How to integrate ICT in teaching maths?

Video Transcript

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- Well, good morning or good afternoon or good evening to whoever you are. My name is Michael Hilkemeijer from ICTE Solutions, Australia. And then it is my great, great pleasure to co-host with you tonight, this morning with adjunct associate professor Rosemary Callingham from the University of Tasmania, Australia. Welcome Rosemary.

- Thank you.

 

About Rosemary Callingham

- Welcome to this webinar. To introduce, just gotta read a little bit about Rosemary. She has done extensive background in mathematics education in Australia in teaching and research. Internationally, she has worked in Hong Kong and with UNICEF in North Korea. She's an acknowledged expert in using the Rasch measurement technique. Is that how you pronounce it?

- Yes, yes, it is.

- Awesome. And has collaborated with some of the top specialists in this field. Thank you, once again, Rosemary. Like you said, I've been so excited about this for a long time. I cannot wait to see what you have for us today.

- It's all yours.

 

Using ICT in the Primary Mathematics Classroom

- No pressure then. I'll just share my screen. Incidentally, the picture behind me is Tasmania. It's Bruny Island on a summer's day. It doesn't look like that at the moment. Okay, anyway, I'll share my screen.

- Also, while you're doing that for anyone who's joining us today. If you have any questions, you can post them into the chat and I will go through them and answer them, whatever you have there in the time we have this morning. So you don't need to have your camera on or your microphone on. You can just sit and listen and any questions you can just post to us in the chat.

- Okay, primary schools now are really technology rich. There's a whole range of technologies that are being used for different versions. So a lot of schools now, in fact, most schools, I would say, have some form of learning management system. They use them for record keeping for reporting for allowing parents to see what the students are doing, all sorts of uses. And often these are linked to individualized programs.

 

There's lots and lots and lots of communication apps, even what we're using now. And these of course, had a big rise in the last couple of years when a lot of schools had to move online, because of lockdowns and so on. And these apps are used those intranets as well as external communications, everything even Facebook groups are used. So there's a lot of communication type uses. There's lots of these standard packages, Office 365. I mean, I have at least two, probably three Office accounts for various organizations that I belong to. It's a bit of a nuisance, but these are very widely available and people are using them.

 

And then there's specialized apps or programs, dynamic geometry, statistics software, CAD software, and so on. There's a lot of these around, and I will be talking a little more about some of those later on. So I just wanna make this as a sort of controversial statement. We've got all this going on in the background, but despite some promise, there isn't really much evidence of good quality use of ICT to enhance maths in primary classrooms. That's a sort of fairly controversial statement, but I was saying to Michael earlier, I went to a maths ed conference recently, and there was only one paper about the use of technology and it was about little kids in kindergarten using iPads.

 

So there isn't a lot going on and there's not a lot of research, despite the fact I think it's needed. I just want to touch on frameworks for ICT use, because I think it useful to put these things into some sort of a picture. TPACK is very well-known, Mishra and Koehler. And I think it has, it reminds us that not only is content and pedagogical knowledge necessary, but also you have to have some sort of technological knowledge. Now that can be at a very basic level knowing how to use the program, or it can be at a very high level being able to network things and so on, but that part of you can't just rely on pedagogical and content knowledge, if you want to use technology in the classroom, I think that's quite useful.

 

The other framework is SAMR, and this is about, it comes from 2006 as well, and it's about how the technology is used, substitution, augmentation, modification, or redefinition. And I'm actually going to use this framework as a bit of a kind of scaffold for the rest of the presentation. But if we just compare these two, TPACK emphasizes the very complex nature of teaching and the demands of technological pedagogical and content knowledge. I mean, this is not trivial and I don't think we should see it as trivial.

 

And I think sometimes people from outside assume that this will just happen and forget that there's quite a lot that needs to be put in place before technology can be used effectively, but TPACK focuses on the teacher's knowledge and the use of technology. In contrast, the SAMR framework emphasizes how the technology is used to substitute, augment, modify, and redefine tasks. So it's about using the technology. And so, at this point, I'm just going to, it's important first of all, to say these are not mutually exclusive.

 

One focusing on what the teacher's needs are and one focusing on the task needs, if you like, but I just wanna stop for a moment, to give you two minutes just to think about all the technology that's being used in your school, and then more closely, in mathematics lessons. So this is something you can think about. And if perhaps you're using this video later as a discussion starter in a staff room, it's a point at which you can have some discussion and think and make some notes about the way that technology is being used. I'll just wait for a few moments. I'm not gonna wait for too long. Okay, let's move on. Using the SAMR framework, I want to look at the different ways in which technology can be used. Substitution, there's a lot of substitution.

