Crescendos, Collaboration culture, and more. Darian Allan joins the crew to discuss the impacts of a spiralled curriculum. Is it a must to have a spiralled approach? What does it look like at Darien’s school? Plus, tips on dealing with different school cultures, environments and characters.
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Hi, I'm Andy Psarianos.
Hi, I'm Robin Potter.
Hi, I'm Adam Gifford.
This is the School of School podcast.
Welcome to the School of School podcast.
Welcome back everyone to another episode of The School of School podcast, and we're here today, we've got Adam and Robin as per normal, and we've got a special guest today, Darien Allen. Darien, just take a moment and maybe just introduce yourself to our audience.
Okay. Hi, I'm Darien, I teach at a independent school in West Vancouver called Collingwood. I've been teaching for 20 years in the public and private sector, and I love teaching obviously, love learning and have had a really, well, what I think is a interesting journey, both formal and informal education and professional development along the way. So I'm really happy to be here and to have a conversation.
Fantastic. So today we're going to talk about spiralling curriculum. When I think of a spiral curriculum, I usually go back and think about Jerome Bruner. That's my kind of where I go back to. But maybe Darien, from your perspective, when you're talking about spiralling curriculum, what are you talking about? What do you mean?
This comes back to, I have a colleague who teaches at a local school as well, and he recommended a book to me called Make It Stick, and that's Brown Roediger and McDaniel. And it essentially brings in the cognitive science of learning. There's sort of four principles there, and one of the ways that you can get at those four principles is by spiralling their curriculum. And so what I'm talking about with spiralling is with mathematics, you are coming back to topics again and again and building on them rather than the very traditional way that mathematics is taught, which is in almost every workbook or textbook unit one, okay, we're going to do integers, then we're going to do fractions, then we're going to do this. And I can't tell you how many times I've heard students say, "Oh my gosh, I totally forgot this entire unit, I don't remember anything."
Because we did it five months ago. And so really what this is it builds on that, one of the principles is spacing is just coming back to things again and again, spacing and hitting things multiple times. And so my interpretation of a spiral is you are circling back to things multiple times and really just building every time on the student's understanding. So I started doing this on a very small scale with one class a few years ago and found that it was helpful. It was actually a calculus class, and so I taught all the principles of calculus with just one type of function with polynomials and then went through again and taught the special cases. And this is very informal because I didn't conduct formal research on it or collect evidence, but I felt that when we circled back that that really helped students. They're like, "Oh, right, I saw this." And that second spiral was much faster and students seemed to, Oh, right, okay.
And it had them practising . In an ideal world, that last spiral would be students would just, you might add on one or two tiny things, but everything is fresh for them rather than at the end of the year doing this full review package. So that in my experience has been good. I'm actually really excited. This summer is the first time I'm co-teaching a summer institute. I'm teaching Math 10, which is 15, 16 year olds. We've fully spiralled the curriculum. This year my co-teacher had taught it and actually the entire group taught Math 9 spiralled and found it to be quite, again, don't have the data, but found it for their perspective to be amazing, because then they really liked it, that it changed up every day. The students had the opportunity over time to revisit things. Because it is, it's developmental. Seeing something again a month from now and having to retrieve it and having to, not relearn it but build on it, is incredibly supported by evidence, by the research. This is, I'm quoting Make It Stick, and there's another book called Powerful Teaching.
If I look at elementary school, primary school mathematics, I can't imagine trying to teach the topics, the content without applying a spiral to it because you need to revisit the topics over and over and over again at increasing levels of complexity. You mentioned fractions is one thing. I mean, fractions, the concept of fractions starts very early, but in a simplistic way, halves and quarters, equal parts to doing operations with fractions later on, which is quite actually conceptually difficult to understand for a lot of people, especially when you get into division, and fractions and division just seems to throw everybody. And unless you did it in a spiral way, the best you could hope for is that people would just have an instrumental understanding. They could just say, oh, if you want to define a fraction by another fraction, you need to find, there's all kinds of tricks, and they may have jargon in them or they may just be really simplified, whatever it is, but it's just a trick and you just do these things and you get the answer.
