ZDM – Webinars – Mathematical Modelling – June, 2025
Webinar on International Perspectives on Mathematical Modelling
Issue 2/3 (2025) of ZDM – Mathematics Education
Editors:
Stanislaw Schukajlow – University of Münster – Germany
Janina Krawitz – University of Köln – Germany
Xinrong Yang – University of Macau – China
Vince Geiger – Australian Catholic University – Australia
——————————————————————————————————-
Video:
00:00:00 – 00:03:31 – Presentation
Stanislaw Schukajlow – University of Münster – Germany
——————————————————————————————————-
00:03:32 – 00:32:27 – A Systematic Review of International Perspectives on Mathematical Modelling: Modelling Goals and Task Characteristics
Janina Krawitz – Institute of Mathematics Education, University of Cologne, Cologne, Germany
Stanislaw Schukajlow – Institute of Mathematics, Education, and Computer Science Education, University of Münster, Münster, Germany
Xinrong Yang – Macau University, Macau, China
Vince Geiger – Australian Catholic University, Melbourne, Australia
——————————————————————————————————-
00:32:28 – 01:00:33 – Identifying and describing generic, specific, and catalytic enablers of mathematical modelling
Vince Geiger – Australian Catholic University, Melbourne, Australia
Peter Galbraith – The University of Queensland, Brisbane, Australia
Mogens Niss – Roskilde University, Roskilde, Denmark
Mirjam Schmid – Australian Catholic University, Melbourne, Australia
——————————————————————————————————-
01:00:34 – 01:25:54 – Pre-service mathematics teachers’ experiences and insights into the benefits and challenges of using explanatory videos in flipped modelling education
Mustafa Cevikbas – Humboldt University of Berlin, Berlin, Germany
Denise Mießeler – University of Hamburg, Hamburg, Germany
Gabriele Kaiser – University of Hamburg, Hamburg, Germany
——————————————————————————————————-
Yeah. Um, good morning, good evening, good day. I would like to welcome the participants and presenters of the webinar. My name is Tanislav Shukov. an editor of TDM mathematics education and it’s my great pleasure to mandarate this webinar which is based on the double special issue on mathematical modeling and was edited by Yanina Kraitz Yang Vince Geer and myself. Of course, special thanks go to Gabriel Kaiser who helped a lot during the preparation um by sending invitation for example from the authors and also during the editing of this special issue. So now uh I would like to share two slides. Uh
has just come out. Yes. Re reached us yesterday. The printed version. It will be sent to the authors in the next few days. Yes. That’s a very nice that’s a very nice news. And uh So now I hope you will all see the screen. So the presentation and um again the SDM webinar recordings are available not only from this special issue but also from this webinar but also from other webinars on on the homepage. So please look uh there and we have uh in 24 contributions in this special issue and uh especially what what I would like to emphasize there were many international collaborations where the contributors came from different countries and we see that also two or three contributions is the same in this um uh webinar that we selected for them. Yeah, we have three contributions that will be presented today out of 24. We will start with a systematic review of international perspective on mathematical modeling modeling goals and task characteristics. It’s a survey paper that introduced the field. Then we will go to identifying and describing generic specific and catalytic enables of mathematical modeling. And the third one would would be on pre-ervice mathematics teachers experiences and uh insights into the benefits and challenges of using explanatory videos in flip modeling um education. So now I would like to share you what is the procedure especially for the presenters. All presenters can share their screen with the audience. Uh I would like to ask the presenters to be mindful of the time. Each presenter has 15 minutes for their presentation and I will announce when the time is up. After that we will have about 5 10 minutes for discussion and uh I would like to ask the participants you are very welcome to ask questions in the chat during the presentations uh which we will try to pick up during the discussion. So now Yanina the floor is yours. You are very welcome to present uh their part about the systematic review.
Yeah, thank you very much. I start sharing my screen. So one moment. Okay. So thanks for the introduction and thanks for the opportunity to share our study um a systematic review on international perspectives on mathematical modeling modeling goals and task characteristic. This uh study was done uh with the co-authors Danoslav and also Rangy young and win sky here. Okay. Um first why is it important to focus on modeling and to focus on modeling perspectives. So it is consensus that mathematical modeling is globally recognized as important for learners everyday life their civic engagement and their STEM education. However the field lacks still a unified understanding and a current theoretical foundation. So our overarching question or our starting point was that we know from previous research that multiple modeling perspectives exist and that they are shaped by different goals, different task characteristics and also regional traditions. But um we still know very little how these are presented in recent modeling research. So our goals were to provide an overview of recent modeling research to identify perspectives in recent modeling research and third to reveal also underexplored or emerging areas in recent modeling research. Okay. um our theoretical background. First, very briefly here, modeling um modeling tasks can be considered as mathematical tasks that are connected to reality and require substantial translation processes between the real world and mathematics. When solving mathematical modeling tasks, you can talk about the modeling process and there are several conceptual frameworks which are analytical reconstructions of the modeling process. Here for example the modeling cycle by plume and lies or the theoretical framework of flesh and dur about model eliciting activities or here modeling cycle by glorious stillman and there are um of course many others um modeling perspectives when we talk about modeling perspectives we um according to Kais and Sri Raman and to Bloom we um focused on different goals of teaching modeling and different task characteristics. And now I want to explain first um what different modeling goals we focused on. We focused on um six modeling goals. First pragmatic goals which are the goal of understand and solve problems in the real world. So you teach modeling that students understand the real world problems and are able to solve them. Formative goals focus on develop developing competencies for example modeling competencies obviously but also other competencies like problem solving or argumentation competencies or others. Then cultural and antipatory goals um are goals that learners um learn to critically evaluate real world phenomena and their models. Cultural mathematics goals focus on um a comprehensive understanding of mathematics as a science. Then psychological goals with a focus on motivation um focus on to enhance the relevance of learning mathematics and psychological