 

Using eTexts, for example, they're essentially the same as any textbook and they have the advantage and it's a big advantage, don't let's knock this of being much lower costs. I mean, textbooks have become very expensive. If you buy a textbook for your child, they only use it for a year, that's a significant amount of outlay, but eTexts are much, much cheaper. And many of them are just PDFs of the textbook. So there's virtually no change. Sites that provide explanations like Khan Academy. They can substitute for the teacher or the Flipped Classroom where the teacher provides explanations, and then the kids come back the next day, often having done this as homework or whatever. Just to point about Flipped Classrooms.

 

There is some research around that suggests that they are less effective, if you say to students, go and have a look at Khan Academy and provide the link, than if the teacher himself or herself actually creates the little video. Kids relate to their teachers, not to somebody else. I think that's quite interesting. I think probably when you're older, you can sort of think, "Oh, I just need to know how to do X, Y, Z, I'll go to Khan Academy," but younger kids need that relationship and I think that's a very important thing to remember, but most of these substitution type uses address practice and fluency rather than developing conceptual understanding. And this isn't a full mathematics program, because you do need opportunities for students to reason, to problem solve, and so on. This is an example from IXL Maths Practice, which is available on the web.

 

They're quite nice. I'm not saying there's anything wrong with any of these, but they are essentially just substitution. And I think there are some disadvantages as well, which I'll talk about later. So substitution is fine, and I think there are pros and there are cons. Augmentation is when you add some value to an activity in some way. It's still essentially the same activity, but technology can add some other kinds of dimensions to it. Virtual manipulatives are one example, where instead of using concrete patent blocks, you use virtual patent blocks and so on, and they certainly have some promise.

 

Using drawing or graphing programs, Paint, even Paint, you can do quite a lot in. I mean, I was in a quite an interesting lesson where the teacher was using some of these kinds of programs as part of a rotation around 4 or 5 activities where the students were developing understanding of three dimensional objects and specifically pyramids. And they made them in concrete materials, but they also drew them using, I'm not sure if it was Paint. I think it might even have been Word, but so on. So these can add to the learning experience, but they don't fundamentally change it.

 

And I think they have a lot of value, but they do require careful planning, 'cause you have to incorporate these into your other activities. I think that's one of the things that we have been a bit careless with with technology. We've assumed that if we provide the technology and the program, everything else falls into place, but it does need to be planned, it does need to be thought through and so on.

 

So this is for example, this particular site Didax, has some very nice free, I always look for free sites, I might add, you can often pay more and get enhanced stuff, but I always start with the free stuff, 'cause I know what schools are like, but this is a balance where you can look at equivalence or develop understanding of equals and a whole range of things. Now it works exactly the same way as the concrete balance is. I mean, we've all seen those in primary classrooms, you're hanging your weights on either either side and so on.

 

As part of a kind of rotation of activities, developing the concept of equals for example, I think that's a very nice enhancement. Kids enjoy it, it's got a bit more educational value than just simply filling in an answer in a box. This is a graphing program, Create a Graph Kids' Zone. Again, it's quite nice and it's easier to use than one of the standard programs like Excel, which frankly, I love Excel, I use it a lot, but it is not a program for teaching. So that's augmentation where you're adding some value. Modification is a bit more difficult.

 

This is where you are actually changing the nature of the task to some extent, again, adding some value. And this is where I think you need to use software designed for education. Most software isn't developed with learning and teaching in mind. Interactive whiteboards are a good example. They came from the commercial world. Anything that happens in commerce, people always want a piece of the education pie, because education is a big spender. So there was this big push. I've been in schools where they've had 3 or 4 interactive whiteboards sitting in a store room, because nobody really understands the best way of using them.

 

They were often fixed on a wall, too high for the kids to use, because that was the standard height and health and safety said you can't do it any other way. So the opportunities that they afforded became much more limited, even with some of the software that was designed specifically for education, which was quite good. The other thing is, I think you can get essentially the same effect by using a computer and an overhead instead of touching the screen of the whiteboard, you can interact with the computer. So interactive whiteboards are not being used as much, but I think it's because they weren't designed with education in mind. Some very good software that actually has learning and teaching built into it.

