Improving math for upper primary and lower secondary

Transcript

Patrick: 

Hello, welcome everybody to this episode of Texthelp Talks podcast. And this is a series of podcasts from the team here at Texthelp where we're bringing a range of  expert speakers, experienced EdTechers for want of a better phrase. We're going to cover topics right the way from education through to the workplace. So please make sure you do subscribe to Texthelp Talks on your favorite podcast player or device and your streaming service and never any of these episodes. 

Fiona:

This is a really special episode because today Greg is not with us. Well, that doesn't actually make it special, but I have two special guests and I've got Louis and Paddy, and it's one of those things where it's good morning, good afternoon, and good evening, which I know Paddy's said before, because we're coming from all different parts of Texthelp. So Louis is based in the US, Paddy's based in the UK, and obviously me being based in Sydney. I'm the learning and teaching specialist at Texthelp in the Asia-Pac region. My role is to make sure that you get the most out of your Texthelp software. So what we're going to be talking about today is about math in EquatIO. So I'm going to let Paddy and then Louis introduce themselves to you.

Patrick:

Well, thanks, Fiona. It's wonderful to be here. I'm Paddy McGrath, and actually much like Fiona I am an education technology strategist based in the Texthelp headquarters, which is in Belfast, Northern Ireland. So my job is very similar to Fiona's in that my focus is purely and squarely on teaching and learning and making sure that our customers around the globe get the very best out of our tools. But I also have a slightly additional role to that, which is to ensure that all of our internal staff, particularly our sales team, are equipped with all of the knowledge that they need to talk about our products really well when they're in front of you as an educator. So it's a varied role. And lastly, I get to speak at lots of conferences at which many of us on this call do as well. So I think we're all like-minded here, Fiona, for sure, in terms of the roles we do. So Louis, you need no introduction, but I'll go straight over to you at this point.

Louis:

Yeah, yeah, no worries. So my name is Louis Shanafelt and I work in the United States, as Fiona said. Our home office is in Woburn, Mass. And I actually live in Florida. So I live just down the street from Mickey Mouse, actually. Two of my favorite people get to join and talk to you about EquatIO today. I learned so much from Fiona and Paddy and they've been absolutely wonderful since I've joined Texthelp.

Louis:

I'm much more new to the team, but my role as product manager for EquatIO is to meet with our sales teams and make sure they reach their objectives, meet with our marketing team, and then of course our developers. In particular, I'm the liaison, if you will, between the users of our product and the developers of our product. So if there's a feature request or something you can't do or you want to learn how to do inside of our product, then I'm a good one to reach out to. So I really, really look forward to this session and helping you all learn a little bit about math. And it's a real honor to join these two here today. It's a pleasure.

Fiona:

So as I said, we're going to be talking about EquatIO, our digital math tool. But what I wanted to do today was really just look at EquatIO from a bit of a different perspective. So there's a guidance report that's been released, and it talks about how we can improve mathematics in upper primary and lower secondary. Now it was produced by the UK's Education Endowment Foundation. And in Australia it's been taken up by Evidence for Learning. And so they've produced eight recommendations, and to be honest, they're not earth-shattering recommendations. I think they're good teaching practice, but I thought we could have a look at some of these recommendations with the lens of EquatIO and see how we can support students in their math, looking at these recommendations and using EquatIO. So does that sound okay, guys?

Patrick:

Yeah. Sounds good.

Louis:

Absolutely.

Fiona:

All right. So one of the recommendations that they make is to talk about developing student independence and motivation. And as we all know, throughout the world, really, is this thing going on where math is something that a lot of parents are saying to their children, "Oh, well, I'm not good at math. It's okay. You don't have to be good at math." Or, "No, I wasn't good at that." And so we really need to, I think, think about unique ways to help develop students' interest in math and develop their independence. So I'm going to head over to Louis, and maybe you can tell us some of your thoughts about that.