goals with a focus on learning focus on to structure knowledge and to facilitate the comprehension of mathematical content. So for reaching these goals, different task characteristics can be considered primarily important and there’s not enough time to go to all of these combinations, but the combinations of certain task characteristics and certain goals um are foundations of the different modeling perspectives. So they can be used to characterize the modeling perspectives. For example, for reaching pragmatic goals, authentic problems can be considered primarily important. Or formative goals, the cognitive richness, which is um to have um uh to focus on modeling activities like the subcompetencies which are necessary to solve a modeling problem can be considered primarily important. Okay, so we used this framework as a basis for our analysis to answer the following research questions. First, what are the characteristics of re modeling research in terms of their geographical distribution, the participants, the methodological methodological approaches and conceptual frameworks. Second, what goals for teaching and learning modeling and what characteristics of modeling tasks are described in recent re research and which perspectives on modeling emerge from these goals and tasks? And third, how do the identified perspectives on modeling in recent research differ with respect to geographical distribution, participants, methodological approaches, and conceptual frameworks. Okay, what have we done? We did a literature review following the Prisma guidelines. So we searched in we used in our search strings model in the title with a wild card. So including modeling or models and in title or abstracts math and model. We searched in Web of Science, Scopus and Eric. And we also included the chapters of the IKMA books from 2020 till 20 um 24 and we focused on learners from preschool to upper secondary school and we started with 4,045 initial studies uh which were screened uh and assessed um whether they focus on learners from preschool for upper secondary school and if they are written in English and so on. And um after this exclusion process we ended up with um 108 final studies. Okay. Now I come to the results. First the characteristics um of recent modeling research. If you look on the distribution uh regarding the uh the regarding countries, you see here that a lot of um uh studies come from Germany and the US but also other countries like Turkey, Australia, South Africa and Spain and also others significantly contributed to recent modeling research. Um so you see here that countries from all over the world contributed but you also see some white spots on the landscape. Then we found that the main focus was on lower secondary school students. So year levels levels 7 to 10. and the most studies applied case studies as research method. Then we found that there were 23 different conceptual frameworks that we identified with uh bloom and lies as most frequent we cited. And it is also remarkably that there is a um big number of conceptual framework works which were cited only by one study. Now I come to the second research question which is uh focused on the goals and the task characteristics and the perspectives of modeling. Looking at the goals of modeling, we found that formative goals, this were the goals of developing competencies like modeling competencies or other competencies were most frequently mentioned as goal to teach and learn mathematical modeling. Second, looking at the task characteristics, we found that authenticity of task and cognitive richness, focusing on um important modeling steps or modeling activities were most frequently mentioned as important task characteristics. And then we looked at the perspectives which emerged from the combinations of goals and task characteristics. So 48 of publications could be matched to one of the theoretically described modeling perspectives and all of the theoretic theoretically described perspectives were found in our research. a little bit more dominant than other perspectives where educational modeling and pedagogical modeling they mo were most dominant in the studies. Further, we found two new combinations which were frequently which frequently appeared which were first the combination of pragmatic goals um that learners learn to understand and solve real world problems and cognitive richness of modeling tasks. And the second combination was psychological goals with a focus on motivation and authenticity of modeling tasks. And here I want to give two examples to make this a little bit more yeah that you can understand what we did and how this looks. So first a study by K Niss and Con um focused on pragmatic goals. They wrote that preparing students for future citizenship carious and scientific issues of life which we coded as pragmatic goal. And they wrote that modeling task targeted students active engagement while experiencing each phase separately moving from one phase to another and applying mathematical modeling subencies within faces. We code it as cognitive rich task. So here this new combination um of goals and tasks appeared. The second combination was um psychological um goals with um authentic tasks. Here in Brunet, Bianas and Alberin uh they focused on psychological goals with a focus on learning. We have um we choose mathematical modeling activities to promote students conceptual learning of mathematics. So here the focus is on the conceptual learning of the learning of ma mathematical concepts and uh they also um highlighted the importancy of using authentic tasks as using realistic context and situation close to their own reality that helps students to understand and um yeah remember things. Okay. The third qu research question was about differences among the perspectives. So focusing on the perspective of educational modeling, we found predominantly German publications within these perspectives and a focus on lower secondary SK students and Blumen lies as conceptual framework. In comparison to this social critical modeling um there we found predominantly Brazilian publications a focus on upper secondary students and no specific conceptual framework. And third for pedagogical modeling we found no specific geographical focus a focus also on lower secondary students and legend as most cited conceptual framework. Okay, discussion. So, our results highlight the diversity of perspectives on mathematical modeling in recent research and also shows um a stronger focus on educational modeling and pedagogical modeling um as yeah most dominant perspectives on modeling in recent research. Then we showed specific focuses within perspectives. Uh and this also highlights some research gaps within the perspectives. For example, we found no studies on upper secondary education in the perspective of applied modeling. So this highlights that there’s a need to go deeper or further in uh future research to fill some gaps. uh as theoretical implication. We see a theoretical advancement um that is needed to integrate and connect diverse conceptual frameworks of modeling since there were a lot of um different conceptual frameworks cited only once and integrating these or highlighting the strength of single frameworks would help to gain more mutual understanding. So thank you for your attention and I’m looking forward to the discussion. Uh thank you very much Yianina and I open the discussion. Um who would like to to start um and with a question? Should I stop the screening? Um
