Here in Australia we are about to start our school year, with teachers back at work next week and the kids the week after that. This year marks the start of my 15th year in the classroom, and I consider myself very lucky to have the career I have had so far. I have had the chance to be involved in a lot of projects that have transformed learning for kids at my school but they have also transformed me as a teacher and transformed me as a leader.
Over the last 5 years I have been strongly involved in the Empowering Local Learners Project and for the last 3 of those years I have had the privilege of leading the implementation of this project across 16 schools and preschools from preschool to year 12. As a result of this work, kids from across all of these 16 sites have shown significant growth in their numeracy outcomes national testing (NAPLAN), but more importantly that that kids are now loving maths and enjoying challenge, this was not their relationship with maths in the past. For me professionally it has transformed every part of my teaching practice. I have had the opportunity to work with some amazing teachers locally as well as building strong relationships with Flinders University, particularly Deb Lasscock and Kristin Vonney, two phenomenal teachers from the Flinders Centre for Science Education in the 21st Century and that centre's leader Professor Martin Westwell. This work has given me the opportunity to present both nationally and internationally at both education conferences well as research conferences and has been recognised in our states teaching awards over a number of years.
However this year I am finding myself in a place where I need to let this project go. I will not be in a position that I am leading it, and there will be much few people involved than previously, the project will be on a much smaller scale than previous years. Therefore my level of involvement in the project will be limited at best. I have taken this hard, this hasn't been easy for me to reconcile in my own head, it really seems like it has been a grieving process. So much of my time and my energy over the last 5 years has been poured into this project, and so much of my identity as a teacher is wrapped up in the work, so the process of letting it go has been hard.
But as the saying goes as one door closes another opens. This year I find myself in a new position at our school, I have responsibly over leading pedagogical innovation across our school, in taking the work that I have done with the Empowering Local Learners Project across the town, as well with my own mathematics faculty in the school, and extending this work to other subject areas in my own school. Part of this position is the development of curriculum and pedagogy for our new STEM centre that will be built over the course of this year. This is a very exciting time for our school, in creating new opportunities for both our students and our staff. In embarking on this new job it is also an exciting time for me and I look forward to the challenges ahead.
I guess the point of this post is that it was started by what I perceived as a big loss to me professionally, the loss of something I had spent more than a third of my teaching career on, but in reality it has been a gain. Even though I am sad my involvement will be limited, this is not a project I need to let go, the work will continue in my own practice despite my level of involvement. As one teacher said "There is no way that you can take this project out of me", and it is true, no matter where I go with my career, this project has permanently changed me as a teacher. I know that with this project I have been given a lot of opportunities that some people never get in their teaching career so in my head I need to reframe it it is something I need to move forward with, instead of something I need to let go.
As with any professional learning experience that we have found particularly inspirational, it is about what we do with what we learned once it is all over. We can be sad that it is over, but we need to look for those open doors that we can use to help move it forward. This was part of my reason for choosing to do the #MTBoSblog18 challenge this year. Part of me helping to move the project forward desipite my lack of involvement is to keep myself accountable to that and this blogging challenge is one small way of keeping myself accountable to it. Much of the work with the project was inspired by MTBoS members so it is only fitting that I share what I have done with this work back with that community, to also let that community know how I am moving forward with some of their ideas.
This post is one I have been meaning to write for a while, at least 2 years in fact, I have wanted to share it as it has had a dramatic impact on my own classes and also on that of other classes in my school, I guess I just never have gotten around to writing it down.
Teachers at our school have made the decision to not to use textbooks to teach mathematics in the middle school. I think that this move has been a very positive one for our school. It is not that I feel that textbooks are evil, in fact I feel their quality has improved in recent years. However I feel there are still some parts of their design that impact on how people with engage with them, staff and students alike.
When making the decision to no longer use a textbook for maths class I needed to find an appropriate replacement.
Textbooks are good at providing lots of questions for students to practice the skills they have learnt, and this practice is important. However I needed to find an option that did not have the excessive scaffolding and the extensive quantity of questions that I saw in most textbooks. Many of the worksheets I found online has the same characteristics at the text books, so I began to think about how I would design problem sets myself.
