How does knowing your students change the way you teach? A conversation with Eddie Woo
This video was originally published 2 August 2017.
Eddie Woo chats to CESE about maths, teaching and what works best. Listen to the full conversation.
Teaching is an endlessly creative profession, because when you’re in the classroom you really can do things any way that you want, and so I like to think that once I have a good grasp of, here’s where my students’ strong points are, here are the parts of mathematics that they enjoy, I can take those, I can accentuate them and the parts that they struggle with, once I know what they are, I can make sure I’m providing additional support underneath those areas. So as a perfect example, algebra is a struggling point for a lot of Year 7 and 8 students. They first encounter it and then they either get it really quickly – ‘oh this is just like patterns that I’ve looked at before’, or they learn it as a set of rules that are sort of arbitrary and they don’t really understand why, but if you do this with the brackets and you multiply both things then you get the right answer at the end. So if I understand quickly, alright students are struggling with this, then I’ll adapt the way that I explain things as I move forward.
One of the things that I love doing is demonstrating that every algebraic expression can be represented with a picture. It doesn’t matter how complicated it is, obviously it can start to get a bit tricky, but this goes all the way back to when the ancient Greeks were doing a lot of their work with numbers, they wouldn’t have said algebra the way we do, but they were constructing things, they were trying to construct, you know, irrational numbers and solutions to polynomials, they would do that all with geometry, and that’s why to this day, a pair of compasses and a straight edge are a necessary set of tools in every mathematics student’s repertoire. We get this connection between numbers and geometry from them, and even though now we’ve sort of left that behind in many ways, one of the reasons why it’s so useful is that if you can say to a student ‘okay A plus B, put them in brackets, two different numbers, any numbers you like, square that, A plus B, all squared’. The number of students who will say ‘that’s A squared plus B squared because there’s two things and you square them’, is countless. However, it is so simple to overcome that misconception by saying, ‘okay, you talked about something that was squared. Let’s draw a square. Let’s make that A plus B. It’s a square, so let’s make this A plus B. What emerges? There’s the A squared, there’s the B squared, but there’s these extra things, there’s these ABs. There’s two of them that are there which escaped your attention before’.
Drawing a picture often helps students. For others, who don’t need that, they just want to get straight into the algebra, they want to go straight to the symbols. They don’t want to have pictures in their way. So if I can identify, alright, here’s a weak point, here’s something where you need additional support, where I want to give you another analogy, another metaphor, another perspective or entry point into this topic, that’s where me knowing my students’ strong points and weak points is really valuable.
One of the things that I love doing is demonstrating that every algebraic expression can be represented with a picture. It doesn’t matter how complicated it is, obviously it can start to get a bit tricky, but this goes all the way back to when the ancient Greeks were doing a lot of their work with numbers, they wouldn’t have said algebra the way we do, but they were constructing things, they were trying to construct, you know, irrational numbers and solutions to polynomials, they would do that all with geometry, and that’s why to this day, a pair of compasses and a straight edge are a necessary set of tools in every mathematics student’s repertoire. We get this connection between numbers and geometry from them, and even though now we’ve sort of left that behind in many ways, one of the reasons why it’s so useful is that if you can say to a student ‘okay A plus B, put them in brackets, two different numbers, any numbers you like, square that, A plus B, all squared’. The number of students who will say ‘that’s A squared plus B squared because there’s two things and you square them’, is countless. However, it is so simple to overcome that misconception by saying, ‘okay, you talked about something that was squared. Let’s draw a square. Let’s make that A plus B. It’s a square, so let’s make this A plus B. What emerges? There’s the A squared, there’s the B squared, but there’s these extra things, there’s these ABs. There’s two of them that are there which escaped your attention before’.
Drawing a picture often helps students. For others, who don’t need that, they just want to get straight into the algebra, they want to go straight to the symbols. They don’t want to have pictures in their way. So if I can identify, alright, here’s a weak point, here’s something where you need additional support, where I want to give you another analogy, another metaphor, another perspective or entry point into this topic, that’s where me knowing my students’ strong points and weak points is really valuable.