perhaps or do you want me to keep the slides? It depends on the question but uh so you we we’re looking simply for now you perhaps can stop and then we will see well uh since nobody else has a question I have a question. Uh so uh thank you Yanina for your presentation and uh can you tell a little bit more about the methodology that you use to to get these papers together? You may need the PowerPoint but if you’re not you just say it. So thank you so much and was a nice uh a nice window over the production. I was just wondering more about what is the time space probably was missing here. It’s it’s early in Brazil and cold for us. Yeah. Um I can uh maybe change to the slide uh where the um method here this um we used um we we used search strings and databases and we used that the string model with this wild card. So this means that in the title of uh studies needs to appear model like modeling models or something like this and in the title or abstract uh needs to be included math and model and then we screened the papers we get whether they focused on mathematical modeling and uh on um learners from preschool to upper secondary school and ended up with 108 studies which were published between 2020 and April 2025 which were further analyzed by us. Yeah. Uh uh thank you Yanina. I I noticed that Stephanie Ra uh had a would wanted to ask something. Am I right? Yes, you’re right. Um yeah thank you uh also from me for this uh very interesting talk. Um you said that there are many case studies you found in your analysts and which main research questions are focused in these uh case studies. Do you also analyze this? Um we we did but it is not in uh in the uh study um in the study on perspectives because it was too much for one paper. Uh case studies focused on describing processes describing modeling processes when I remember right. Yeah. So they were very um also often very descriptive uh wanting to find out how modeling processes can look can yeah describing the different activities. Yes, there are very rich studies that try to capture it in a kind of holistic way what is going on in modeling. Yes. And of course that’s why it’s also not was easy to find out what exactly is in the focus because they simply the process are are very rich. uh tavit. Hi everyone. H first thank you for the presentation and I really really liked reading the full paper. Uh you had done a really good job all of you. H I have a question regarding the searching for modeling or mathematical modeling through the method that you see here. When I do search uh for mathematical modeling, I sometimes get um not sometimes but most of the times get not just studies in the area of mathematical modeling, education, mathematical modeling but also in similar areas like physics or science etc. So how did you differ between these studies and others and how do you see um the similarity between mathematical modeling in our community and to others? Yeah. So we focused only on mathematical modeling and math education. So we excluded the studies which were mathematical studies. Um and we um this was done in the exclusion process um in the search and also we limited in the databases the research areas. This is also described in the paper. So we limited it to psychology and education and so this fields of research and did not ex include uh pure mathematical studies but generally do you see some resemblance between um the mathematical modeling framework within the mathematical community mathematical education community and others not just related to this specific speific paper but generally
ah generally that is that is a good question I I think I I’m not into the mathematical modeling framework in the mathematics community so I can’t answer this question maybe one of the co-auors could add something so I I also not I know that from physics as in physics education So I’m more familiar with educational area because mathematics we do not look that so so exactly but in for example in physics education they also have uh yeah similar descriptions. Gabriela would you like to add?
There are actually are wonderful to see you and thank you very much for all the four ores for their very interesting task. Actually um there were in former times and we lost a little bit within the community. This group of mathematicians who worked in higher education and who were interested in mathematical modeling at higher education especially in engineering. uh and they actually had developed several frameworks which were very close to actually uh the framework by either Peter Gorbra and Flores Durman or by the actually very more simple one I had developed with Peter Stender. So it is not this sophistic uh modeling framework but a more easier one using only five steps. So this uh so these are and of course we had very close relations with mathematicians here at the University of Hamburg carrying out modeling days and in this way uh there were several publications about a modeling cycles and uh there were strong discussions how to distinguish between a mathematical modeling and a real modeling and the mathematicians I had been in touch with uh that where modelers from mathematical from mathematics they claimed that you cannot distinguish between a real model a real world model and a mathematical modeling. They would always say that look you have this mathematizing phase and there you have the real world and then you mathematize and then you go actually uh into uh the mathematical model. So I think that are my experiences with um mathematicians. Probably Mogans and Peter who are much more knowledgeable than I in this area could add a few things. I would support that comment. Okay. So I do not see any or Morgans do you like to comment too? Yeah just just if one one sentence please. So so I think that one of the reasons why it is not so easy to distinguish between a mathematical model uh and and a real world model is that that requires a clarification of the notion of reality. And it is clear that lots of mathematicians uh have a different view of what reality what constitutes reality in comparison to what is happening in the math education sector. So so that is basically a philosophical issue rather than a pragmatic issue as I see it. Yeah, thank you very much the very interesting comments by Gabriel and by you Morgans. Um yeah and uh Yanina thank you very much again for your presentation and thank you for the question for the discussions and now we move and I don’t know Vince would you like to share your Oh I’m not sure who will start so please go go ahead. Uh, thank you, Santa. I’ll see what I can Oh, hang on. I’m having a problem here with sharing. Uhhuh. Do you have a green button there, Vince? Uh, yeah, I do. It’s That’s not the problem. I’m getting a very strange screen I’ve never seen before. Um, no. So, didn’t you send your our presentation to Stannislav? Maybe.
Yes. status, are you allow able to share our presentation because there’s something on this is a new computer. When we had the cyclone, it destroyed my previous one. So, there’s obviously some a few switches that aren’t right.
Don love, you have to unmute. I think that’s the best.