And that's what we resort to. But if you do it in a spiral, you can build up that understanding those foundations right from the beginning and you've got to address it at two points. If you want to, let's say talking about dividing a fraction by fraction, you've got to deal with it when you teach division and you need to deal with it when you teach fractions. And then the two need to coincide at the same time because if you don't do that, chances are they'll never understand what you're doing when you divide a fraction by a fraction. And the only way to do that is to introduce the topics and spiral them over the years so that you have this crescendo when you hit, and every lesson should be, or every topic should be a crescendo, but in primary school it's a lot easier, I think, because the nature of the complexity is you can still draw on a lot of concrete examples to illustrate what's happening.
By the time you get to high school or secondary, mathematics gets really abstract. Nevermind when you get to things like calculus and whatever, there's so much to remember and there's so many things that usually you're just grasping at straws just to get the knowledge in them. Your hope is that they're going to get it right at the test at the end of the year or at the end of the semester that we kind of tend to resort to, or it's easy to resort to just like, let's get through this module, let's just do this module, let's get through it, and then let's forget it, and then let's do this other completely unrelated thing. We are going to jump from geometry to calculus or whatever, and not make any connections between what's going on. It's just like all of the sudden we're doing something entirely different.
Do you think it's too much to ask for teachers to try to... How could we solve this? Because the reality is it's a lot of work to sit and think about how do we do this? Should teachers be collaborating more? Is there room for somebody else to help? I mean, how do we tackle this? Because I feel teachers all too often are just left to their own devices to work this stuff out, and they're already pretty busy, especially secondary school. In high school how many students do you have when you teach mathematics? It's not like you have one classroom of teachers, you've got a lot of kids. Anyway, I don't even know what my question is from there, it's just a bit of a rant. But I suppose it's like, how could we address this really? How do we get momentum with this idea in secondary school where it's so much more difficult?
One of the things is, I have grade teams, so I happen to be head of the math department here. And so I've put together teams who would teach a course, and ideally that's like three people, three people teaching all our math 8, three people teaching all our math 9. And so I'll speak to that for a minute. The collaboration that happened just because everyone has different strengths.
I have someone who is such an expert on inclusive education and problem-based learning where he has these amazing ideas, and then there's other people with skills in the group who can develop them and formalise them and grow them. And it's so much that just the conversational piece and the collaborative piece is exactly what it is, that makes everyone's job easier, even though you're putting in a bit more time in terms of having time to meet. And that's honestly one of the wonderful affordances I have and my group had. And so being really intentional about planning their schedules so that they have that time. So that that is a priority and we have to put value on that, on giving teachers time to collaborate, meaningful collaboration.
And one of your previous guests is a big supporter of that for my school. So that's really helpful. So the collaboration piece is huge, but it's also, you don't have anything to build on if you don't have a spark. And so you need ideas, and those ideas come from professional development experiences, whether it's independent, somebody's reading a book, and so you need to figure out how to curate those and provide them to people. They also need to have their own motivation to do that. And also giving them, inviting them and finding opportunities for them to attend Pro D. So in BC, we have an association of math teachers who host an annual conference, which is absolutely fabulous. So my team was, the math team attended that this year. And that's actually where we learned about the book, Make It Stick as a Team, and we're provided with copies of the book from our school.
And my Math 9 team was like, "Yes, we're doing this, we're planning this." And just ran off with it, and it was amazing. So having... I've also found in my experience, because I've worked in the public system for 12 years and saw the changes there, and it really depends on, I hate to say this, but it depends on the bar. Where's the bar? People will rise to the bar. If everyone is doing this, if everyone is interested in really improving learning and putting in the time and giving effort, and they see that as recognised and valued, then people rise.
