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.
I have been wanting to talk about this for a few months but have only just got around to it now. It was a conversation I had with one of my students whilst he was attempting some difficult questions in class and having little success with them. He had asked for help and I had provided some assistance with the question, however the conversation quickly turned to him wanting me to show him how to do it. It would seem to be quite a reasonable request but I knew that if I did, I would be taking the learning away from him, it was just a question that he had tried and failed a few times and he didn't want to think about it any more. The assistance he was given was enough to get him started, but not enough to show him what he should be doing. This is where he said to me
"This class is pointless, you don't teach us anything, you just make us learn"
It was said in a way that I think was supposed to make me feel somewhat bad about what I was doing, that by not showing exactly how to solve the question he believed I was being a bad teacher and I should feel bad about that. However the comment had quite the opposite effect on me. It made me more convinced that I was on the right path with them. As I said to him at the time, I believe that it is one of the most positive things anyone has ever said about my teaching.
I think in that moment he had recognised that the schooling process was not about me as the teacher anymore, I was not the central person in the process. He discovered that he was the person central to his learning, it is only my role to be there to support that learning. I have been making a very conscious effort to support productive struggle in my class, to not jump in and save them at the first sign of struggle, to let them to continue to think about it and to try new things to work with others. This comment I believe was a clear indication that I am on the right track.
In mathematics, I think the focus on getting the correct answer has permeated much of maths education, with a bit focus on tests, worksheets and textbooks in a lot of classrooms around the world it is easy to see maths as a range of questions that you need to get correct answers to. I can tell that students believe that this is the case as often all they write in their book is the answer thinking that it is that number that I am only interested in.
This focus on trying to find one magical number amongst all of those infinite possible answers I believe is a major contributing factor to maths anxiety. I can see the nervousness on the faces of students as they ask me "is that right?". I feel that if I say that it is correct then they will feel a sense of accomplishment, but the level of anxiety will come back on the very next question. Conversely if the student gets the question wrong then their whole world tends to cave in, and you start to get comments such as "I can't do maths", "I'm stupid" and "this work is too hard" creeping in. Their whole self-concept as a learner of mathematics tends to hinge on whether each question they come across is correct or incorrect, this self-concept can change from question to question as they get questions correct and incorrect.
With a quick google search I find the following definitions for the word answer.
What I find really interesting about this is that when you look at it, especially in the first definition, it mentions nothing about correctness, it simply describes an act that you do in response to a question. It also points to the idea that an answer is more than a single statement response, it includes how you thought about it, your solution, how you thought about the problem becomes an important part of the answer. So in this way we can define the answer to a problem as the point where you felt you could not add any more to your thinking about the problem. The answer is not some magical number, it is where your thinking about the task stopped stopped.
Therefore I tell my students now that I don't care what the answer is, that is not important to me, what is important is your thinking. By looking at their thinking I can see how they thought about the problem, what mathematical thinking they may have used to solve it. By looking at where their thinking stopped I can see where they believed was the end point of their thinking, the point where they believed that there was no more to do. If they are multiplying fractions and have followed a correct line of thinking but have not simplified the answer it is not wrong, it just tells me that they did not recognise that they could do more thinking about the solution that they had come up with.
So why is this so important? I have also pointed to some of the reasons such as the anxiety it causes. But I also think it is because students believe that if they don't get the correct answer, then they haven't learned anything, the time they spent getting a wrong answer they feel is useless. But wrong answers can teach us a lot. Often with more complex problems mistakes are expected and celebrated as they gives us more of an insight into the problem. If you are sitting there for an entire 90 min double lesson and working on one complex problem without giving up there is a lot of learning that has gone on there regardless of whether you have got a correct answer or not. The simple act of trying different approaches means that you are learning a lot and using a lot of mathematics in some highly flexible ways. On multiple occasions through my teaching career I have seen a number of students get the correct answer with some incorrect thinking, and an equally high number of students get the wrong answer with highly insightful and correct thinking.
For me now it is really about changing the messages that I give to my students, it is no longer "what is your answer to the problem" it is now "can you tell me about some of the thinking you had in relation to this problem?"
With the new school year starting for me in just over a week I have been thinking about what I want my mantra for the year to be. What is it that will not only raise the achievement of my students, but also that of my own work and the teachers in my faculty. "Fail more often" is going to be my starting point for the year as I think it has the potential to be the path to greater success. This mantra is similar to what was said during my leadership training with Education Changemakers, quite often the program facilitators Aaron Tait and Dave Faulkner would say "Don't worry, be crappy". This idea really resonated with me and fit well with some current reading I have been doing on the Growth Mindset by Dr Carol Dweck.
The idea of failure, no matter how small, is debilitating to lots of people. They would rather not try and avoid failure, rather than give it a go and having the possibility of not being successful. Why is this... because generally as a society we are very intolerant of failure, it becomes a label on the person rather than a commentary on the situation. Instead of "I failed to get this right", the internal dialogue becomes "I'm a failure", instead of "that program didn't really have the intended outcomes" it becomes "They are bad at their job". This view has to change, students need to see that failure is a major component of success, it is not the opposite of success. They need to see that failure is an important part of the learning process and that it is vital to fail if you are going to identify and rectify those areas of weakness.
So why do I think this idea of failure is so important, well I have a few main reasons. You will have to forgive me with this post, I am a bit of a fan of a nice quote and this post is going to contain a few
I am curious to see how this goes and how students and staff respond to my quest to fail more often, but I will comment on this as the year progresses.
I have been thinking about my previous post on the importance of developing a growth mindset towards all aspects of your education and how this can be done. The word 'yet' has the potential to dramatically improve your outlook on your education and encourage you to try harder, but why?
Saying 'I am not good at Maths' gives the impression that it is a feature that defines you, it says that you are just a person that will never have the ability to do well in the subject, it just isn't in your DNA. However by saying 'I am not good at Maths yet' it completely changes this outlook. It does acknowledge some difficulty in understanding, but it also acknowledges that it is something that can be improved on, it is something that is possible to attain. 'I can't do it' says that no matter how hard I try, it just won't happen, so extra effort is pointless. 'I can't do it yet' means that with extra effort there can be improvement and if I continue to work and continue to improve then I can eventually overcome those difficulties.
This is a message I need to instill in my students and in my feedback them. Whenever they say 'I can't do it' I need to make sure I get them to also say 'yet'. I don't want them to take this easy option as it limits their improvement and their outcomes.
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.