Yes. Thank you very much. Now um I would like to I would retrieve it from my because I thought ah I do not need it so only for the specific case but I’m
yes I didn’t think you need it either but
yes but but I but I have it in my uh post so I will um share it now with you and try to to go through the um through the slides in the appropriate It time I notice okay so because I’m also uh recording the webinar so I took I should took an additional pathway but now it will work. Thank you. Yes. So please go ahead. Yeah. So um um this this paper is uh related to identifying and describing um different types of what we’ve called enablers or disenablers. Um the contributors to the paper were myself, Peter Galbrath Moes and Miriam Schmidt. Marian couldn’t be with us tonight. She’s um while she’s working in Australia, she’s returned to Switzerland for a short time. Um but um Peter Galbra’s going to we’re going to share the presentation and Peter Galbrath’s got the um the opening um bit on it, I suppose. So next screen. Yep. Okay. Right. So really can you hear me? We we can hear you. Y.
Okay. Right. So looking at the box at the top, there are really two elements of that that Henry statement really is talking about what mathematical modeling can do across the board something unique it can provide and that’s really essentially our interest and the John Rey comment representative of scientific American is that really there’s something that needs to be learned made second nature if our students are going to be able to get the benefit from what this particular approach can do. So the consequential goal is to achieve efficiency and fluency with a complete modeling process.
Peter is holistic. Uh Peter, we hear you double because you are apparently locked in twice. It’s very difficult to understand you. Sorry for interrupting even poet. We hear you twice. It’s an Is that any better? Yes, it’s a bit better. Hang just a moment. I think at the host you can mute the user P galp and then the issue would be solved.
That is yes
I will I’m share the slides but I will will try to I I will try
is that any is that any better?
Yes that’s much better. Oh
uh I I’m I have because um I I will look for advice that Yanina told me that I can Okay. Could can I have the slide back? Yes. I think simply go ahead like that. I think the problem is
it’s okay.
Yes. It’s little bit too time. We need to share work.
Okay. Then I I I will go on simply and share the screen again. Okay. Uh but Pet uh we do not hear Peter now. So Oh, I tried. Peter, you have unmuted. Can you turn on your micro? Yes, but that was the problem before. Yes,
we can hear you well now, Peter. Yes, it’s great. Is this okay now?
Yeah. Yeah. Okay. Right. So, what I I’ll skip then the consequential goal two aspects efficiency and fluency. Now, we talk about Whoa.
Oh, that was I was not sure what. Sorry. Yes. I I’ll I’ll say in a moment the logical analysis of modeling pro project starts of course with a model and goes through systematically these various steps which we know about and I won’t repeat here but they are the same whatever the project is that’s what Henrik Pollock is saying whatever the area is that is our point about a holistic modeling process So it leads to the representation of a generalized modeling progress. I’ve called it an onlogical modeling cycle because it is the reflection of reality and we know that there are many many different modeling cycles around and some of them are confusing. What this does is represents a modeling problem solving process iterative sequence applicable to all modeling projects. If you look at that logical analysis those particular or aspects in the same order will occur in all. So if we move on to the next slide. Okay, that’s typically then the holistic aspect which represents that particular model and that will be familiar to a lot of us but that is in a sense the onlogical cycle which applies to every particular project we can think of and that is the thing that we are trying to get our students to grab hold of and be able to use effectively and efficiently. So next slide. Now we know that that that is the basic cycle or the onlogical cycle that is the modeling cycle which students and and ourselves must use. Now we move on what is the difference when we begin to teach it and that’s when we have various holistic experiences for teaching modeling and we have examples of elaborated cyclic representations which which contain also the teaching focus. There’s the familiar one from Verer and Dominic and that contains of course the aspect situation and real model of scaffolding procedures. Next slide. And there is for example Dick Leash and and uh and his collaborating authors using the model and modeling perspectives modeling eliciting activities with various properties. That’s the scaffolding process there. And now the third the next slide. And this in fact is is situating our study at the same level as the two that I’ve just shown before. We call this the enabling project and there is a modeling cycle with pedagogical aspects added from our aspected. The box at the bottom indicates all the different things that teachers might use. We don’t know which of them they will use at any particular point until we begin to unpack each particular problem. The diagram itself as with the uh the the u the Verer and Dominic and with the Dick Leash one does have that basic modeling cycle embedded in which case here you see it has the single-headed arrows going in a clockwise direction. The double-headed arrows indicate there’s lots of other things going on pedagogically and it’s just there representing the fact that there’ll be metacognitive activities and other support activities there and what we are saying now is trying to put flesh on the bones of those in the final my final slide the next slide which is where we begin to talk about enablers and unenablers and what these are doing is What we are doing here is unpacking and and or putting flesh on the bones of what that previous slide showed and Vince will be elaborating on this in a moment. So an enabler we consider is a factor that helps foster and further learners development of comprehensive modeling competency or holistic competence. the scope of them. It might be mathematical. It might be cognitive, social, dispositional, environmental, any aspects that impinge at all on the modeling process. It’s teaching, learning and enactment. And our focus in this project is in the identification and functioning of the enablers either singly or together for instructional purposes. And we also know that there are unablers which which can act and these can we consider as instructional factors that can slow down, impede, hinder or block progress towards achievement of modeling competency. And both of them need to be considered when we think of providing a floor under students as they learn to develop holistic modeling competence. And I think at this point I’m I’m sorry it’s been a bit confused. Uh but now I’ll pass over to Vince who will be unpack in detail what some of these things mean in practice. So just a brief note about the methodological approach. We won’t be able to do that in depth because of the time constraint, but the project took a designbased research methodology in which we worked with um five teachers in their intact classrooms over a period of around 3 years. And the purp the idea was to work with cycles of um teacher professional learning, classroom observation in cycles of theoret theory generation and refinement and teachers were very much a part of a collaborative process of theory generation. This was bringing together two different types of expertise, that