I have been thinking a lot lately about the best way to address student misconceptions on the unit of work that they are currently studying. Ideally I hoped these misconceptions wouldn't develop in the first place, we spend a lot of time discussing and developing the understanding of the ideas before introducing any more formal procedure, and when we do introduce a procedure, more often it is theirs, not mine. The aim of doing this is to ensure that we have thrashed out all of the ideas and tested their veracity so that the misconceptions can be brought to the surface and addressed as the new content is introduced .
However in looking at the work I receive from students from time to time it is clear that misconceptions creep in, despite my best efforts, I may not have covered all the bases. The other day I tried to address misconceptions in a different way to had previously. After looking through their books I picked up some misconceptions that were common across multiple student's work, but instead of talking about these in class and trying to correct it myself, I wanted them to notice and to correct the errors. The hope in doing this was to get them to think more deeply about the errors.
To do this I wrote up some solutions to questions like they were legitimate solutions to the problem, but in reality these solutions incorporated the errors that I saw in their books, these samples are shown in the images below. Each table was given a different proposed solution, these were put in the centre of the table and students were encouraged to discuss the solutions in their table groups.
It was interesting for me to see that when we had the discussion about the questions every group was happy that their solution was correct, none of the groups believed there was an error in the solution. To me this was very interesting, these errors were prevalent in a number of students work, but they definitely were not there in all of them. Even those students who had answered questions similar to this correctly in their books were not able to identify the error in these solutions. So this was quite a surprise to me.
I was caught a little off guard by this, but I also had to think carefully about the way forward. At this point rather than telling them what the errors were for each problem, instead I just said "what if I was to tell you that every question on the table is incorrect. Knowing this, what is the error in the problem". This seemed to surprise them quite a bit, being utterly convinced the solution was correct and being told that it is incorrect created that conflict in their mind, and stimulated a lot of discussion as they tried to find the solution. They did not find this easy but eventually were able to notice the mistake. What I hoped they would get of this process is exactly what was achieved, they were then able to successfully examine their own work, and their own thinking, and correct any of the mistakes that had been previously made. They were able to look at their own work, which they thought was correct, and find the changes that they needed to make. I feel that it was a much more powerful way of looking at the errors they made, as the fix was not handed to them, they still had to work for it, they still had to own the learning.
I was reading a post on Dan Meyer's blog the other day titled You can't break math. There were a number of aspects to that post that resonated with me, but I came across the passage below that really made me think about the subject I teach in a slightly different way, this passage is..
One advantage of my recent sabbatical from classroom teaching is that I am more empathetic towards students who don’t understand what we’re doing here and who think adding 2x to both sides is some kind of magical incantation that only weird or privileged kids understand.
I started thinking about my own experience with my own mathematics education and in many ways the approach I took to my first few years of teaching. I realised that when I was learning maths in school, it was presented as magic rather than logic, and that is the way I presented it in my first years of teaching. My teachers didn't intend to present it in this way, and neither did I.
Part of the beauty in mathematics is in the patterns that emerge and in the certainty we have in our conclusions. However in the highly formulaic way that many classrooms still operate, more time is spent practicing how to use the formula under the guise "trust me it works", rather than spending the time to get students to develop a sound line of reasoning where that formula is the only logical conclusion.
The formula is simply the highly refined end point of a lot of thinking about a particular mathematical idea. That formula is the point at which all the uncertainty in their argument has been stripped away and what remains is the pattern that has emerged. When we present that formula without the thinking behind it, without developing that understanding prior to presenting the formula, this is when when it appears that we have 'pulled a rabbit out of a hat', it is something that has come from nowhere.
However it is important to remember that even magic is not magic to everyone, this has become abundantly clear to me through watching a lot of the TV show Penn and Teller Fool Us. For those who do not know the show, a range of aspiring magicians come on to a show and try to fool a world famous pair of magicians. Most of the time, these magicians cannot fool them. Even though the trick has been previously unseen, these magicians strongly understand the principles of magic, concepts such as misdirection and sleight of hand, so even if the trick is unseen, they can unpack the thinking that may produce that result. Their knowledge of these concepts is so strong, and so flexible, that they can apply them to any trick and to create new tricks of their own. This is what I want for my students in relation to their mathematical knowledge. More than just understanding the individual tricks, I want them to understand the underlying framework of the mathematics they are studying so that they can apply it in unfamiliar and sophisticated ways.
