I haven’t blogged in quite a while and I have a lot to reflect on, so this is a long one.
The timing isn’t always right when opportunities present themselves, but who wants to miss out with so much to learn? So at the end of June I was in Sydney at an iTunes U course, committing to writing and publishing a course aligned to the Australian Curriculum by mid August, knowing that I was signed up to start Stanford Uni’s 8 session online “How to Learn Maths” course with Jo Boaler on July 15th, day 1 of term 3. Needless to say the holidays were spent working on the iTunes Course. I’ll write more about that in a future blog. I am so glad I made the time for both.
I’m half way through the How to Learn Maths course and it’s excellent. I have always believed that all students can make progress in Maths if they make the effort, and I’ve always encouraged and tried to support students. I had some knowledge of the growth vs fixed mindset research by Carol Dweck and had been more actively sharing what I knew of it to encourage my classes, but this course and the research presented in it has nonetheless been something of a revelation.
The course has encouraged me to be even more explicit in the growth mindset messages that I give students. I have talked about the value of making mistakes in growing the brain and the importance of working on tasks that they struggle over. Of course, that also means I have to give them tasks that do take them out of their comfort zone, and resist the urge to step in too quickly to assist, something I have been guilty of in the past.
The Yr 10 Advanced Maths class I teach has students who have pretty good mathematical skills. Many of these students are, however, uncomfortable when presented with questions in an unfamiliar form and a few, anything completely new elicits comments such as ‘oh no, it’s too hard, I can’t do this’ to which I reply, ‘yes you can, it’s good for you to struggle, it’s how you learn and get smarter’. More recently, 6 months into the school year, there has been less of this resistance as they realise that they have said this before and it’s been proven false. We have worked through some of Dan Meyer’s 3 Act Maths tasks and this week I adapted Fawn Nyugen’s similar triangles mini-golf task to a vector task. Students had to represent the path of the ball using vectors, work out the total distance the ball had travelled and find a vector to represent the displacement of the ball from it’s starting position to the hole. One of the things I personally enjoy about these tasks is that while it involves some struggle to understand the task and how to proceed for all students, it’s often those who wouldn’t be considered the strongest mathematicians in the class, who offer the first suggestions.
Yr 10 Mini Golf Vectors
In Yr 12 we are learning how to find the areas under curves using calculus. Students often get confused about questions where they are finding the area between curves, or where they instead need to subtract one integral from the other. I had them work in groups to produce pictures of graphs that would need to be solved in three different ways. They were told that everyone in the group had to be convinced that their sketches were correct and could justify them, as I could be calling on anyone to explain. The activity generated a lot of discussion and a lot of crossing out and starting again. The students found it challenging at first, but once they got started they were really thinking about what features would have to be present to match the required method. Each group then had to draw their suggestions on the board, and the class evaluated, discussed and suggested changes. It was really successful and while it took longer than I had planned, it was evident that students developed a stronger understanding and I would definitely do this again.
Yr 12 How do we draw this?
Sharing their solutions
Some of their responses
The clearest evidence that I am having some success getting the growth mindset ‘you CAN do Maths’ message across came this week from two year 7 students. Both of these students have big gaps in their maths knowledge and skills and both have told me, ‘I’m not very good at maths’. I received unexpected emails from each of them this week.
I’d used an approach shown in the course: Does it make sense? Convince yourself, convince a friend, convince a skeptic, at the end of last week when we discussed how to decide which fraction is bigger. It was clear from the look on this particular student’s face that she was not ‘convinced’ by the explanation given by others in her group, so I pressed them to find a way to make sense of it for her. Her email contained a link to an educreations video. She wanted to show me what she had learnt about comparing, adding and subtracting fractions. Her video contained 4 examples, each with full working and a clear narrative. Yes, she subtracted a larger fraction from a smaller fraction and got a positive answer, but we haven’t covered negative numbers yet, so that’s just something for her to learn. And her answers weren’t simplified either, but she was rightly proud of the progress she’s made.
The email from the second student said something along the lines ‘you said we could improve the work we did and show you again. I read what you said about the mistakes in my stem and leaf plot, I have redone it correctly and here is my Data Keynote again.’ There have been opportunities to improve work in the past, but this student has never taken them.