 

GeoGebra is one and CODAP is the other, I'll talk a little bit more about both of those. They have a lot of built-in interactive resources, which is essentially augmentation, but both of those programs have the capacity for students to explore ideas for themselves or to work in groups, exploring ideas, which I think is a better way to go. So GeoGebra is as it suggests, it focuses on geometry and algebra and particularly geometry.

 

So it's very useful for developing understanding of properties of shapes, for example, and you can get really good learning when students explore in a meaningful context. So the other thing that I really like about this software is that both of them have the capacity built in for students to produce reports. I'm actually a great believer in mathematics of kids producing some sort of explanation of how they got their answers, how they went about solving the problem, how they collected their data, what they've discovered about triangles, all of those things. So asking students to produce a report really, really modifies the task and adds value to it.

 

The other thing about both of these pieces of software is that particularly with the statistics software, you can use much bigger datasets. It's very tedious for kids to deal manually with more than perhaps 30 kids in a class. Once you want to extend your investigations, it becomes very tedious and very hard. And the kids get lost in managing the data and forget about the big picture.

 

Programs like CODAP, which actually developed out of a program called TinkerPlots, which is still around, but which I wouldn't recommend now, because you have to buy it and download it and put it on computers, and it's all far too hard. Whereas CODAP runs in the Cloud and is free and will always be free, so they say, but it does allow students to deal with much bigger datasets much more easily.

So this is a true modification of the task. It extends it in some way, and that's true also of the GeoGebra software. So just as an example, this is taken from GeoGebra, the idea is to compare two rectangles, the area of two rectangles, and you can do it in a way that you really can't do with paper and pencil. You can, but again, it becomes very tedious.

 

You have to pick this up and drag it onto the other box and you can see there's a little bit of blue sticking out the side and you cut it down here and then drag this one over to here and you can see this is part way through the drag. So it rotates itself, very neatly, sits itself down, and then you get the divide line again and so on, until you get to a point where you can genuinely compare the areas of those two rectangles and say one is bigger than the other.

And you can actually go further and say, by how much and then pay attention to the dimensions of the rectangles and gradually build up that understanding of the development of the formula for divide, for finding the area of a rectangle.

 

This is CODAP, and I have to apologize for it's a pretty poor screen grab I'm afraid, but it looks like any software program or any spreadsheet program, except that you have different ways of displaying the data and it's drag and drop, so you can drag these attributes they call them onto the axes and it will create a graph. This particular graph shows it's taken from a dataset of First World War soldiers.

 

And it's amazing the amount of data there is available on these people. And when they went into the Army, they used to do various tests, they've got things, eye color, hair color, which kids find fascinating and are completely useless statistically, but kids really like them, but they've got things like normal chest and chest expanded.

 

And there's a very high correlation between the two as you might expect. So you can do some very meaningful explorations of data. This one happens to have 165 people in it, but there are other really good datasets, which children in primary schools can use with some modification. One is the Titanic. There's a very good open dataset available. You do need to do some tidying up, particularly if you want to make it usable by primary kids.

 

And the other one that is really good is the First Fleet, where it is a very good open dataset on the First Fleet, which covers where these people came from, where they went to, which ship they came on, and so on. So there's, again, there's some quite meaningful activities and explorations that students can do.

 

One of the things we have found is that when you do this particularly, most the bigger datasets would be older primary students and into lower secondary, kids are fascinated by the fact that these are real people and that many of the kids are not far off their age. I mean, some of the crew on the Titanic were only 14 years old and they drowned, the women and children first didn't extend to crew. And in fact, didn't extend much beyond the first class either.

 

So you can explore those kinds of things with that dataset. So this is modification and I really think more could be made of this. We're not using software as effectively as we could, programs and apps as much as we could be in primary schools in mathematics. And these are really good ways of extending and modifying at otherwise good activities, but bringing them into a new position. Those are just the sites to go to.

 

You can go Google any of those, CODAP or GeoGebra will come up. Okay, definition. And I want to make this a huge and controversial statement. I do not believe that there is any software currently available that totally redefines mathematics, learning and teaching. And in many ways I'm not surprised, because the history of mathematics has come from developing a symbol-based language. And our current software actually doesn't deal with that at all well.

 

There are some software packages that are used by mathematicians, but they're not really easily accessible to primary age kids. So even believe me, getting things into Word, fractions for example, are a nightmare. They're really difficult to get into Word. And until we have a really, really easy way of being able to do that and a fully accessible way, I don't think we are going to see any true redefinition. There are glimmerings of hope.

