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.
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?"
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.