Louis:

Yeah, absolutely. So when we think about increased ownership through choice, the reason why I put this slide up and really wanted to speak to this in particular was because I know that when you're in a digital classroom setting, it's important to give student choice. And I know we're here to talk about math and we want to talk about EquatIO and there's other tools out there to be able to allow students to be able to express themselves. I just am a really firm believer that students will really take ownership of their own learning if they're given the opportunity to pick the platforms that they want to use in creating their math. So some of the bullet points here that I added in was just using tech to gather information, increasing that ownership, which can produce higher-quality outputs, in my opinion, of the learning. And then the second point here is just solving higher-order thinking questions. Giving kids the opportunity to become better problem-solvers, I think, is really, really important.

Fiona:

Yeah, look, absolutely. And I think about the problem-solving is even though we're focused on math, if you can become a better problem-solver in math, you generally become a better problem-solver. So it's such an important skill.

Patrick:

Yeah. And I think one of the terms that we would use regularly here is computational thinking. And from a computational thinking perspective, if you think about it naturally, that's simply breaking down a problem into smaller chunks, and that's very much a mathematical skill, but that is applied to and can be applied to all areas of the curriculum and indeed all areas of life. So if we can apply that within the context of math, then it has much wider implications, I think, for learning in general.

Patrick:

If we start to think less about objectives and more about goals and take a goal-based approach rather than a very clear objective, for me, it's like looking at a ski map. And we all know, for those of us who've been skiing, which I'm sure many of us have, when you pick up your ski map, there's the easy routes, there's difficult routes, there's the very difficult routes, and there's the very, very difficult routes. But ultimately our goal in all of us is the same. It's to get to the bottom. And that's the end goal from the top.

Patrick:

And if you translate that and to teaching and learning, for me, when we start to set goals, students quite naturally gravitate toward the right path for them. There are students that will take that stretch and challenge approach and automatically choose the more difficult route, but equally there are students who need a very direct route to that goal. And I think changing the language to a goal-based approach, I think imparts that with our students. And going back to you, Louis, is that choice and that flexibility and that the choosing of that path, I think, is very, very important.

Louis:

Right. And I know that I spoke of choice in digital tools, but when we think about that UDL approach that you just mentioned, really we think about, there's many different ways that students are going to get to the bottom of the hill, like Paddy mentioned. And I think with EquatIO and providing all those UDL input methods allows students to not be solely focused on, "I can only make math this one way."

Louis:

And the reality is that math has always been thought of, and when a student enters a math classroom, typically it's, "Get out your paper and pencil. You're going to take notes." Well, maybe that's not the best way for every student, right? So with using digital tools and providing flexibility for students, whether it be using the speech input or using the EquatIO mobile, or using handwriting recognition, there's just multiple ways to get to the bottom of the hill. And that's what EquatIO was really designed from. And we partnered with the original developer on EquatIO, and the goal was to provide those flexible avenues, if you will, for students to be able to get to the answer in the manner which best suits them.

Fiona:

So let's think about collaboration now. For me, there's of different types of collaboration in schools and in classrooms, and in math classrooms as well. So you've got student-to-student, you've got student-to-teacher and you've got teacher-to-teacher as well. So I thought that maybe we could just chat around this a little bit and your ideas around how we might use EquatIO to collaborate.

Louis:

Yeah, perfect. So when I think of collaboration, I mean, that was one of the most strategic things that we looked at when I was working at a school district, is we would literally do classroom walkthroughs. And we would really just search for students that were collaborating on a Google doc, for example. In other words, we didn't really look at the work on the Google doc. We just wanted to see multiple icons or multiple Bitmojis of students working in a shared space. I know that, and obviously since I'm on the product management team here, that we would love to be able to eventually get to a place where EquatIO mathspace could be a place where multiple students could maybe make something together inside of a mathspace.

Louis:

I can tell you that collaboration is obviously really important from a teacher standpoint, because we know, and the research tells us, that the students don't necessarily have to just sit back and wait for the teacher to explain things at a whiteboard or at a chalkboard, wherever you might be. So we know that students can learn from one another, and students can obviously collaborate and work in the same space together. So one workaround that I often tell folks is you can have a Google doc open, have multiple people collaborating in the Google doc, and everyone could put their own mathspace into the Google doc, which essentially becomes that collaborative space. And the thing with EquatIO is really, you can insert mathspaces into pretty much anywhere that it works inside of a platform. Especially, I often tell people, "Did you know it works in Google Forms?" But we can let students create in a mathspace and then they can put that work into a Google Form so it can be used for formative assessments and things like that. But anything to add, Paddy, that you can think of?