 

I'm not not saying by that, that we should go away from any of this at all, but I want to be a bit controversial here and get people thinking about this. So if we want to transform classroom mathematics, it's the teachers that have to change. You have to change the approach from a focus on skills and it's largely arithmetic skills, and I'm not gonna go into why I think that is, but we have to move away from basically teaching skills, which was very suitable in days when we didn't have technology, when much of the work that was done was done manually, I'm thinking Charles Dickens and all those clerks writing things in big ledgers and so on.

 

The learning all of those algorithms and ways of adding and subtracting and so on, critically, critically important then, they are, I'm not saying they're not important, there should be less emphasis on them and more on using that.

 

Also, I think the other thing is that really to learn mathematics while students need to be able to talk through what they're thinking, they need to talk to their peers, they need to talk to their teachers, they need to talk to more knowledgeable others. They've got to be able to reorganize those cognitive structures. And that requires some form of language.

And to do that, we need to set up lots of opportunities for children to explain what they're doing to justify their responses. I've been in classrooms in very, very low socioeconomic schools and the kids are wholly engaged and they're talking mathematics to each other.

 

They're explaining mathematics to each other. They're up at the whiteboard, showing each other what to do. At the conference I was at, that was the one of the messages that one of the keynotes gave us and I won't go into a whole lot of other things that he said, but essentially kids need to work together to solve problems. And we're not doing that terribly well at the moment.

I'm being a bit generalized there, because I do know that in many classrooms, there are some really good things happening, but overall, I think there's less good things happening than I would like to see.

 

The other thing that has changed is the new curriculum. And I believe it is a much more demanding curriculum. And I think that, because there's a heavy emphasis on, for example, mathematical modeling, right from early years. So not just writing number sentences, 1 plus 3 equals, what does that mean? What does that stand for? How is this a model for a real world situation? And similarly with statistics, it's not just a question of teaching mean, median and mode. Now we've actually got to carry out investigations.

 

Kids have gotta pose the problem, decide how to collect the data, how they're going to analyze the data, represent the data, to tell the story and write reports and explain it. So all of that makes a lot more demands and will transform classroom mathematics and technology can certainly help and support these, but in and of itself is not redefining. It's how it's used to support a new kind of approach.

 

Interestingly, there's a lot of technology used in literacy. Kids are writing stories, they're illustrating them. My grandson came home with an audio recorded monologue that he'd written, 1,000 words, which was really a faction story, it was based on fact, but it had been modified. Lots of innovative use in literacy, but not in maths.

Why not? Why aren't we asking kids to explain what they're doing? Why aren't we asking kids to write mathematics reports and so on? So I think we need to make more use of mathematics, of technology in mathematics to transform the way that mathematics is taught. So here's some ideas, I don't know what you'll think about these, but keeping maths journals or blogs.

 

I've kept maths journals with kids, very, very interesting. At the beginning, when I started doing this huge resistance, kids, "What am I doing this for? This is literacy, not maths." About halfway through the unit to work, I got one from one boy who was not the best mathematician in the world. And he says, "I think my brain's beginning to work. I solved three problems today."

 

And by the end of the unit, the same child wrote a whole page explaining how excited he was that he and his mate actually managed to solve, not just the straightforward problems, but they worked out how to do things in reverse. That kind of thing is transformative. Now putting that I did this 20 odd years ago, we didn't have access to the sort of technology we've got now.

But you think about that using some kind of a tablet with a notebook on it, that sort of thing, that's exciting, and kids would enjoy doing that. And there's lots of easy to use software for that sort of thing.

 

And maths journals or blogs can be of different kind. So there's a description. So you get kids to make a course in different ways. I'm choosing deliberately quite low level, in low level, low grade activities. So things that will be done in sort of grade 1, grade 2, grade 3. We're not making enough use of taking photos. We could take photos of concrete materials or drawings.

 

If you've got a tablet that uses a pen, they can use sketches. And I think that those actually do have a lot of promise. They're probably too expensive for everyday use in classrooms at the moment, but they're moving and they will come down in price.

 

And I think they have a lot of promise in maths, because then it doesn't matter how you write the thing, you can always turn it into text, but it will turn it into text as you've written it. So fractions, for example, can be written accurately rather than with the diagonal slash, which is what you often get in word programs or word processing programs.