So that school culture, the support system within the school, the school leadership team, making sure that they're not only promoting and encouraging, but making it possible. It's one thing to talk about it, it's another thing to find ways to get your teachers to free up their time or whatever it is to actually get together and collaborate or do professional development. And if you don't have that as part of your culture in a school, it's not likely to go very far. And not all schools are great schools.
And it's not a public versus independent or anything like that. There are amazing, amazing teachers in, and amazing schools in both systems, and there are schools that maybe aren't as supportive in both systems.
And so what happens when you're at one of these amazing schools and then you switch schools and perhaps the culture is different and the teachers aren't being supported in the same way. Is that where you have to rise to the occasion and try and implement that in the culture? Or what do you do?
I mean, the short answer is yes, that's what should happen. But that's hard, that's so hard, if you are putting in the energy and you look around and nobody else is, and it is, it's human nature to meet that level of expectation. And it's really hard to push yourself. And to be completely honest, that's part of the reason I ended up where I am, is because I came in and I saw the culture and the community here. And to be in an environment where everybody is so passionate and wanting to do everything they can to help students learn and to help themselves become better teachers, it's incredible. Yeah.
Yeah, when you see it's amazing.
No, I was going to say, I think also, I think ultimately if a school doesn't suit someone, it becomes really hard work and chances are you'll move schools and you'll go somewhere else. But I also think that you can be slightly subversive too. And I don't mean to sort of topple the top or the top, but I think say with something like a spiral curriculum, and I think to myself, all right, if I'm speaking to someone who has nothing to do with education, but you just want it to make sense. And you often hear in sports teams, elite sports teams talking about going back and revisiting the basics and making sure that that becomes part of what they do. And I think that of course, I say of course, but I think it's easier in the primary curriculum in any given curriculum, whether it's in Canada, the UK, New Zealand, wherever.
But trying to spot those really core ideas that underpin it. And I think that does two things is that if we know that, then we also know that's what we're building on. So that idea Andy talked about before, just equal groups and how prevalent that is throughout all years in a multitude of different situations, not just for fractions. But then you can start to develop that idea around asking assessment questions around that and developing your own understanding, and it changes the lens. And I think having those wee conversations with people that may be easily accessible to them, that they might just start to see things differently. And I think that can help get conversations going. And it's almost like, oh yeah, when that understanding grows, we can start to label that and maybe we should be looking for that and perhaps that's a good thing.
So I always think there's a real skill involved, and certainly people that I've found that I've learned a lot from, there's a real skill involved in being able to pick out those right small graspable, attainable ideas that can just give me enough, but I don't have to work too hard to get them.
But it will kind of open three doors. And once I've been through each of those three doors, it's another three doors. So now I'm in nine doors. You know what I mean? And I think that that's something that is just something to manage because if it's too big in a school that's not going to be supportive, you give up. I don't care who you are. At some point you say, actually enough's enough. I want to try for the children, but actually I also want to work in a school where at the very least they'll kind of give me a wee, "Oh, you're not doing a bad job every now and then." That's enough. So I think that that just understanding an idea and putting it out there for people to test for themselves without even really knowing that they're doing it, maybe that's a way in.
And that whole healthy school environment where also you're going to forgive your teachers if they get it wrong a little bit too. So it's like saying, okay, you guys go and collaborate and work together. And yeah, you know what, you might come up with something really silly and it might not work at all, but that's okay because that's a learning experience and now you know that didn't work. And now you can go and figure out why it didn't work. And it may be that actually the idea was good, but the implementation wasn't correct or vice versa or whatever. And creating those healthy environments where, school's a learning environment, not just for the students, but it's for the entire faculty and everything. It's working together to become better all the time. And if you have that over time, you'll just get a lot better. That's just the reality of it. And if you don't have that, you'll probably get worse.
And that's what we want to model for our students is that we're going to try this, take a risk. Yeah.
Thank you for joining us on the School of School podcast.
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