Incidental Mathematics: Uncovering Hidden Learning through Digital Technologies with Dr Margaret Marshman & Dr Emily Ross

In this episode of the Technology and Learning Podcast, host Ellie Manzari from Monash University speaks with Dr Emily Ross (University of Queensland) and Dr Margaret Marshman (University of the Sunshine Coast) about their recent research on integrating digital technologies in mathematics classrooms.

Dr Emily Ross is Deputy Director of Teaching and Learning, Director of Primary Programs, and Lecturer in the School of Education at The University of Queensland. Her research on curriculum interpretation and implementation has shaped government policy at state and federal levels, providing a critical nexus between policy and practice. Additionally, Emily leads research and innovation in STEM, mathematics, and science education, advancing disciplinary pedagogy and teacher capability across primary and secondary contexts. 

Associate Professor Margaret Marshman is Discipline Lead Secondary and Outdoor Education in the School of Education and Tertiary Access at the University of the Sunshine Coast. With a background in medical physics, laser physics, and MRI, she transitioned into secondary mathematics and science teaching, later serving as a Head of Mathematics. Her research focuses on mathematics teacher education, exploring beliefs about mathematics, inquiry-based pedagogies, statistical thinking, and spatial reasoning, and she supervises doctoral and masters’ students across these areas.

Link to study:

Teaching the incidental mathematics: How integrated tasks with digital technologies unlocked mathematics concepts in primary school classrooms. Ross, E., Marshman, M. & McMaster, N. (2025). Mathematics Educaation Research Journal.  https://link.springer.com/article/10.1007/s13394-025-00529-0

Transcript

Ellie Manzari: Hello and welcome to Technology and Learning podcast series. I'm Ellie, a member of AARE, Technology Learning Special Interest Group. Today we're exploring the fascinating paper recently published. I'm joined by Dr Emily Ross from the University of Queensland and the Dr Margaret Marshman from the University of the Sunshine Coast. Their research looks closely at how integrating digital technologies into mathematics classroom, can create unexpected yet powerful moments of learning we call incidental mathematics. Emily and Margaret, welcome to the podcast.

Dr Emily Ross: Thanks so much for having us, Ellie.

Dr Margaret Marshman: Thank you for having us.

Ellie Manzari: I really enjoyed reading your paper. It challenges the assumption that mathematics always sits neatly within STEM. Margaret, I might start with you for the first question. Your paper position mathematics as often overshadowed by integrated stem. Why do you think Mathematics, despite being so fundamental, consistently gets pushed to the margins?

Dr Margaret Marshman: Well, often people do STEM from their own specialisation. And often this is Science or Technology. And it's not frequently Maths that they're coming from. And so they see Science and Technology as the fun ones. The ones that are really able to engage the students. And so they're so focused on their Science and their Technology that they're not looking for the age appropriate mathematics. Now Mathematics to a maths expert is fun. There's so many opportunities to come at STEM from the Maths point of view, so that often people are bringing in Maths that's not age appropriate. That's both either too high for early years people, so thinking they want to measure temperature, but then use thermometers. But then little people can't read decimals, don't understand decimals or that it's too low a level for the upper primary. And sometimes if they're not Maths experts, they might have Maths anxiety. And so they're tending to steer away from the Maths or they can't see the Mathematics in it.

Ellie Manzari: Oh, that's such an interesting perspective on why mathematics often gets sidelined. I'd love to hear your take on the curriculum. So how did the Australian Curriculum Version 9, shape the way you design and frame this research? Do you see this curriculum reform as enabling or maybe even constraining integration?