This post is corresponding with the start of a new school year. For a few months now I have been watching the #observeme hashtag on twitter. The trend began with a teacher called Robert Kaplinsky (@robertkaplinsky) from the US and he has written a blog post about it and presented a 5 min talk on it. When I saw this begin to appear on twitter I was really excited by the idea.
I have been an instructional coach focused on mathematics for a number of years now as well as the mathematics coordinator at my school and have become very used to working with teachers and providing them with regular feedback. I have been fortunate enough that those teachers have felt that the feedback they have been given has helped the to move forward as a teacher, they found it to be a rewarding experience. But over that time I have also realised that I have not received the same level of feedback on my own teaching, any feedback I have received has been limited, and very general in nature, I have not had the same opportunities to grow in my teaching by using the feedback of others to improve my craft.
So over the last few days I have been slowly chipping away at my own sign. I was really excited to work though the process. However I came to a realisation near the end of completing the sign. This #observeme movement is much different to the normal process of teacher observation and although the normal process is more formal I think #observeme is much more daunting, more than I initially realised. This is not yet based on putting it into practice, the school year hasn't officially started yet, but it is based on what I feel it has the potential to be.
With more formal observation processes the visits are arranged in advance, your observer and you decide on a time, a place and in many instances a focus. Early on in my career I put a lot of extra work into making sure these formal observations were top notch lessons, they pulled out lots of bells and whistles, I wanted to really nail them. Over time I came to the realisation that this didn't help me as it was not my normal way of teaching at the time, if I tried to teach that way all the time at that stage of my career I would have burned out. Any feedback I was given at that stage was not based on my normal teaching but based on my inflated teaching, I saw these observations as a threat rather than an opportunity, and therefore it did not help me to move forward. Eventually I came to the realisation that I just needed to teach my normal lessons, but looking back on it over the course of writing my own sign I realised that I was still subconsciously teaching to what I thought the observer may have wanted to see, but this is only because I knew the exact time this person would be visiting, it primes it in your mind.
This is where the difference was in making up my #observeme sign. I came to the realisation that this observation and this feedback could occur at any time and without prior warning, I could not predict when it might occur and therefore I had no way of specifically planning for it, consciously or subconsciously. Anything those teachers see, and any feedback that I receive will most likely be based on the truest representation of my practice as a teacher, it will give me the greatest insights into the quality of education I am providing for the kids that I teach. Those goals that I have committed myself to on that sign cannot be covered by isolated activities once a fortnight or once a week (not that I am aiming to do that anyway), they need to be a strong component of most, if not all of my lessons. Someone should be able to drop in at any time and provide me with feedback on any or all of those three goals. Therefore I needed to make sure that I was really comfortable with these as goals.
lemsHowever at times I will want them all working on the on task. These tasks are normally the ones that will be super important for establishing the conceptual base. In these cases I would not want different students working on different tasks, instead the task will be differentiated through the the questioning that I use to support, probe and extend their thinking. The use of enabling and extending prompts will be important in achieving this appropriate level of challenge.
2 - Learning Conversations
I put a lot of work into designing activities that aim to build an understanding of mathematics on a conceptual level rather than just a procedural one. However the key to extracting the greatest amount of learning from these tasks is the conversations that go on in class both between students and between myself and the students. It is important that their thinking is represented strongly in these conversations, not my own. I want them to be able to develop their own reasoned arguments and then use the discussions with others to test the veracity of that argument. I realise that in the past may of my conversations in class have been getting students to share and talk about alternative pathways to solving prob, which is important and a good start. However I also recognise that I have not spent as much, or enough, time getting kids to critique reasoning. In the past I have had some great success and some spectacular failure with this, most of which hinged on the classroom environment. Ensuring that I develop a classroom environment where critiquing is seen as a opportunity rather than a threat will be vital in moving this forward.
