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.
When students think about presenting their solution to a mathematical problem visually I get very excited because I find those visual solutions hard to generate myself, I am getting better it, but I don't see the mathematics in that way when I am solving a problem generally, I get too wrapped up in the equations in the formal mathematical notation. The reason I get excited about those visual representations for a problem is that they often are much easier than the formal mathematics and they lead to some great mathematics.
The other day I did a task with my class that I got from Professor Peter Sullivan from Monash University who I had the pleasure of working with once per term for three previous years in my work as a numeracy coach. The question is as follow
I like this question on a range of levels
One of the groups working on this task came up with the solution shown below, it has been altered from the original (which was just dots showing the same information) but the same thinking was there. They first started by looking at the 0.7 and 0.6 and converting them to 70% and 60% which they then turned into 70/100 and 60/100 which simplified to 7/10 and 6/10. From this they reasoned that ten was the minimum number that could be on the train. From here they attacked the main part of the problem by first assuming that there was as much sharing as possible, making sure everyone with a computer also has a backpack. This gives six people having both items, this is shown by the image below on the left. They next thought about orgainsing the same but with as little sharing as possible, by making sure everyone who didn't have a backpack needed to have a computer. This scenario gave the image on the right below, an overlap of three. Hence they gave a range of answers as being between three and six out of ten people.
The animation below shows they range of answers with more clarity
What occurred to me as I was documenting their thinking on the board is how nicely this representation led into the intended purpose of the lesson, Venn diagrams and two-way tables. Simply by circling the laptops in one colour and circling the laptops in another I had generated a fairly accurate Venn diagram as shown below. You could clearly see in each case how many were in the intersection of the two sets, how many belonged to only one of the two sets and how many were outside of those two sets.
What I really liked about this is now easily it made the transition to Venn diagrams and two-way tables. from our initial starting point of probability of simple events.
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.