 

So there's lots of of possibilities to use a journal or a blog to describe what you're doing. You can evaluate things. So there's a classic problem it became Pikelets. But if you go to the AAMT Topdrawer website, they've changed it to pancakes.

If you give this problem to children, this is again, probably grade 2, 3, something like that, sharing three pancakes among four people, you can make it more complex, sharing seven pancakes amongst nine people, for example, and so on. Kids have all sorts of ways of doing this.

 

And there's always one child who says, "Well, I'm gonna eat the extra one," but again, you can put those sorts of things into a blog, use pictures, use photographs, and so on. But again, decide which of the various ways that the group has come up with, do you think is the best and justify that decision. You can create things. We don't do enough of this in maths either.

 

Why don't we take a 3D object and create a story about it? There are a couple of quite famous books. One is called "Flatland", it was written in about the 1930s, and I have an original copy, in which it describes life from a two dimensional perspective.

 

I might add, women are very dangerous in "Flatland", 'cause they're straight lines and they can pierce any two dimensional shape and potentially injure them. But the other one is called "The Dot and the Line", which a dot becomes a line, and the mathematics behind it is quite profound. But the idea of creating stories about something is one that leads kids to think about the properties of shapes, for example, or what a fraction means.

 

We're doing this a little bit at the moment with things called Think Boards where one of the quadrants can be a creative story, but again, you can do this on an iPad or on a computer or with some form of technology and it's more engaging for kids to do that. But the thinking that they have to do is still there and that's the important thing.

 

And then there's investigations how they work together to solve a problem or how they decided to collect some data. And this ultimately, can become part of the report that you're going to ask them to do at the end. So there are lots of ways in which maths journals or blogs can be used very, very effectively and technology is a great support for some of this. Then we get to STEM, and STEM is another ball game altogether.

 

You will find now in the new maths curriculum, they talk a lot about computational thinking. And I have to confess that when I first heard the language, I thought this was about doing operations. It's not. It's about the logical sequencing that is developed through coding and there's lots and lots of these coding programs, Scratch, Rock, Studio Code, lots of them.

 

Most of them have some sort of free access, some you have to pay for and schools often typically take out a school license for these. I know particularly Rock and Studio Code being used quite widely.

 

And I have to say, they're not that easy either. They've challenged me. They very much develop problem solving skills. And again, if kids are working together to do this, they're reorganizing their cognitive structures. This is taken from Studio Code, I think it is, this one. And it's very engaging Studio Code. This one it's actually, it's been solved. It's one of the easiest ones, I thought I wouldn't try and do a difficult one as an example.

 

The birds started here, it's based on Angry Birds and it has to move forward two places to jump on the pig and you have the blocks move forward, it starts with when run and you have to put in two move forward blocks.

 

This is fairly straightforward, it's very easy. But I tell you, by the time you get up to the final levels, they are really, really demanding. You really have to think hard about them. Robotics is another thing. Now they've been around in schools for quite a while as well. Years ago, we had Logo and Turtles Turning and that sort of thing. It's the same kind of thing, but they're often using code similar to the Studio Code stuff.

 

So there's Lego, Robokids. Again, schools often buy into these, that's one of the Lego things, but there is real criticism, and I think it's partly justified that the mathematics gets lost. Kids, particularly with the coding, you're dragging tiles and things like that.

 

They don't realize and in fact, they're thinking mathematically in a very logical way. Even Minecraft demands that kind of thinking, but kids don't necessarily realize that it's mathematical thinking. I think we need to explain to kids and show kids that it is that logical sequence that mathematics is built on. And the criticism that maths gets lost, I think is a real one. But I also know of teachers who are doing some very exciting things in all of these areas where the mathematics isn't getting lost, so it can be done.

 

So let's go back and say, okay, all levels of the framework are useful, but there are affordances and constraints within each level. So substitution and augmentation have advantages. They're a very familiar environment for teachers and students. And that's not to be sneezed at. If you're teaching on a windy Friday afternoon, you want something that the kids are not going to have to grapple with, you want something straightforward and easy, but it does provide for different ways of looking at the problem, particularly once you shift into that augmentation level. So I'm not knocking using things at the substitution level. I think they have some advantages. There are constraints.

 

They develop fluency and understanding far more than problem solving or reasoning. Again, I'm not knocking this, but it's not enough. It's a necessary but insufficient condition. So let's move to the modification, redefinition. It builds on that fluency and understanding to develop reasoning, problem solving, and so on, that is part of the curriculum that we tend to neglect.