3 - Feedback
High quality feedback is vital in helping to move kids forward in their learning and improving the overall quality of their work. Early on I probably gave a lot of 'autopsy feedback', by this I mean the bulk of feedback I gave was on the final piece of work, at that stage the feedback was not of much use because it was too late to do anything about it, although it could help them in completing the next task. When I started giving more feedback during the completion of the task it was only then that I began to see the quality of work improve. But I still have room to move on improving both the quality and the quantity of my feedback by trying to give much more feedback during the learning, at the time it is occuring rather than just looking as the samples of work after hours.,
As an addition to my #observeme sign I have also created the capability for students to fill out the feedback sheets. I definitely welcome the feedback of the teachers in how they feel I am progressing against those goals. However I am also intensely curious about how students will fill out my feedback sheet. I really like that idea that these signs are not just up there for teachers to see, but also for students to see, when they walk into that class each day from day 1 they will know what I am aiming at and therefore their feedback, is equally if not more important than the staff that visit. They are the recipients of the education I am providing for them and they need to be able to provide feedback about how I am going against these goals and whether they feel these goals are working for them.
In speaking to some teachers about mathematics learning there is sometimes a bit of misunderstanding about what constitutes mathematical understanding. The most common one is that if they can get it right, and they can regularly get it right then that shows understanding. But it is my argument that being able to apply a procedure is very different to understanding the procedure, it is easy to follow a procedure, but not so easy to know why it exists and why it works.
In workshops I run with teachers from pre-school through to secondary I like to use the following problem to explain the difference.
When three numbers are added in pairs the sums are 22, 39 and 45. What are the three numbers?
What I like about the problem is that it is simple enough that anyone from any level of schooling can understand it, but it is also complex for all those people. It also lends itself to a range of different ways to attack it.
When I present the task to teachers in workshops I split the room in half, one half have a go at it themselves with no prompts, hints or scaffolds, whilst the other half are given a very clear proceedure to follow. This proceedure is as follows
Typically I give each group about 10 mins to work on the problem. When I give teachers the method described I get responses as shown below. They normally work though a few of these in the 10 mins.
When I talk to the other group of teachers they have made some progress on the problem, but don't have an answer by the end of the time they are given. So if we were only looking at understanding as being able to get the answer then the group with the procedure would be seen to be more proficient. I give both groups the opportunity to talk about how their group approached the problem and after this I ask them one more question which is
Why do we add the sums together and divide by 2 in the first step?
This question throws them, initially they think it is an average until they realise that there are three numbers and we are dividing by 2. But a really interesting thing happens, the group that didn't have that procedure seems to pick up on why that first step exists and the group who did have the procedure doesn't pick up on it at all. The group with procedure where so used to following it without having to think about it that they could not see the reason for that step. The group who didn't have the procedure, and also didn't get the answer had to think much more deeply about the question, and in struggling with it they were able to develop a deeper understanding of the underlying framework.
In looking at the procedure I chose to answer the problem that first step is not intuitive and I choose that method particularly for that purpose. It is a very simple way of solving it and it takes some shortcuts, both of which are common practices for teaching mathematics in many classrooms. But in my experience, the easiest method and taking shortcuts also leads to a lack of understanding. Realising that you add the sums and divided by two because in adding the sums you have added each number twice, so dividing by 2 gives you the sum of the three numbers is an important pattern that they could have made for themselves had they not been first given the procedure.
A way of solving this problem I have found online and in textbooks is in the way below
Although this does not take any shortcuts, I also think that it tries to make it to "mathsy", it makes it more complicated than it really needs to be, it complicates the thinking to a point which the method of solving it does not closely resemble the original problem. Although some students really understand and can make sense of this method, for many in the past this has just become like the first way, a method to follow rather than something to understand.
For those who approach the question more intuitively and without the procedure I at times give them the following diagram to help them make sense of the question, normally though without the blue dot.
with this image it is clearer why the dividing by 2 is important, but when given this image most do not solve it that way. They look at of the boxes and notice that it is common to 2 sums, 45 and 39. They reason that the difference between the sums 45-39 = 6 is also the difference between the other two boxes. and the method they follow generally follows one of the two ways below.
Both of these methods make more sense intuitively of how to solve the problem and they don't bypass seeing the connections in the problem and developing a deep understanding of how it works. Hopefully as they progress though solving one or more extra of these problems they will be able to progress from the method on the left to the one on the right. Although the endpoint is the same the difference is in the connections they have made along the way and this gets to the heart of the difference between fluency and understanding.
