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.
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.
Senior Leader of Pedagogical Innovation and Mathematics Coordinator in Regional South Australia.
Opinions in this blog are my own and do not necessarily represent the views of my employer.