of researchers and that of the practical knowledge of teachers themselves. And from that collaboration, we developed um a framework around the um those things that enable or unenable or disenable um mathematical modeling capability and practice. So maybe the next slide. And very broadly speaking, there are uh we identified both genetic enablers, those things that enable mathematical activity in classrooms, including mathematical modeling, that aren’t necessarily specific to mathematical modeling itself, but are still important as sort of I guess background enablers. And then that there were those enablers that uh were specific to mathematical modeling. We also identified another class of enablers which we’ve labeled catalytic enablers but mowens will talk about that in detail a little bit later on. So next slide please Stannis long. So we saw a number of categories of enablers and I’ll um just reiterate what Peter said earlier. Each of these enablers if absent or enacted in a way that’s counterproductive can be an unenab or disenabler. So there was the impact of learning goals external to or related to internal processes within schools or might even be teachers personal preferences that weren’t connected necessarily to modeling itself. So it could be things like broader educational goals such as promoting 21st century skills. That might be a goal of the teacher of the school. It’s not necessarily directed to mathematical modeling, but if that’s a flavor of the school or the classroom itself, that can influence how mathematical modeling is implemented. There are specific enablers from these external influences. For example, the way in which uh formal curriculum or in some uh countries uh it’s called syllabuses that refer to modeling specifically or perhaps infer modeling without mentioning them directly. Another class of enabler um were classroom expectations about ways of working. So generic en enablers includes um teachers encouraging diverse approaches and risktaking or questioning or student collaboration um or opportunities to report findings. So you could imagine if any of these things were discouraged or absent that mathematical modeling may not be implemented in the ways we might hope. Sp specific enablers under this category include shaping the physical ent environment to support modeling. And we saw schools in which for example the desks themselves or the walls could be used to draw graphs or uh manage equations or set out strategies um for which modeling could be take place. We saw that the use of digital technologies was very important in mathematical activity and uh if it’s to be enabled we would see that very few restrictions were placed uh in in their way. We did see occasions quite interestingly where even when teachers did not in a specific classroom did not impose any restrictions on technology, students thought that they were not allowed to use it from previous mathematical experience. So it’s quite important for teachers to be very explicit about what can be used and what can’t be. So on to the next slide. Um the category of managing the learning process of course involves a genetic enabler. Um that you know the learning process has to be um enacted in an active manner and not just the students being left to themselves to work it out. Um we saw that specific and explicit reference to the modeling process was key. uh those classrooms that were most successful actually would put the modeling um a a modeling cycle on students desks or up on the wall around the classroom to remind them about the process. Um but students were also encouraged to utilize or generate their own resources to support modeling. Um and we also found something um key was that the development of a mathematical question before students set out about their work. Um so typically the process involved the teacher doing an introduction talking to students about the aims of a task then asking them to go away and discuss the problem but to come back with the specific mathematical question that they would answer via modeling. um and then bring students back together to get some sort of um agreement on what question they were actually going to enact. Um in other classrooms where this didn’t take place, students often went often while goose chases and didn’t necessarily get to the places we were hoping they were going to get to. We also saw that there were was a place for two types two ways of responding to students. One of them was a measured responsiveness. In other words, only providing enough information for students to get on with the activity and no more. And that was very often just referring to the modeling cycle and asking students where they were up to and where they were going to next. But there was also occasions where direct responsiveness was necessary. For example, helping students to clarify um aspects of the problem. Um, we had occasions where we used problems where students didn’t understand what we thought were common terms um um that were used to describe a modeling situation and that needed to be unpacked for them. So the next slide and finally the last charact the last category was about what we think is a new idea related to instructional anticipation. And this was about how teachers thought forward about um where students may have blockages or anticipate ways in which they may respond to um questions that were quite common from their previous experience. Again, this was always brought back to the modeling process. Um being able to anticipate of course does not um obviate the need to be able to think on your on on teachers being able to think on their feet. Um but we haven’t actually got a lot of strategies for that at this point in time because that becomes back to the teacher themselves and how they can respond which of course is based on experience and expertise. I think it’s over to moans from here. Next slide please. So taking a little bit of a helicopter perspective u having studied intensely what has happened in different sorts of classrooms with different sorts of teachers and students it seems that we are actually dealing with at least three major challenges that deserve research and practice attention in the future. So the first challenge is to make students and sometimes teachers as a matter of fact realize and experience that mathematical modeling is not just an exciting game which it is to some but not to all but is crucial for nature, culture, science and society. That is that realization and experience is a challenge for us to achieve. We also understand and see in many occasions that mathematical models usually give rise to discussion and even controversies. Uh which is a phenomena that call uh calls for critical analysis and thinking. And finally the perhaps the most important challenge is that students have to learn and realize that they can learn mathematical modeling if properly assisted. So uh we have focused so far on generic and specific enablers that are capable of fostering and furthering comprehensive mathematical modeling competency with students. And we have also identified corresponding unenablers. And we need certainly a lot of research to actually better understand the nature of such enablers and the actual use and their potential roles in an impact on me the challenges mentioned and developing of mathematical competency with students. Next slide please. So however we have also as as Vince indicated identified another type of enabler uh which we have chosen to call analytic enablers. um um and uh we see that they can contribute to meeting some of the challenges that we have mentioned. So in chemistry a catalyst is is a substance that