I am mid way though a few other posts on the EC conference but I started this on on the plane ride home. The speakers from the stage at EC16 were people working on a diverse range of things on a range of different levels. Even though each talk was only for 10 mins the stories they told in that time were so incredibly powerful.
I had all intentions of writing some notes as I went though listening to the talks so I wouldn't forget, but I found myself captivated by what they were saying. Not only did I forget to write things down at the time, but I think it would have almost felt rude to do so. Therefore I am writing most of this from memory and trying to fill out the details some two weeks later, so I don't feel I am giving some of them justice..
Hayley and Liz
Most schools have avenues for student voice but how authentically are we actually seeking and listening to that voice. They are who we are go to work for, they are who our efforts are directed towards so their voice needs to be heard clearly and loudly. Many student voice models are run by teachers based on agendas organised by teachers that align with the priorities that the school wants them to work on. But if we go large and truly give students a voice then big things and much better outcomes are possible. Their student leadership model is fantastic. I really loved the ideas of students organising and running their own meetings and agendas and also loved how they research and run professional development sessions for teachers, I also loved the idea that student engagement/learning proformas were designed by the students themselves and used as part of performance development process for teachers
Schools can and should be places that we are not just nourishing the mind, but also the body and soul, they are also places where we can do some good for our planet. Their sustainability program is a great example of what can be achieved in this area. Setting them up with a range of life skills that will serve them well moving into their futures. From her talk I also took away that we really need to invest in what we value. If we promote healthly lifestyles in our education programs then we should also be promoting them though all aspects of our schools, including our canteens, this is hard since good food isn't cheap and cheap food isn't good, but they make it work.
Brett's message was a powerful reminder of the impacts of kids lives outside of school. Some kids that we work with are coping with a lot outside of the class, Whether they are acting as carers for siblings are having to work a lot to support their families who may be unemployed, they are dealing with a whole lot of stuff that at most times we may have little or no idea about. As much as we want their focus to be on their schooling during the day, for some kids they have much bigger things going on and their behaviour at school is probably a result of that. Care and compassion goes a long way to supporting kids.
As a student it was interesting to listening to Amy talk. What became obvious really early on is that she was very aware about what works with her in relation to learning and what doesn't work with her in her own learning and I suspect this is the same for a lot of kids. But are we listening to them? I also picked up from this talk ideas around curiosity and creativity. These are things that we have a lot of when we are very young but it manages to get driven out of us by the time we get out of the schooling system. However the future needs creativity and it needs curiosity, it may even be the key to getting more girls involved in STEM fields
There were a few messages from Jason that I picked up on. Firstly when you empower kids with the same sorts of entrepreneurial skills as we have developed though our involvement with EC then they can show you some really amazing things, they develop a whole lot of skills from that type of thinking, even from a very young age. Secondly was his message around working with and within systems and showing that sometimes you just need to do it and prove it gets results instead of asking for permission all the time, their response may be based on the perceived likelihood of success rather than how successful it could actually be.
Companies can be commercially successful and socially responsible, it doesn't need to be one or the other and we need to be encouraging much more of that. Unlike individual schools or individual teachers the have the resources and the connections to tackle some really big problems. However in deciding what problems they can or should tackle they need to talk to teachers like Yoobi did. Even though most teachers do not mind paying out of their own pocket for school stuff, they identified that teachers shouldn;t have to and that they can help. I loved hearing about their business model, for everything you buy, they donate one themselves to a classroom in need
We all we open up our schools and invite our communities in to learn from what we have to offer, we offer a whole range of things. We offer these opportunities based on what we think it is important for them to know, but is that what they want to be learning? Is that something that they really want to know? Are they getting anything out of it they will find useful. If we want to promote learning as a life long pursuit then surely our school environments should play their part in that. However in educating our communities we are not dealing with a set curriculum, if they are going to come in, we need t offer what they want to learn. When we truly embrace our communities as learners and as partners in their own and their families education, then the school community that builds is powerful.