 

Students are also more engaged and motivated and it's more student-centered approach provided I will qualify that, they've gotta have opportunities to talk about things with their peers, with the teacher, but there are constraints, and I'm not going to say that it's just something that will just happen. It is much more demanding for teachers and students.

 

You've got that added dimension. If you go back to the TPACK framework of having to know something about the technology, so you have to invest some time in learning the technology. And I know that teachers are very time poor. And I'll be honest, I haven't invested all the time I should in learning some of the technologies. I can use some quite competently, others I'm really blundering around.

 

The other thing is that you have to think differently and set up different kinds of lessons. And if you're moving into wanting to use technology, I'd suggest you split your week up and have three fairly standard lessons and it may be every other day and a couple of lessons where you get engaged with the technology, particularly, as you're beginning to learn how to use it effectively.

 

Don't try and change overnight, it's a nightmare for everybody. And you got to remember, that the kids also need to become familiar with this new environment, it's not just teachers. If kids think that doing maths is about getting answers and ticks on a page, changing that mindset to one where they actually have to think about things is actually not as straightforward as it seems.

 

So we have to hasten slowly is my advice in this, but do try to hasten a bit, because there is so much potential here. So this is something to think about again, whether you're watching or your own, or whether you're looking at it with a group of people, think about your technology use, how often you use those kind of higher level or more demanding levels of modification or redefinition. And just think about that and make some notes about it. I'll give you just a few minutes now.

 

- And if I can just add there too, Rosemary. Your point about in relation to teaching knowledge of technology. One of the key things I think that we need to be aware of is that there is so much technology out there that is being presented to many teachers in schools, you try this and try that and do this and do that. And it's very hard to keep track of and be able to make a decision on what they need to use and how they can use it.

And one of the strategies I think that teachers can do is that if they feel that they're not as tech savvy as their students are there was a very simple way that they can get around that. And that is to choose an ICT device or software that they know that the students are familiar with and to become familiar with that themselves in such a way that they can imagine the potential of the technology within the mathematics context.

 

- Yeah, yeah, no, I'd agree with that. And that is an absolutely beautiful segue into my final two slides, which is all about evaluation of digital resources. And there's a very nice little framework devised by three researchers from Morocco of all places. And they have a number of dimensions that they suggest that you look at. First of all, they talk about academic quality, is the information provided, in this case, it would be the mathematics appropriate and relevant, is it reliable?

 

Does it do what you need it to do? It's no point in teaching a grade 3 classroom if the program you've got is throwing up questions at a grade 6 level, for example. What's the pedagogical quality? Does it allow kids to really develop conceptual understanding?

 

What's the structure behind it? What are the strategies that it's promoting? And this, I think fits nicely with that whole redefinition idea of using technology. So these are things to think about. They've added an assessment, whether it's built in or separate. And again, this may become an issue. Most of the technology I've seen, I'm very dubious about a lot of the assessment in it.

 

Most of it's multiple choice, there's some constructed response, but it's at a relatively low level. Developing multiple choice questions that really tell you something about how kids think is extraordinarily difficult and time-consuming, 'cause I've done a lot of that and you can spend a lot of time and at the end of the day still have something that doesn't work. Kids will always see things in a different light.

 

It doesn't matter how much you kind of put around it. What's the learning quality of your resource? Does it address real problems? And by real problems, I mean, problems that kids can engage with. As you move through school, kids will engage more and more with what we call real world problems, but problems that are genuine to them.

 

And you have to have a really good match between your audience, your content and your objectives. There's no point in saying I wanna teach kids fractions and then using software that really doesn't get at the conceptual understanding or doesn't give any real purpose for learning fractions. And I have to say that these days, while we need to know what a fraction is, what the meanings of fractions are, we really do not need to be able to add and subtract mixed fractions unless you're doing algebra.

 

And then there's other ways of doing it, which are quite easy. What's the technical quality? You want it to be really easy. What's the design features? What's the quality graphics, the production values, if you like? how easy is it to find things within the product? What sort of multimedia are they using? One of the things that you often get is a lot of loud noise. And a lot of the kids who respond best to technology are kids who are somewhere on the autism spectrum scale, but often they react badly to loud noises. So you've got this real tension between wanting to use technology, but technology that is over busy and noisy.

 

So the first thing I always do is look for a product where you can turn the sound off or at least reduce it. So things like that you have to think about. So these are just the final two points. If you're choosing technology, look for technology that has a high pedagogical and learning quality, as well as ease of use, which is that technological quality, the quality of the design, and so on. Don't choose software that really has low value. And I think this is what Michael was saying, choosing software that kids are familiar with.

