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.
in looking at all of the aspects of maths that are expected to be covered over the course of a year I feel that statistics offers some really great opportunities. It allows a really authentic way for students to get into some real maths with data that matters to them and to others. It is not that there is not authentic ways to engage with the other aspects of the course and get into some real maths, it just sometimes seems like it doesn't seem like an authentic situation for them, there is not the emotional buy in. With statistics you have the opportunity to introduce some very provocative data sets or ones that directly speak about them. You can have some really great discussions about how statistics are used to make decisions, how others use them to make decisions that effect you, to look at how you or other people can use them to build convincing arguments (even if the stats are quite deceiving).
I am at the very start of my unit on statistics, but I wanted to start it with them having a discussion about some data, their own diagnostic testing data. I chose to use this data for a because sometimes I feel they don't see the use of doing the testing, they don't always treat it properly and that skews our data. I also chose it as I feel that they do not always understand the results of the data, I wanted them to have much more awareness of what the data tells them and of how we use the data as eduators.
The last person to talk picks the next person to talk (from those with a counter out) by throwing them a ball or similar, only the one with the ball can talk. Once a person has used all of their counters they then cannot contribute any more to the discussion, they can sit and listen, but that is it. The teacher in this process is a facilitator, but tries to stay out of the discussion as much as possible. They provide the provocation to start off with, they pick the first person to talk and they will ask questions to stimulate the discussion if it dies off completely. In this role you need to avoid jumping in to help with that I tend to give myself the same number of talking stones that everyone else gets, if they only have three opportunities to add to the discussion then I only have three to stimulate it, it forces me to be strategic as well. This is hard when you completely disagree with what is being said, but you need to let students be the ones to respond them and to challenge that thinking.
I gave them two prompts to start their contribution with they could start with
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.