Tristan's talk was one of the power of community, our local communities that we live and work in, and our shared communities such as the EC tribe. What we are doing in our own communites is important and needs to be shared with our wider communities like the EC16 conference, people need to hear our story, our journey, our success. It is through sharing this that others can learn from us and hopefully have the same success. However we also need to listen to the stories of the EC community to learning what we can from them t really hear what they did and how they did it so that we can go back to our own communities armed with this new learning to strive for better outcomes.
I learnt a lot from this talk, it was a really strong example of being able to be amazing things, in really tough environments against some significant odds. Her drive and her passion for what she is doing was, I think, key to her success. On message I really took away from her talk was a conversation she said she had with her father about understanding the reasons for doing things. It went something along the lines of if you don't understand why you are doing it and I don't understand it either, then I can't make you do it. It made me think about the nature of schooling, how many things do schools still do because they have always been done that way, do the teachers and do the students understand why it is done that way, and if not, why are we still doing them?
At times our kids with disabilities are being denied things that we take for granted, like the ability to communicate. Schools are places that can help kids with communication difficulties to have a voice, but how do we make sure our communities are listening and helping to support these young people to use this voice outside of school. It was also really great to hear her ideas or scale with developing apps to replace physical resources, stickers in cafe windows to identify which places are 'friendly' towards the change she is leading, etc. She had a very clear idea of where she wanted it to go and is a strong advocate for her students.
Jessica and Kerryn
Through EC we know the power of storytelling in sharing what we have learnt with others. Learning stories that I have started to become accustomed to because my daughter is at kindy. I know the power there is in being able to see her in the moment of learning something new, or working with others to complete a task, to have that photo or that video as well as the short story to go with it. For many kids I think that that grade at the end of the term and even the comment is too abstract. Kids need to see what we see in them when they are learning, it is incredibly exciting for us to watch but most of the time they may not be aware that it is happening. Made me think a lot about the nature and role of feedback in class.
Thanks for your contribution to the event it was very much appreciated, I would love to see how your projects are progressing in the future.
Part of setting her along the right path is sending her off each day with the right frame of mind, I want her to understand the important things that she can do each day to make sure that she is getting the most from her education. The video above is of my daughter talking about the 3 things it is important to do each day at kindy. These things are
We talk about these regularly, when I get home from work we talk about these three questions and what she did in relation to them that day. We also incorporate these into our own play. When I play with her I encourage her to do tricky things, to ask good questions and to do things that are fun.
I want her to "have lots of fun" because I want her to enjoy her education, I want her to love learning, I don't want her to see it as a chore. I want her to "do something tricky" because I want her to challenge herself, to try something new, to try something she is not sure she will be able to do, to fail, to try again, to develop that persistence that means she will not give up in the face of difficulty but enjoy the challenge. Finally I want her to "ask a good question" because I want her to be curious to look at what she is learning and ask those "what if..?" questions, to be interested enough in what she is learning to want to know more. I want her to know that it is important to ask questions when you are not sure or when you need further clarification. These are three important things for her to do as a 4 year old, they are also three important things for her to do as a 14 or 24 or 54 year old.
Sometimes she comes home from kindy having tried all those things, sometimes she has only had tried one or two. I feel that she has made a good start if she can keep those three things in mind each times she steps though the door of kindy / school each day. My concern is always is she going to get the opportunity to do these things, are the adults in the room going to provide those opportunities for her and for my son when he is old enough. Are her teachers going to make learning fun, I know it is not always fun all of the time, but I also know that just having fun, doesn't always mean that she is having fun whilst learning. Are her teachers going to provide her with the opportunities to be challenged to see what she is doing at the time look for ways to be able to push her a little bit further, are they going to encourage her to keep trying when she gets frustrated (which she will) or will they give her a way out and reduce the challenge. Are her teachers going to evoke her curiosity, to give her situations where she needs to ask good questions or will they just tell her lots of stuff and stifle that curiosity.
I want her teachers to know that these are things that I find important and I want my daughter to be able to talk to her teachers about why she thinks they are important as well.
It was interesting to talk to my daughter the other morning about these thing. She said "Dad sometimes it can be two of those things" When I asked what she meant by that she said "Most of the time doing tricky things is fun so it is two things". This was fantastic for me to hear because she realised she could enjoy challenge, I am so proud of her making this connection.