 

You may not have the choice because the school may make those decisions for you, and that's another thing we have to remember, but to use technology appropriately, you have to have intentional planning, learning mathematics requires thinking, and it requires cognitive engagement. And that requires planning to make the corporation of the activities worthwhile and part of quality. One of the things that I'm very concerned about and which I'm seeing quite a lot in classrooms now, is that kids are often put onto a computer.

 

It's often done to keep them quiet, because they're troublesome kids and they're basically left on their own, they have their headphones on and they're playing games. I actually think some of that, it doesn't lead to learning, but I actually think it's potentially harmful, because if you just sit and watch kids doing that, there's often no real engagement with the interface. They kind of guess things and they get this noise if they get it wrong, and this noise if they get it right. And they know that if they click often enough, they're gonna get it right and they'll be rewarded and they can move on.

 

There isn't really an incentive to think about the problem and then answer it sensibly. It's a kind of just a hunt and peck type of arrangement. I mean, I don't know, I'm a bit of a game player and I use it as a way of deescalating after the day, it's mindless, I can sit and play match three games and not have to think about anything. And I think a lot of kids are doing that as well. If you're going to use technology effectively, you have to invest time in it.

 

I think this is a message that schools need to get. They spend a lot of money, technology is not that cheap, and you need to have time to play with it, to become familiar with it, to work out the constraints, the affordances, and to build it into programs effectively.

 

I don't think this happens overnight. So you do have to set aside actual time. I think you've got to talk to parents. There are still parents out there who say, "Oh, technology, bad thing." Won't let their children, they worry about screen time and all of those things, all of that needs to be taken into consideration and you need to communicate with parents. Oddly enough, most of that communication requires quite sophisticated technology these days.

 

Most of all, enjoy it, technology's great fun. And really, it has lots of potential to transform mathematics teaching and learning that I think we are not making enough use of. And just as an aside, you'll notice I haven't said anything about calculators, which is a technology use and certainly has its place in maths classrooms.

 

I've focused more on the bigger picture technology, ICT, and so on, rather than on those sort of smaller handheld devices, I haven't talked about phones. Most primary age children don't have phones accessible to them. Although that's becoming quite common in high schools. Things like graphic calculators, again, common in high schools, but not in primary. So I haven't touched on those. I've tried to restrict what I've said just to primary classrooms. So with that, I might just stop sharing. And I think there might be a few questions that you can answer.

 

- Well, thanks very much Rosemary. Just as a final note there on that last slide there, on your final comments there, I would happen to agree with a lot of those, particularly, that all ICT need to have high pedagogical and learning value to it. And I think, in relation to, as we all know, teachers are time poor in many areas and being a teacher myself for many years, I know how it can just be a continual drag on what you can do. And to add a note to that, I think, it's an important thing to remember too, that if you really believe that you may not have that time, then you use what you have there.

So many of the resources that schools have these days, you could use the new version of Microsoft Word, has features there that students can use to create 3D objects. They can draw with it. They can use things such, other free programs like Paint 3D, which is Microsoft new version of MS Paint, to do that same sort of things. Getting graphing and drawing, painting programs, spreadsheets, pick one and master that in the mathematics context and work on that. And then when you believe you are at this stage where you have really integrated that into the curriculum, then move onto something else and go from there so that you don't have to think, "Well, okay, there's new technology there. I really wanted to do that, but I don't have the time."

So choose that one thing that you are familiar with, the students are familiar with that has high pedagogical and learning value to it, work through there and become a star in integrating ICT in the maths curriculum at your school, through that process. And then when you are confident with what you have in your school, to move on to other areas, to more advanced technology that is out there and use what you've learnt in the past to move on to those more advanced technologies that you have spoken about Rosemary.

 

- I think you're actually making a very good point. Education is kind of subject to fashions and the new best thing comes along and everyone says, "Oh, we've gotta get rid of this, it's old hat, let's use this." Now, there's still a place in education for using an exercise book and a pencil. There's a place in education for using tablets, for using interactive whiteboards. You don't throw everything out. And I agree with you completely, use things that you and the students are familiar with and build on that rather than throw it out and get the next best thing. One of the problems I feel with education generally, is that nothing is ever given time to settle down. You don't ever embed it properly.