Designing the problem sets
When I sat down to think about how I would design my problem sets I wanted to keep some design criteria in mind these criteria were:
One of the question sets I came up with are shown below. Underneath that image I will explain the design of them.
Impact of the problem sets
Greater levels of metacognition
One of the most interesting observations I have seen from students engaging with these problem sets is that they seemed to become much more metacognitive. This is evident in where they choose to start with the question sets. Some have talked about believing they can do the level 2 questions, but really want to work on a few level 1 questions first to make sure they have it. Others have attempted the level 2 or three questions, given it a go for a while, haven't made progress and have moved back to try the level 1 questions. There have also been students who have looked at the level 1 and 2 questions and have made the determination that they know how to do them and have spent their time only working on the level 3 questions. This process of having three different levels of question to choose from has made them much more aware of themselves as learners and of what they need to do to move their learning forward.
All students have had the time they have needed to work on their questions of choice
In looking at the problem sets with my class now, I feel that they all feel as if they have enough time to work on the questions they have chosen and feel comfortable attacking. If I take the level 1 questions for example, I know that some could be through those questions very quickly and there are some that will take much longer. If I look at my classroom about 5 years ago I would say that the time I gave them to do the questions was aimed at the the middle, the ones who had it finished early and got bored and the ones who were struggling never had enough time to finish them. With students working on different difficulties of questions they all seem now to have the time they need to finish the questions.
They are attempting much more challenging work
The comment I get a lot when students are working on these problem sets is "why do you have to make it so hard". This is normally from students who are working on the level 3 questions. My response in this situation is always the same "Doing the level 3 questions is your choice not mine, so you are making it hard on yourself" to which they normally reply something along the lines of "yeah well those other ones are too easy". What is clear through this is that they they are no longer just happy to do the easy ones, the could do that and finish really quickly, but they don't. Students seem to be really working on questions that they feel are just beyond their current level of understanding and they are striving to understand them.
I can now see the slow, deep mathematical thinkers
Having done the Jo Boaler courses one point that is emphasised a lot is not to make maths about speed. It talks at length about how mathematicians do maths, how they are deep slow thinkers. Reflecting on previous practice I realised that for those deep slow mathematical thinkers, there was a time that my classes did not offer anything to those students, I didn't even know they were there. I didn't see them because their diagnostic data backed up what I saw in class, but that was because I was asking them to work in class in similar ways to which the test was administered. What I am seeing now is that there are quite a number of students who do not perform well under the time and pressure of diagnostic testing, but have flourished with these problem sets as they have the time to sit with the problem and think about it rather than being pushed through endless problems. They are showing much greater levels of mathematical thinking than some others who score much more highly on those high stakes tests.
The quality of their work is much better
I have seen a noticable improvement in the quality of the work I recieve since using these problem sets. Much of it I think can be attributed to giving them problem types that allow them to demonstrate their understanding and then the time to work on them.
What I find challenging about these problem sets
Despite the massive, dramatic change these problem sets have made to my class, I still struggle with some aspects of them. Most of these are still the tug of war I have inside myself about getting the balance of mathematics right in my classroom
A lot of the activities I have talked about on this blog, or the ideas I talk about, are generally ones I have put significant time into. The activity I am talking about in this post has been a very successful one for me over the last few days. I would like to say that it was because of the careful and deliberate planning I did on the task prior to the lesson, but that would be a lie. Sometimes as the lesson is unfolding you see an opportunity present itself, and by following it through, sometimes planning the next step on the run, you can have a really good lesson. Planning the next step on the run was not a result of being disorganised, but a result of identifying an emerging need and recognising the need to follow up on it before moving any further.
They then had a conversation with their table groups about what they thought would be the colour of the other 5 blocks. Not surprisingly all the responses were some combination of red and blue blocks, however despite knowing that there were lots of other colours of blocks in the storage tub, they had not considered they could be part of the final five.