Over the past few years I have heard one phrase a lot It is a phrase that although not unexpected, it causes me concern. This phrase is:
"Teacher's don't read research"
The obvious question then becomes "If they are not reading research, what are they reading?". For most teachers I have come across it is books of resources, articles about their content or maybe blogs such as this one that might describe activities that a teacher has done. They tend to read stuff that they can pick up and take into their class the very next day and use it.
So why is reading research important?
My simple answer to this is that reading resource books changes might change a lesson, reading research can change your outlook on education in general and can transform your classroom over a much longer period of time. Educational research is not about finding a great lesson on area of a square, it is about the big questions in education
This is only a small fraction of the questions that researchers are attempting to answer. They spend years investigating even investigating a small part of one of these questions with the aim of shedding some further light on the rest of the story. The answers they come up with are important, they describe how the outcomes changed not just for a few, but for hundreds or thousands of kids. The answers are important as they force us to examine what is currently happening in our schools, and in our classroom. They get us to judge our own day to day practice against the research piece we are looking at and look for commonalities or differences. It forces us to fundamentally examine what we believe about our profession and the way we approach it. It has the potential to change every part of our day to day practice. This same level of scrutiny is not put on individual lessons.
Research is also incredibly important as there are a lot of practices that are prevalent in many schools that have been disproven strongly by research. This means that there are a number of practices occuring in schools around the world that have been shown to have a negative impact on student outcomes. Some examples of this that I hear a lot when talking to teachers are:
Why don't teachers read research?
I think there are a number of reasons don't read research, I think some of the reason are based on the teachers and some are based on the researchers.
In conclusion if we are going to continue to grow as a teacher as we expect our students to continue to grow then looking for lessons just won't do it, we need to really pay close attention to the research so that evidence-informed practices can better influence our teaching. I see it as my role as an instructional coach and a faculty leader to digest this research for and with teacher so that it may better inform our practice.
.There are times when you are teaching that you realise you are looking outwards when you should be looking inwards. When looking through many of the tweets I read about teaching I came across one that seemed particularly appealing and that I wanted to know more about.
The reason I found it to be so appealling is that it seemed to take something that I have used with students for years and instead of turning the spotlight on what they choose to spend their time on in class, it was putting the spotlight on what choose to spend my time on in class.
Typically I have used this idea of time to give students a sense for how much of their school year the may be wasting by some of the choices they make in regards to being slow to start and in attempting to pack up early. The idea I look at with them is quite simple. There are 40 mins in a lesson and 40 weeks in a school year. Therefore if they choose to waste 1 min every lesson then over 1 year this will equate to 1 week of schooling, Therefore it they take 5 mins to get to class and get ready to start and then try to pack up 5 mins early then that is 10 mins each lesson and 10 weeks or 1 term of schooling missed each year.
I was really excited to see that the talk was posted online (see below). The way Andrew Stadel looked at this in his talk was in ensuring that we look at ourselves and the way we choose to spend class time with the same level of scrutiny. He advocated the idea that we need to use the lack of time our advantage to really focus on those practices that are most effective, to squeeze as much learning out of that time rather than focussing on ineffective practices. I would take that one step further, but along similar lines and say that I should not be spending 1 minute on something that I am not prepared for students to spend 1 week on.
There have been a lot of books previously that I have got a lot out of, normally it is a chapter or a passage or a series of activities, but none that I have felt compelled to write about, this book was an exception to me. Although I feel that I was still engaging with many of the ideas I learnt though the course I wanted to be refreshed, re=invigorated and re-inspired, I wanted to that burst of enthusiasm that I got when I was doing the course. I wanted that renewed sense of purpose, to look critically at what I am doing to see if I am on the right track and to look for what the next challenge is. With a project that I am working on already at scale within our local area (http://www.empoweringlocallearners.weebly.com) I wanted to really look at how it was travelling and despite the success, where the current issues may be
I wasn't disappointed.
I guess the first thing to say about this book is that it doesn't feel like a book, it feels like you are having a conversation with a mentor. It feels like you are sitting down with someone who believes in you, believes in what you are trying to do and believes that you are the person to be leading it, they are just there to give you what you need, when you need it. Sometimes it is that dose of inspiration such as a story from their own or someone else's desire to innovate, sometimes it is a supportive word to help pick you up when things might not be going well. Other times it is is a tool to help you move forward when you may have hit a wall. Sometimes it is about giving you the kick up the backside and the reality check you need to make sure you keep your ego and potentially your tunnel vision in check and to keep you focused on who you are really trying to make this change for.