 

There's a comment in the chat I can see. So we're going on a merry-go-round over a 10-year cycle. I've been around more than 10 years, and it's been a merry-go-round from the time I entered education. So, it's like a churn, constant churn. I do like Sue, your comment using Math Eyes, try to look at things with Math Eyes and see, look at the technology with Math Eyes and think, "How can I use this to enhance my mathematics program?" With all of those things that Michael has said and keeping in mind some of those ways of looking at programs and evaluating it, I've put the reference of the evaluation into the PowerPoint. There is apparently an online tool, but I have to confess, I couldn't find it.

 

So maybe it's buried deep in the desert in Morocco somewhere. But I couldn't find the actual online tool, but I did find the papers around it. You'll probably do better than me. And I believe it's an interactive online tool, so you can actually give a score out of 5 or 10 to each point and decide on that basis, whether the technology is worth investing in.

 

Now, whether you want to go to that sort of trouble. My gut feeling is that most of these decisions are made in staff rooms where people are sitting around and talking about it, and that's fine, but there are tools available. So yeah, yes, there's a political thing. "Have you got Maths Eyes?" Oh, I should go and look at that. Thank you, Sue, I will go and look at that. "Have you got Maths Eyes?" Excellent in the chat there?

 

- So I'll just turn on the video and just say that for you. I saw that one recently, and if you watch the video and they're using just your whole environment. And for me, it's about children understanding maths isn't just what you do in the classroom, in a school.

- Absolutely.

- Maths is about what's out there in your environment. When you start to look at things with Maths Eyes, it just brings this whole new picture.

- That's true.

- And love of maths and that's what we wanna build, positive mindset.

- Yeah, we sent kids out with digital cameras once and said, "Just take photographs of anything you can see that's maths-related." Well, the variety of things that they came back with was just extraordinary. I mean, you could do that with an iPad taking pictures, Lots of possibilities for things like that. And I agree with you totally. We actually have to get kids looking at maths in a different way.

- Yep, and they need to get that love in primary school so that when they get to secondary and it's a little bit tougher, they're not put off by what they're encountering in class.

- Yeah, yeah. And we need to change some secondary teachers as well.

- Yeah, absolutely.

- And there are ways of doing it. Yeah, no, that's very helpful. Thank you for that. And I just popped in the chat can we have access to the recording? 'Cause I had technical issues. I was trying to do this on my iPad and discovered that I couldn't.

- Yep, absolutely. I'll have the link for you after this is finished, no problem.

- Great, thanks.

- Good.

- So Rosemary, have you written a book? Did I miss that?

- Yeah, no. Yes, we have this book, which it was actually written for I don't know if that's right. So this is the third edition. We're in the process of redoing it, revising it. And the fourth edition will probably out early next year. I'll let Michael know. We have deliberately tried to focus on using technology where it's appropriate. Just trying to find an example, which I can't at the moment.

- You can provide me-

- It doesn't matter.

- With a link Rosemary, where teachers can get a copy of this book.

- Yeah, I'll send that to you, if you like, get an appropriate one from Cambridge, it's published by Cambridge. As I say, the new edition will be out early. We're including in that new edition Sue, teaching online, because so many teachers had to suddenly cope with teaching online. And other ways of using technology, we're beefing up the STEM chapter, for example, with a lot more the computational thinking and coding, and so on.

So we've made a deliberate choice to emphasize technology, but it's not totally about technology. And we try to put in lots and lots and lots of real life examples. We have sections called classroom snapshots, and every one of those is taken from some real life scenario, sometimes modified to make the point we want to make, but they all come from real experiences.

- I'm just gonna put in-

- Is there anymore questions.

- Sorry, I was just gonna put in the chat another link. I don't if you've heard of the Mathematics Hub.

- Yes I have, yes.

- Maybe for Katie, yeah.

- Yeah, yes, put it in, that's very good. Youcubed is another good one. That's the work of Joe Boaler. There's lots of really good links out there, yeah.

- Any more questions for Rosemary?

- We sort of run out.

- No, we might just end it there then. And thank you once again, to all those attending, and to you, especially Rosemary for this.

- My pleasure.

- For this presentation. It's been my great privilege and pleasure to have you and to co-host with you today. So thank you so much. And I'll provide the link for those who want to re-watch this recording. You'll find it in our ICTE Solutions LinkedIn site as well. So thank you once again, and we'll hope to see you again soon.

- Okay, thank you.

 

How to integrate ICT in teaching maths

ICT in Education Teacher Academy