increases the rate of chemical reaction without itself being consumed or permanently altered in the process. If we use that metaphorically, we can then define a catalytic enabling mathematical modeling as a factor which can further modeling competency with in and of it without in and of itself being a direct part of students modeling enterprises. So for example as to the first challenge of convincing students that there are actually serious work being done in society and in the world uh by way of mathematical modeling. We should provide examples to students uh of such cases that demonstrate that questions and problems uh in various mathematics domains mathematical domains have actually been solved by means of mathematical modeling. for example, growth of an epidemic. And there are multiple other examples that we can come up with and also uh uh the construction of social artifacts by way of mathematical modeling. For example, the design of election systems. These uh such examples can provide a catalytic catalysis enabling students to realize that mathematical modeling is intensely important out there. Next slide, please. The second challenge uh presenting alternative models of the same context and situ situation uh alternative models in population growth could be an example. Um will may also serve as a catalytic enabler to students. uh there are lots of certain s such alternative models that deserve to be presented and discussed also by students and and and teachers. As a point in case we know that AI nowadays can generate mathematical models of certain situations and contexts. uh an AI generated model can be analyzed and discussed by students in the classroom and can be compared with models that students have generated themselves of the same situation and context. This helps catalytically enable students to undertake critical analysis of models they are presented with with which is an most imper most important thing to achieve. We should note that however that AI used to generate models. If this is done without student involvement, AI may actually be likely to work as an unenabler rather than as a catalytic enabler. As finally regards the third challenge, uh presenting students with presenting students with cases that have actually been undertaken by other students to successfully construct mathematical models. Our paper contains three kinds of of examples of this uh also may serve as a catalyst uh to students belief that they themselves can learn to undertake mathematical modeling. Uh next slide please. So all the kinds of catalytic enablers presented above ought to be made objects of research in the following sense. To what extent and under what conditions can the introduction of such an enabler serve as a catalyst for the development of students mathematical modeling competency? We know very little of this and we need to undertake very specific research projects that uh uncover the the ways in which such enablers and also the other enablers that we have been talking about the generic and the specific enablers actually work. uh so we have identified them in our project but we have not yet studied them in great detail and there is a lot of things to be done in that respect. There’s also a lot of there are also a lot of things to be done when it comes to classroom practice. Uh where uh we would like to see in the ways in which teachers and schools may decide to involve uh generic specific and catalytic enablers as part of the teaching of mathematical modeling. And we need reports from uh classrooms where this is happening uh and uh and perhaps to be able to compare also the conditions under which this can successfully take place and uh further mathematical modeling in our students. Of course, this is just a brief overview. There are lots of things uh that ought to be said and to be dealt with in greater detail. Uh but this is not possible within the time frame. So uh thank you for me and I think this concludes our presentation. Uh thank you very much. uh and perhaps we can uh because of the time constraints you have can ask one question and then we have to move to another presentation perhaps somebody have one question and otherwise please simply um wrote the authors they will be very happy to answer you via email if you have any questions please Alina go ahead
hi thank you very much uh for this interesting insight um just a quick question I was wondering what if you could elaborate a bit more what exactly you define as an enabler. Is it like a part of teachers competence or is it an aspect of the learning environment or is it on like different levels and includes all of that? Um well the framework itself can includes both these things and more. So it is it is about the environment. So the example I provided was about having write on desks you could write on or walls you could write on. So that environment in itself is conducive and enables mathematical modeling. Um but in the main it’s probably more about what teachers do or don’t do that enables modeling. So for example, we found um where modeling was most successful when was when teachers made explicit to students the modeling process itself and were able to constantly remind them about you know what their objectives were, what what were they were trying to do in terms of a process, not just get to the product. Yeah, Vince, thank you very much and thank you Morgans Peter and Vince. Thank you for your presentation again. And Gabrieli Mustafa, you are welcome to share the screen. Yes, Mustafa sharing.
Yeah, thank you very much. Um, I’m sharing my screen. Could you please confirm if you see my screen now? Okay, perfect. Yes, thank you very much uh for inviting us to share our paper or the few elective insights from our paper published in CTM. So we are actually uh have written or presented a study about pre-ervice mathematics teachers experiences with explanatory videos in not only modeling education but in flipped modeling education. So in the next few slides I will actually describe uh yes what everything about mathematical modeling about flip classroom and then of course about explanatory videos which are actually the three currents of our paper. So first of all very quickly a few uh words about mathematical modeling. I mean we are here uh uh within I would say a community interested in mathematical modeling or experts in mathematical modeling. So we have heard in the last few presentations that mathematical modeling is vital for mathematical literacy and that it is so important uh for understanding the real world and actually for actually securing that humanity can survive. that was said much better by Morgans and others. So, and the modeling process however and that was emphasized as well in the previous discussions or presentations, modeling processes are or modeling um examples are characterized by their open-ended nature. That means when you carry out a modeling process, you don’t know where you are actually landing with your students. So there are the it is unpredictable and you have to actually uh yes have a two-way translation between mathematics and the real world phenomena and we have actually described that empirically in the last I would say 30 years even how demanding that is and how many barriers we have and I mean this last paper you just heard about enablers and un enablers uh or unablers is actually a nice example what we mean with that. So we have but there are of course there is hope that there are effective strategies to overcome these barriers and here technology can place uh can play an important part. Next slide. So digital technologies can play an important role in order to overcome uh uh these