As I moved though the book I realised that it doesn't necessarily frame this type of innovation and leadership as all puppy dogs, rainbows and unicorns. The book is all about "unleashing teacher led innovation in schools" so they talk a lot about leading change when you don't necessarily have a "leadership role" in the school. It talks about the people who will keep telling you no, that you can't do it, that they don't want to do it, that it is too much work, but it also gives you ways to work with these people to try and get them on side or to make sure they don't impact on what you are trying to do. It talks about how you will fail over and over again, that some of your ideas will be awful and that people you respect may also tell you that ideas you like are a bad idea, but it also talks about how this is an important and necessary part of the process. It talks about how you will probably put more of your physical and emotional time into this than you ever have with anything also before in your working life, but it also shows you what the rewards of it can be. In implementing this myself from the course back in 2012 I can see that it paints a realistic picture of what to expect. What I like is that they not only tell you what to expect in terms of the challenges, but they also tell you at what point in the process you can expect to come across those challenges.
The first section of the book really gets you think a lot about what you are passionate about changing, not just what annoys you, but what keeps you awake at night, what you lose sleep over, what you see day after day that you know would make all the difference if you could just change that one thing. However it also gets you thinking about what their world would look like if that did change, how it would be different. This focus on narrowing you down to what you are deeply passionate about changing really sets the scene for the rest of the journey though the book.
As you get into the second section of book the really get you drilling down in understanding the problem you are trying to solve. They are very clear and deliberate in slowing you down so that you don't jump to implementing something to solve the problem when you really don't understand the problem enough. They work with the premise that the better you understand the problem, the better you can design a effective solution as you are getting to the root of the problem.
The third section moves into how you create, test, reflect and refine effective solutions to your problem. But it is more than that, it is really about how you do these things in short cycles, how you can get a quick idea for how effective your solution will be before you pour too much of your time and effort into a larger scale test of concept that may or may not work. Finally the book looks at how you share your success and how you can scale it to involve more classes, more schools, more communities, states or countries and ultimately have a positive effect on more children.
I would recommend this book to anyone who is passionate about creating change and working towards something better for your students. The simple idea of working towards solving a problem that you are absolutely passionate about means that you are much more heavily invested in it, but also more likely to succeed if you stick with it, this book seeks to keep that journey on track, to keep it progressing and to building it in a sustainable way. With that focus in mind I think if every teacher in Australia read this book and took on the ideas seriously then a lot of the current problems in education would be moving towards being solved by the end of the year. However in saying this not everyone is at a point in their life where they can commit to a project of this kind and a book such as this may be too daunting for them.
This is the sort of book I would give to those teachers that I have really strong, thought provoking conversations about education with. I would give it to those who identify problems in their classroom or school but don't place the responsibility for fixing that onto others, they strive to be the change that they want to see in the school I would give it to those who speak with a great deal of positivity and optimism about where their students will end up given the right opportunities. I would give this book to them because they are the ones I want on my team when I start to implement this more formally again, I want their ideas, their insights and their criticisms. Though giving them this book I would also hope that they would keep me honest to the process. I also hope that if they found inspiration from this book for their own change project then I hope they would bring me along to do the same.
I can see myself picking this book up again and again, In fact I have already gone back and revisited some stuff based on my current thoughts and I have only had it for a week (it is looking a bit worse for wear already). The thing is for me, is that they get you thinking different and working differently to what you have ever done previously, Never before have I written in or highlighed a book, but I have done both these things with this book (although my OCD made me use an orange highlighter because it kinda matches the front cover.). It feels like a working document that I can continue to come back to because it has been set up that way
If you can ever manage to get into a course with these guys, don't hesitate, just do it. If you don't get that opportunity then this book is a great start for you.
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.
Mathematics Coach and Coordinator in Regional South Australia. Current driving the Empowering Local Learners project as a numeracy strategy from pre-school to senior secondary.
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Opinions in this blog are my own and do not necessarily represent the views of my employer.