Next I wanted to introduce the idea of using probabilities to describe exactly what is in the box so I gave them the information listed below and then gave them the time in groups to have the discussions required to figure it out
I have filled the box now with blocks according to the criteria below, can you tell me how many blocks of each colour are in the box?
What was exciting about seeing them work on this was that I finally saw the classroom culture that I have been trying to build all year with them. In working together on the problem they were talking about the problem, they were critiquing each other's reasoning, they were asking questions of each other, they were willing to tell the group when the explanation still didn't make sense to them, forcing the person giving the explanation to justify their thinking more strongly. I think one of the most important aspects of their work though was their confidence with their answer. With these sorts of questions when they tell me they have the answer I try to ask a few questions to head their thinking down a line that creates some doubt that they have found the answer. This isn't done to trip them up, but is more designed to see if they have got to a point where they feel the have considered everything and have come to the only answer that works, to gauge their confidence in their own thinking. Normally when I ask students a question about their answer they take this as an indication that their answer is wrong, but this time, no matter what question I asked them about their answer they had confidence with it as they had determined that 12 was the only possible number of blocks as you could not have parts of blocks.
The next day the aim was to move towards students being able to determine how to calculate the probability of pulling a block of a certain colour out of the box, to help facilitate this i made up a simulation of the box compostion from the previous day using excel. The excel file and a screen shot is shown below.
Like the day before i got students drawing the blocks from the box and this time we tracked the probabilities. when the first green block was drawing I asked them to predict what would happen to the probabilities of each colour.
Overall what started as a sidetrack, developed into some really great thinking, on some really important concepts and I couldn't be prouder of that lot today.
The other day I did something that I have been meaning to do for quite a while now, I deleted every maths test from my hard drive. I did not do this selectively, I searched for the word test in my maths folder and deleted everything. I haven't done a test in any of my maths classes for the last 3 years (other than the compulsory 1 or 2 all maths teachers must do statewide) and can't see myself wanting to do any in the future, it is not a practice I place any value on any more, so this step is me wiping the slate clean.
I have come to this decision by watching my students engage with tests over the years, and in more recent years through what I have learnt about the 'science of learning'. By the 'science of learning' I am referring to the interplay between the neuroscience and the psychology and how this impacts on learning. In particular in recent months my focus has been on developing a stronger understanding of the role of maths anxiety. To be honest I knew that maths anxiety existed, however it wasn't until I saw the video below that I realised how prevalent it was, nor had I taken the time to understand the neuroscience that underpins it.
.The anxiety felt is a result of increased activity in the amygdala, this part of the brain is responsible for processing our emotions, including fear, and for determining what memories are stored in our brains. This consequently reduces the capacity of our working memory which we use to make sense of, and solve, mathematical problems. Because our working memory is reduced we then do not perform as well as we could on that test and this further raises our level of anxiety and the cycle continues. All of this is symptomatic of maths anxiety regardless of the maths being worked on, however the effects of maths anxiety are further emphasised if a time limit is put on the piece of work like what occurs in tests.
I guess what prompted me to think a little bit more about why I hadn't just deleted all my tests was in watching the documentary "Race to Nowhere". In that documentary there were numerous occasions where kids spoke about cramming the information into their head for just long enough to put it down on the page but only a week or two later they could no remember the work at all. This is not the type of learning I want for my students, they deserve better than that
To make that final move of pressing the delete key I needed to ask myself a few questions about tests, these were
However to finish this post off I want to address something you may have thought as you have read this which is, "they are going to have to do tests/exams eventually". I am not naive, I know that eventually, the kids I am working with be required to do tests and exams in their final years of schooling, I wish they didn't have to, but that is the reality of it at the moment. However I also believe that the putting them through timed tests regularly for many years before that is not the best way for me to prepare them for tests later on in their schooling. Kids need the time, the space and the opportunity to develop robust and flexible mathematical knowledge by understanding the connections between key mathematical ideas, this is where I feel the secret lies for success in tests many years down the track, and developing this understanding is where I feel that my role lies. This focus on understanding rather than speed may help them in their tests much later down the path, but more importantly it helps them out a lot with what they are doing right now.