Dr Emily Ross: It's a question Ellie. Because I think there was very purposeful work done in moving to version 9. And we saw a lot of that in the connections, particularly between Maths and Digital Tech. Which is why we chose these as two areas to focus on for our project. We saw in Version 8, things like computational thinking as an example, was sitting really heavily and described quite well in Digital Technologies. But of course it has a wonderful place in Mathematics as well. And when they were working through this current recent reform, look to see those connections, and in trying to declutter the curriculum a little, have tried to give them a home, one place or another place and then make a few connections here and there. And that's been useful because then you can see some of those big broader connections, but they're sitting within the curriculum. So we need people to be looking for those things in curriculum as well. So our project where we started, the first sort of area we started with, was data. Because we saw that they had made very purposeful the use of the same definition as a background piece to the Digital Technologies and to the Mathematics. So if you were the teacher going into those two areas, and looking to see what they meant by data, you'd find the same words. And that's a really helpful starting point for someone who might not be seeing those connections. And as Margaret said before, if Maths isn't your strong suit, but you're saying something really cool in Digital Technologies, you might see that opportunity then, that you hadn't thought of before. So there is an opportunity that curriculum can enable a lot of work in this STEM space. And we kind of capitalised on that a little bit, so that we could show teachers those connections. But at the same time, we need teachers to be going to the curriculum to find those connections and going into, not just the content description, or not just the achievement standards, as  the have to pieces of curriculum, but also the background pieces, like those definitions, and other things that really show those connections. Maths is a wonderful myriad of ideas that are interconnected, as is Digital Technologies. It's very hard to sometimes describe it in a linear fashion, yet we're forced to teach in a linear fashion. So the more we can show some of those connections, the more opportunities we can give.

Ellie Manzari: That's a great point about how curriculum design, shape what teachers plan to do with mathematics in the classroom. But could you also share with us some of the most meaningful learning that happens beyond those plans, in those unexpected, spontaneous moments of incidental Mathematics. Margaret, can you unpack why these moments can be so transformative for students? I'd love to hear how teachers, recognise and acted on those opportunities in practice.

Dr Margaret Marshman: So often when teachers are planning Mathematics lessons, they tend to plan in chunks. They have these Mathematics descriptors, content descriptors that they're wanting to address, and they're not always thinking about that connected web of Mathematics, and how the lessons link between what happened last week, last month, or what's going to happen into the future, or even with the other strands of Mathematics. And so, if they focus just on their own chunk, then they're not planning for, what they call unexpected or incidental topics that come up within the Mathematics. And so, if the teacher has horizon knowledge, so they know Mathematics beyond what's at their year level, maybe it's the next year level, maybe it's something it's a bit tangential. When these new ideas come up, they can use that in the moment thinking and take it as a teachable moment and start looking at that Mathematics, or make connections to that different area of Mathematics. The Rowland and his colleagues talked about the 'knowledge quartet', that contingency. They get an unexpected student response, and then they can capitalise on it, and make those Mathematics connections. Whether it's in the same areas. So taking their decimals further or it's going into a totally different strand of Mathematics. There is those opportunities for that. But without the horizon knowledge and without that knowledge of all those connections, it's much more difficult for teachers to see those opportunities.

Ellie Manzari: I really like how you describe those spontaneous discoveries. And the last remark, it shows how responsive teachers can be at that moment. But of course, making that kind of integration happen constantly can be challenging for the teachers. Your paper highlights both the potential and errors to integration. Emily from your perspective, well, from your experience, what do you see as the biggest barrier stopping teachers from making these meaningful connections? And do you think there's barriers or more about the confidence, resource or beliefs about what counts as real Mathematics?

Dr Emily Ross: Well, that's a really good question. And there's so much to unpack in that as well, because some of the work that we started with and a conference paper that Margaret and I had published some time ago. Was looking at those barriers. First and second order barriers through the lens of Ertner's work. And we found that some time since some of that original work that Ertner did, and yet we're still seeing first and second order barriers pop up in the work of Primary school teachers, when they're using Digital Technologies. We use that to inform some of this work as well. Because what we were seeing was that combination of the confidence within the teacher, to feel that they could take it on. Both the technologies, but also we found it in the Mathematics as well, that they didn't feel the confidence to do something different or new in Mathematics. Sometimes that came from the positioning of the school and how the school felt that they wanted the more traditional style of Mathematics teaching. That they didn't see that potential, of having the Digital Technologies in the Mathematics classroom with them that they wanted to see that very textbook driven, heavy style of Mathematics teaching. But sometimes it was also about the teachers feeling a little bit more comfortable and confident when they had it there in front of them, and were able to teach from something that they knew to have that credibility in the space. But we also saw some of the external barriers that impacted these teachers as well. Sometimes STEM isn't valued in the school. That sometimes it was something that was an after school club or a lunchtime club. Or that a STEM specialist would come in and do that for the teacher, that the teacher didn't have to have that integration or knowledge of how to bring the different learning areas together in that lovely weave we get in integration. But then sometimes there are also policies and it might be school based or it might be broader. So things like timetabling. We found it really interesting with some of our teachers that particularly and P to 12 schools, that Senior school timetabling was affecting the Primary school just as much, particularly if that STEM specialist was the Senior school teacher that was being sent to the Primary school to help out. Then it meant that it had to be in their timetabled time and therefore STEM got pushed to being at those particular times. Some of the broader policy positions, at state level, and not just in Queensland, in other places as well, that doesn't value integration necessarily. So some state policies that show that teachers need to report in individual learning areas, for instance. And so if I have to report in the learning area and my employer is saying I have to do this, then is it worth my time to do all that work to integrate the learning? If I'm then going to have to pull it apart at the other end to report on it. Even though there's a lot happening in a STEM space, there are still little things, little places and pockets that are inhibiting the teacher from feeling that, yeah, okay, this is a good idea and I should go with it. And we haven't even unpacked that feeling of overwhelming, that people feel from the curriculum being so big and so broad and having, as a primary teacher, having to have eight of those under your belt to then plan with. It's just another thing. So anything we could do to try and show that it has already has some of those connections, or that it will make things a little easier or buy back some time, any of those sorts of things we found were really helpful, because it showed the teacher that it isn't the big burden. It can actually make things a little easier, but you need to know where to look.