barriers. Of course they are creating a barrier by itself. we have to be a little bit cautious. But of course there are in the last two decades there are have been a lot of proposals how to use digital technology in order to enhance mathematical modeling education and we have actually just described with the three bullet points how a technology can serve as a useful tool for to support modeling processes by for example simplifying algebraic procedures. We have here listed the work by Barry 2002 that was one of the first IGMA conferences. So that is and the work by Vince Gigger and his group is of course emphasizing as well. uh the work by the German group around Gilbert crrad is supporting uh is clarifying that visualizations can play an important rule role and of course active learning uh can be supported uh by digital technologies that is actually the work by Mustafa in the last few years. So there are a lot of frequently used tools, digital uh uh uh so dynamic geometry systems of course car system uh computer algebraic systems spreadsheets graphing calculators and so on and of course it was just mentioned of course artificial intelligence GDP uh we are actually not diving into that because we wrote the paper before we have carried out new work on actually the usage of AI but in an upcoming special issue of ZDM we will we will elaborate on that. So es especially important within this usage of digital technologies in mathematical modeling are explanatory videos. They are of course have gained very high prominence especially during covid and postcoid education as an prominent uh promising approach to enhance mathematics education in general. Next slide. So and uh I’m now coming to the third column of actually our uh paper namely flipped classroom and the role of explanatory videos. Flip classroom has been discussed in the last few uh years especially during COVID and after COVID very intensively especially as we all were forced during COVID to uh develop some kind of flipped classroom. But of course the flip classroom approach is much uh older uh it was developed long uh before uh the co covid pandemic. uh and we have brought with us one generic definition of flip classroom by Lag and others uh covering that or defining flip classroom as inverting the classroom means that events that have traditionally taken place inside the classroom now take place outside the classroom and vice versa. So that means you have actually a lot of uh individual instruction already before the lesson takes place so that you have more time for interactions during the classroom. And uh here you and we have brought actually I think a very nice uh uh visualization by Bishop and Fava uh in which we see that you actually have this teacher centered learning theories already uh before uh uh teaching and this is actually then combined with human interaction and that actually leads to flipped classroom and uh explanatory videos are a very essential element in this computer technology namely in the explicit instruction method. So here explanatory videos play an important role. Next slide. So I’m already now coming that was a very brief brief inter introduction into the theoretical frame of our paper. So uh we have carried out actually a study um we will describe that in a minute. uh and the research questions we wanted to uh uh actually to answer was uh and actually the research gap we wanted to close. We wanted to find out which benefits and challenges of explanatory videos in flip modeling seminars at the university with pre-ervice teachers uh h are exper or are actually experienced by teachers. So it means how actually how well do you or how evaluate a a pre-ervice teachers the benefits and challenges of explanatory videos in the flipped model seminar in detail. We uh evaluated how far the pre-ervice teachers uh perceive benefits of using of developing and employing explanatory videos in a flip modeling seminar. And what challenges did they actually perceive when they used developed and used uh explanatory videos in flip modeling seminars? And you see on with the emphasis on developing and employing we taking up actually uh the emphasis of our earlier uh uh uh uh uh uh speakers who emphasize that you have to do it on your own and then means what are the experiences of pre-ervice teachers in developing their own explanatory videos with a focus of teaching modeling. Next slide. So we have carried out actually a qualitatively oriented study based on flipped modeling seminars in which we use explanatory videos in a flipped classroom setting. Uh we have used uh this kind of design in two cohorts in 2021 2022 and another one follow up 2022 to 2023 and we had actually 42 pre-ervice mathematics teachers. These were master students and the modeling seminars uh were carried out at a large German university. We actually used uh Bishop and Figga’s uh framework uh on on the flipped uh uh education and uh in addition we actually used a lot of eight explanatory videos developed by ourselves. be used as usual lecture notes, articles and papers from uh the uh uh from uh uh special issues on mathematical modeling from the IGMA books and of course we used uh very famous modeling task uh which you probably have heard all have heard about like the hot air balloon or the lighthouse. uh and um the pre-ervice teachers attended the seminar and created their own explanatory video as a part of the seminar assessment. Now Mustafa your turn. Yeah, thank you Gabriel. Um I going to continue with some um further methodological details. Um indeed in our study we collect data from 44 P service mathematics teachers uh using sort of online questionnaires with open-ended questions. Uh to deepen our understanding we conduct seven follow-up interviews. Um we also analyzed 44 modeling videos generated by the persist teachers. Um our video analyst was based on framework developed by chik bar 2024 focusing on the structure content and modeling focus of the videos uh using um coder software we conduct qualitative analysis and we collaborative de collaboratively develop the coding manual and drawing on our earlier research in technology related modeling education. Uh lastly, we ensure reliability. We applied M and Huberman’s intercoder reliability formula and reached a strong agreement. So now I want to briefly present the key findings of the study. Um our results show that uh videos provided both cognitive and effective benefits for preserves teachers uh in Philip modeling seminars. Um according to the results um explanatory videos helped them better understand real world context supported them in solving um sort of modeling problems and made uh complex real world stations easier to grasp. So um compared to reading texts um many persist teachers found uh videos more accessible and easier to follow and features like P and replay allowed them to learn at their own pace. Uh reducing anxiety and boosting their uh confidence. So importantly by shifting foundational content to videos more similar time was available for hands-on modeling activities and deeper engagement. Now let let’s look at the main challenges our service teachers reported when using and creating videos for modeling. Um first the video quality and accessibility were a concern. uh preserves teachers um note that it was hard to find uh appropriate videos focused on modeling uh I mean on the u publicly available platforms like YouTube or other platforms uh creating good ones took time and effort of course and when creating videos they found it quite difficult to strike the right balance between making a video short enough to mention but detailed enough to be useful. So, it’s quite