their solution is also important
2. With extended tasks students work collaboratively on large sheets of paper to try their approaches.  Like with the messy thinking book they then formalise their solution on a different sheet of paper.

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These are two things I have tried this year with some success, but I am always on the look out for further ways for students to be more comfortable with making and learning from mistakes and from showing their messy thinking because as my blog title suggests I value this messy thinking myself.