Patrick:

Fiona, at the outset of the collaboration piece, you made an interesting comment which a lot of people don't necessarily think about, which is collaboration you automatically think, "Right, I'm going to have pairs of pupils. I'm going to have three pupils. I'm going to have four..." But you talked about teacher and pupil collaboration as well. I think that's really important. But this particular activity, what I saw happen with this was a couple of things. I designed it so as a teacher would put in a single image, and they could put that in then obviously from mathspace, and it would be a shape and words. So it's an early years piece to describe a shape so we can help students describe the actual shape itself in words, so it's spoken text. And then we could also ask them to get real word pictures so they can make those connections.

Patrick:

So what I found happen was teachers that were taking the resource, or at least taking the idea, they were simply putting in the shape from mathspace and then sharing the Google slide out, and there were parents, students up. One student would then go in and they would effectively type the spoken text out. So they would type out, how would I describe this shape? And then they would remove the actual shape itself and share it with their peer, and the job of the peer was to read the spoken text and be able to go back to mathspace and find the right shape that would match up. And then together they would work on real-world connections of this.

Patrick:

So I found that really useful, but then also I saw teachers use it just directly with one-on-one to their students. And so they would put multiple slides in, multiple shapes, drawn from mathspace, and they would ask to build real-world connections. And the interesting thing actually that came out of this was I designed this as a very simple illustrative activity for students' primary skills, we call it in the UK. So students that were six, seven years of age. But we found it being used in what we call our Key Stage Three, so our middle-school level, because they were starting to learn more complex terms. So when it comes to a pyramid, they were picking up vertices and they were picking up apexes and then they were getting into volumes. And so a very base-level thing drawn from mathspace, but put into collaborative space, can start to scale quite a bit.

Fiona:

Absolutely. So what I want to talk about now is using tasks and resources to challenge and support students' math, which I think we really already have talked about, but I know you've got some more great examples. And I guess for me, what we want to make sure is that the tasks give them some responsibility, that they play an active role in their learning and that it gives them lots of opportunities to demonstrate, which are all the things that we've talked about. But I know you've got more good examples, so I'm looking forward to hearing about those.

Patrick:

So I actually have a very simple example, but I thought it was really useful in mathspace. So the how many squares can you see. So starting off with a three-by-three grid, but in mathspace, you've got the grid tool obviously there, but you've also got freehand. You've got multiple colors. So as a student who's working very visually, I can start to easily identify the square sections within there, but then I can move on. So in terms of a task, I can set a very basic-level task, but then I can say, look, record your results. So we start to type those out, write those out, however we want to do them. Students will record the results in differing ways. We can get them then to think through, right, well, if that's a three-by-three grid, what would a four-by-four grid look like? Maybe they will need another page in the mathspace to do that.

Patrick:

So we can go with this as far as we want, we can keep pushing our students, but the importance for mathspace in this for me is that it gives them the canvas to express each of those individual areas and expand that out, and then gives us a great chance for really good questioning after that, because we theorize as, right, well, it's actually n squared plus n squared, and they keep going on and they produce the answer. Then we can start to introduce some good questions there to push that task forward, to get them to explain and articulate. And again, I think that joins up very well with the collaboration piece and the goal-based piece.

Fiona:

So another recommendation was the use of manipulatives and representations. And I know that well for us with EquatIO, this is like, "Oh, we can get out all the bells and whistles and show you all the cool things that EquatIO has." Manipulatives is such an important part, and the multiple way that you represent the different kinds of math, exactly like what you were talking about before, Paddy, with people have so many different ways of thinking about it. And it's so important for our students that we show them lots and lots of different ways so that they don't think that something is just one way or one particular direction. And I think this is a real strength of EquatIO, that it actually does this.

Fiona:

And the other thing that I should mention is that we're not suggesting that you ditch concrete materials and manipulatives. We're just saying that on top of all of those resources you have in your classroom, you've now got all of these fabulous digital ones. And from the classrooms that I've come from, where often you're using base-10 blocks and you've got plenty of tens, you've got plenty of units, you've got quite a lot of hundreds, but you get to the thousands and all of a sudden you haven't got enough for everybody to do the same activity at the same time. So being able to use a digital format for things where you perhaps haven't got enough of those is great. Louis, what are you thinking when we're thinking about manipulatives and representation?