Ellie Manzari: This really ties into the broader system, especially how curriculum and policy can support those and what happens in the classroom. And Margaret, if policy makers or the curriculum designers were listening to this podcast, what's the one change you would urge them to make to better support Mathematics through STEM integration. And Emily, I'd love to hear your thoughts.

Dr Margaret Marshman: Well, I'd like to see them value it. So there is a lot of talk about STEM, how important it is. They're pouring a lot of money into STEM projects. They're ensuring that there is Technology teachers in all State Schools, and they're saying that's going to help with STEM. But it's not really valued in terms of the curriculum. If it was valued, it would be a cross-curricular priority. They would be opportunities for teachers to learn about integrating subjects, learn about some of the interesting STEM activities that can be done, not just the fun ones, but the ones that are actually doing curriculum learning. Like, yes, they're fun, but when teachers can see the curriculum learning that is happening so that becomes more than a rhetoric.

Dr Emily Ross: Picking up on that as well that Margaret was talking about. I think for teachers, when we talk about ITE and Initial Teacher Education, it's so full right now. Particularly in Primary. Our Primary programs are chockers, with everything we're being told we have to teach. So that we have our Primary teachers ready. That we don't actually have the space to do something like integrated learning or STEM or something that's a little bit different. The other part I also think we miss out on, is the side that actually would show teachers how to value curriculum. We don't have that time anymore to do that curriculum theory or curriculum scholarship that actually shows the value of what curriculum can be. And it's really unfortunate because in the media space, in the public discourse, we're starting to position curriculum work as burdensome as an administrative task of teaching, as opposed to something that actually helps us to unlock learning for little people and bigger little people. It's that opportunity that we have, in going to the curriculum, seeing that beautiful map of all the things we can do, and picking a wonderful journey to take our students on. And then having the knowledge that if it came from the curriculum, we are still taking them on a journey that's going to lead to their further learning and the destination they want to go. But until we value that work as well, we don't give teachers the permission to do something really interesting, engaging and different with it. They're too busy having to, and feeling they have to tick the boxes of what's in that curriculum. And that's not what it should be. It should be there to give them that opportunity. We got into this to be Maths teachers, Science teachers. We didn't get into it just to read a script of what this lesson should be. We got into it to unpack something wonderful and take kids on a journey so that they could be engaged, invested and want to know more and continue that curiosity. And instead, at the moment, certainly in the public discourse, we seem to be willing to give teachers the script and tell them just to follow this and it'll be okay. I don't think it will.

Ellie Manzari: And it's not surprising that the teachers call the curriculum, 'the prescribed curriculum', and we cannot ignore this workload factors on teachers. 

Thank you both for joining me today. And for such an engaging discussion. Your work really highlights how integration can cover deeper Mathematical thinking and when teachers are supported to see those connections. I think our listeners will really connect with that vision of more authentic Mathematical rich STEM learning. Thank you very much. 

And for listeners who would like to explore the paper, with link to it in the podcast notes. Thanks again and I hope this sparks new conversations about Mathematics and Digital Technologies can work hand in hand. Bye for now.