I am in my 14th year of teaching, when I look at how my own teaching it is sometimes hard to know just how much it has changed. But sometimes some small moments that bring that into real clarity, for me this moment was when I was clearing off my hard drive to make room for new stuff as it was getting too full. As I was going through my hard drive I sorted it by age, I figured that if stuff was going to go, it was probably the oldest stuff that hasn't been accessed or edited in a long time. I realised that I still had on there all the stuff I developed in my first year of teaching over 14 years ago. I was curious about the work I gave to my students back then, I was curious about how far I had come since then, so I had a look at it. When I looked at it I noticed a few things
When I reflect on that work now, I realise that at that time I didn't know any better, I didn't intended to do this to my students, I didn't think i was doing a bad job at the time as it was how I learned maths, it was what I learned at university in my preservice teaching program and it was what was expected when I was a student teacher. All of the models and examples around me for maths teaching that I was using to establish myself as a teacher were all saying the same thing.
So out of interest I printed out just the practice problems that i am going to give to my students in the coming term of 10 weeks and then printed out all of the practice problems that I gave to my students on the same topic all the way back in my first year of teaching and the gif at the top of this post is the result of that. 14 years ago, for my 10 week unit of work, I was giving them 70 pages of practice problems. When I then looked at what I am planning on getting them to do the page count came out at 8 pages of practice problems across the 10 weeks. Just this little bit of data has made me reflect on what has changed in relation what I value now that I didn't value then. I am not expecting any less learning from them, so how am I spending the time that those extra 62 pages would have taken up. This additional 62 pages morphed into...
So 2 stacks of paper and 14 years later I have realised I am now asking them to do less busy work, so they can engage in a lot more, and a lot deeper thinking.
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.
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.
Viral videos online attract a lot of attention and normally I don't buy into the hype, the video below is not one I had seen before until I saw it in another teachers blog. However with over 20 million views in less than a year it was clear to me that a lot of people had seen it. It was video I came across in a link in Dan Meyer's blog. The link was a link to another blog that contained the video below, watch the video before you read their post or mine. I would encourage you to support the people that led me to this post by following the links in orange to their blogs.
I really like how the teacher used this video..... I really like it a lot, why I said to watch the video first is what that teacher got out of it when they saw it was not what I initially got out of it, but after reading their post I also realise that there is a whole lot more that this can be used for. In the post the author writes
After we watch this, I like to make the connection to the classroom.
I think that this video works so well as almost every student can relate to two people in the video, the lady trying to fill up and the person watching the monitor.
When you first watch the video you find yourself as the person watching the monitor, you find it hard to put yourself in the place of the lady trying to fill up because you don't really understand why she is finding it difficult to figure out, why she is continuing to make the same error over and over without seeming to learn from it
But after reading that post I started to see both myself and some of my students in the role of the lady trying to fill up because to be honest there are times in our schooling and our lives where we feel like (and we are not) making any progress, we seem to be making the same mistakes over and over and we just can't seem to break the cycle. Quite often I feel that kids won't share their thoughts about the work we are doing or they won't ask for help because they don't want others to know that they are finding it difficult, they don't want to be the only one who asks a question because they feel that others are laughing at them. For some reason they have this reaction to maths more than any other subject. However it also made me think of a few other questions that I may ask such as.
What really struck home though is the last question that this teacher asked about what would happen if the lady gave up and just drove away. It got me thinking about what are the short term consequences and what are the long term consequences on giving up on it. Does she just fill up tomorrow? Does she run out of petrol on the way home? If she does run out of petrol what does she miss, is she late for work, does she miss something really important.