Louis:

Yeah. Well, you guys have touched on this quite a bit. And one of the things that I found, and certainly anyone that watches this after the fact, if you're not on Twitter, it's a worthy investment just to gain resources from other folks that are EquatIO users. Simply put, this was something that I saw on Twitter. I didn't know the gal. I think she's up in Canada. Really, really nice lady. I private-messaged her. And she had put this out there and just said, "Hey, I made this really engaging mathspace." And my first thought was that probably took a little time to create, but any digital tool, it's going to take time. I think the payoff is going to be worth it.

Louis:

When I think about this particular scenario and putting toppings on a pizza and allowing students... I believe this teacher was a first-grade teacher and I think it resonated with me so much because I have a seven-year-old at home and he was a first-grader at the time that I saw this. And I thought, "Boy, my son is in remote learning right now and he's not doing anything like this." He's sitting there at the dining-room table, staring at the old-fashioned paper and pencil PDF that probably got printed out of dad's printer, and let's face it, not everyone's going to have a laser printer or the ink to print all these resources that could potentially be sent home. But when you think about how inexpensive an EquatIO license could potentially be for an entire district, and the manipulatives that come with it, to be able to create highly engaging mathspaces for students where they're interacting with their math. They're not just scribbling a number down on paper. They're being able to make real-world connections with students that inspire curiosity and their desire to learn.

Louis:

When you think about... And I often give this example, and I can't think of the particular student, but I spent many years in the classroom. And I often think, if I have a student who absolutely loves basketball, right, and we're talking about spheres or we're introducing geometry, and there's just nothing that even he likes about the sphere in mathspace, we'll go back to Paddy's example. Remember Paddy said you could go and import your own files into mathspace. So what if I gave that student a basketball and I made him find the diameter or the circumference or the radius or the area? Anything that you can do to help make those real-world connections. Sometimes just the conversation with the student.

Louis:

I think I've even told the two on the call here that I'm with, there's been no greater compliment as a teacher than to have a student come up to you at the end of the school year and tell you... And I never minded that they said this. They would literally come up and say, "I hate math, but this is my favorite class." And I think it was being able to make those connections and provide an engaging and a comfortable learning environment for students. And it doesn't matter what you're teaching. It just so happens that we're talking about math.

Louis:

But what if you make a connection with a student and their favorite food is... I don't know why, but I get asked at the dining-room table what your favorite food is all the time. And it doesn't change from night to night, by the way. But I always tell my son, "Hey, it's pizza, man. It's pizza." If someone gave me a mathspace where I was curious and I could drag pizza toppings, versus taking a piece of paper and just scribbling down some numbers, I just think that we're providing students a much more desirable place to be able to show their growth and their learning throughout giving them these processes.

Louis:

So that was the thought process behind showing this slide in this particular mathspace is to think outside the box. And that's hard. I get that that's hard, especially for a teacher that's been teaching a long time, but you probably heard the analogy, you wouldn't want to go to a physician or a doctor that hasn't gone to classes and had their own professional development and is still practicing the same thing from 30 years ago. So you want a teacher... Doesn't have to be young. I'm not saying they have to be young and fresh out of college. They just have to be willing, I think, to explore and to be able to create and to think outside the box, like, "How am I going to make those connections with my students so it promotes those higher-order thinking skills that we talked about before?"

Fiona:

Yeah. Well, look, I think that our little chat, which has maybe turned into a big chat, is testament that, guys, we should chat more often. Just saying. But thank you so much for sharing your expertise and giving us the different perspectives, because we all come from different math backgrounds with different experience. And so it's really good to sit down and chat about all of that. I'm hoping we can do it again soon.

Patrick:

You're very welcome. It's a pleasure, Fiona.

Louis:

Yep. My pleasure. So it's always fun being with both of you. So have yourselves a great day.

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To watch Fiona, Louis and Patrick’s full discussion and see them demo the ways that our digital math tool EquatIO can support teachers and students, click here.