It got me thinking about both the short and long term consequences of giving up in the classroom, I had obviously thought about this before, but this got me thinking about it in a new way. In the short term it might mean they don't understand that concept, they might not be able to do that work over the next lesson or two but from that point it begins to snowball. The course is hopefully built in a way that one idea helps to build on the next, so if you don't understand the concept from this week maybe you also won't be able to follow the ones next week and the week after. Maybe this will mean you can't do the assessment task and that you get a failing grade. But a failing grade again is not the end of the world, but since your program is structured in a way that the ideas build then not understanding that topic may also mean that you don't understand the next topic and the next. Since the work in a year of school builds upon the previous year then maybe you don't understand next year either. Maybe after all this you give up on maths completely and maybe when you have kids yourself you pass that onto them, and they pass it onto their kids.
The account above is a bit dramatic I know but over the days, weeks months and years this builds into a self-concept of yourself as a mathematics learner. Your experiences shape you as a person, you make a decision as to whether maths is something you can do or you can't do. Your self-concept towards a subject effects how you approach it and how you talk about it. How you talk about it can influence how others see you as a learner of a subject and can also effect how others see themselves. If they feel they are doing as well as you and you start saying that you are really bad at maths then they may start to feel that they are not doing as well as they think. This self-concept is something you can break by doing something different, you just need to stop doing the same laps of the same petrol pump.
A few weeks ago I came across an article on my Twitter feed that I thought was really good, it was not a long read but it was one that really challenged me to think deeply about my practice and what constitutes a good day of teaching, I would strongly suggest that you give it a read at some point. The article is 'When is a Good Day Teaching a Bad Thing' by Timothy F Slater (click the link to open the article). The article starts with a description of most teachers idea of an ideal day. Limited behaviour issues, got through the work you planned, students seemed to engage by both answering questions correctly and asking questions that you could answer. It goes on to say one particularly important point
"I submit to you that when everything seems fine, it s probably the perfect time to carefully find out exactly what depth of learning is actually occurring in your class."
The article goes on to talk about a hidden contract between students and their teachers which is an unspoken set of rules that both parties follow. Students agree to behave, do their work, ask and answer questions if the teacher agrees to organise well detailed lessons and work, try to make it interesting, assign work that is very similar to that clearly gone through in class and show them exactly what they need to do to achieve a high grade.
No one ever speaks to each other about these contractual agreements, but you notice it in a class if someone breaks them. If the teacher breaks it by assigning a question that has not been specifically covered as an example in class then the off task behaviors and the cries of "this is unfair, you haven't shown us how to do it" ring out. If a student breaks the contract by not behaving then they are often removed from the class.
When I read through this I went back and re-read the first part and could clearly see that hidden contract at play and the greater importance of that quote. It was seen as a good day teaching because everyone was meeting their part of the hidden contract. However one of the fundamental parts of that contract is that there is little emphasis from the student or the teacher on having to truly think for themselves, they just need to reproduce the work the teacher has already done for them. Students could easily answer the questions as the teacher had already given them the answers, they had written them on their page, they didn't have to synthesise a response, they just had to find it. The teacher could easily answer the questions from the student because the student was only engaging with the work on a superficial level, the work they had gone through, and the questions they had been asked didn't challenge their thinking, didn't target their possible misconceptions, didn't deepen their understanding or draw connections to previous work, it was more than likely just a slight extension on the previous lesson. There was no way of them thinking deeply enough about the work to ask a really good thoughtful question.
Those days where there are tasks given to students or questions asked of them that target some deeper thinking are often not associated with quiet classrooms, Students are challenged and sometimes this means they are frustrated that they are making some mistakes or that their approach just doesn't seem to be working as they thought it would, they might be frustrated that the are not sure where to start. This may be coming out of them thinking they should already have the answer somewhere in their book, it might be coming out of the idea that they have to think about things differently to they ever have before.
What ever that reason for the frustration it can be a powerful motivator for learning and a powerful tool for improvement, but the key is just keeping them frustrated enough to keep trying rather than so frustrated that they simply give up. That frustration of knowing you can do something, but you just don't know how to yet is a frustration I know well, but it is one I have had to learn to become comfortable with. The idea of knowing there is just something small you are missing, someone you need to talk to, a different way of looking at it, something that is just outside your reach is one that is important in not only building conceptual understanding but students who know how to learn and have resilience in the face of setbacks.
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.