challenging. Um, second, uh, they mentioned a lack of immediate expert support when watching the videos. Indeed, watching videos alone, uh, in some cases meant no immediate help, which made understanding the contact uh, difficult for some service teachers. Um, and third, uh, there were technical and practical barriers for some participants. Some had issues with internet access at home and therefore not all professors teachers engage with the videos before similar hours. Uh which is not quite nice in the Philip classroom settings you know. Um additionally uh producing um high quality videos was seen as a time inensive and technically demanding task um even though they have some experience u in the post-pandemic term. Uh so while um explanatory videos offer many benefits uh these practical uh and pedagogical issues must be addressed for effective implementation in modeling. Uh in terms of developing videos teachers report significant uh pedagogical growth. uh they deepened their understanding of how to teach modeling through videos and refined their skills in organizing content and using u various visuals effectively. Um when it came to design priorities uh they focused on clarity, accuracy and strong visual elements and many many of them also emphasized the importance of creating reusable explanatory videos uh given the time and effort involved in production. So we also evalate um uh expert videos generated by P service teachers using an analyticical framework mentioned earlier. According to these results, uh 77% of them met sufficient criteria for structure and content and 70% uh showed strong focus on especially key modeling elements such as a modeling cycle, mathematical background and validation purposes. So to stay on schedule maybe I I can skip this slide that just summarize the key results and then finally um uh looking ahead several research directions are promising of course first future work should explore additional phases of modeling such as mathematization interpretation or validation that were less addressed in our studies. It of course it depends on the characteristics of the videos u because we we provided some videos on the um theoretical foundations of the modeling and we provided sample solutions to some modeling problems but uh yeah as said it depends on the video content. So second, we need to better understand how different types of videos support both the cognitive and effective aspects of learning modeling. And third, uh there’s a clear need to design high quality, engaging and concise uh videos ideally between five to 10 minutes that combine visual clarity with strong pedagogical structure. Um finally I would say we should think beyond the core teaching hours. Sharing modeling platforms for example on pl uh platforms like uh YouTube can broaden access and contribute to open educational research. And then uh our final message could be welld designed uh explanatory videos in Philip classroom settings uh can enrich modeling education if they are supported by of course sound pedigogy, good infrastructure and expert guidance. Thank you so for your attention. Uh thank you Gabriel. Thank you Mustafa for this very interesting talk. And now we have a couple of minutes for discussion. So, please ask your questions. Um so I do not see any questions. So I simply perhaps for for breaking the ice. I’m interesting because one of the conjectures was that we need this open uh yeah open education so the people can use however we know with the same with the information we have so many information now available that is very difficult to to deal with this variety. What do you think about that? how how we can highlight or what can we deal with that part uh to to to be yeah to highlight the the the the useful uh things and to I don’t know filter uh the hindering uh videos perhaps what do you think um I would say yeah I said it is challenging not easy to develop high quality videos on modeling but um some are better than nothing you know there are not so many videos on uh publicly available platforms. I u uh had a quick search on YouTube and um hardly find some videos. Of course, there are some long videos like conference um keynote or similar talks but you know the attention time of the students uh is not so high. Uh therefore they prefer uh maximum 10 minutes videos. So we need to sit on uh stick to these uh guidelines. You know there are some criteria to develop effective videos. Uh there are some uh uh general papers in educational sciences to emphasize how we u uh create effective videos. We can benefit from these studies and we can uh customize uh these guidelines to mathematical modeling education. So I would say we need some collaboration on it because it is time consuming but we we we have a a big community so we can do it. So in the in the further stage
thank you. I mean it looks a little bit trivial to be honest explanatory videos because we all use them but I mean we actually we created more or less everything all the videos we have used by ourselves. So and because we want to have content in it uh and sometimes I feel a little bit like being up outdated but I mean it’s it’s about mathematical modeling so we want to have put mathematics and mathematical activities connected to the real world in the foreground and of course we want to have theory in it so otherwise then you cannot use that in a university seminar so I I know that others are using explanatory videos as well as well and it would be simply nice to share them under a quality perspective. So that is actually what I think would be work on the long run. I mean it as said it looks everything looks a little bit trivial but if you start it and I mean Marcelo has just left but I mean he’s using a lot of video and we had a hot discussions about the quality of these videos when they are done by the students at school or at university by themselves. So we have to really start theoretically theoretical discussions and I think that could be and as our president is there and a few other members I think it would be good to have such a discussion at the next for example the go I mean and of course a discussion about artificial intelligence we it’s time is running and we actually must uh beside ourselves. Yes. Uh thank you very much on this collaboration and now I would like to thank the presenters for their brilliant talks and for the part participants for taking time to to hear to to our presentations. Now uh then I wish all of you a good day, evening or good sleep tonight. So see you perhaps a digma on in other conferences or in the next tium webinars that that will come this year. Gabriel do you like to to announce something? Yes, we have not finalized dates but there will be certainly a special issue on expertise in competence in memorial that is actually special issue six uh and uh yes and it will be about competence of teachers and expertise of teachers. So I think a highly important topic and I’m pretty certain that Marcelo Ba will uh uh run a a special issue a webinar about the Latin American special issue of set ambit issue seven in this year. So it will be either before Christmas or directly uh in the new year. So at least these two uh uh webinars are uh yes are already planned although the dates are not fixed and maybe we can hear I I personally would love to hear a little bit from you or have attended either send it to Stanislav or to me about the format. What would you like? Would you like to maybe focus one more on one or two presentations and discuss then in more detail like tr is is it doing? Do you want to have a stronger overview? Yes. And so on and so on. What do you want to have it more discursive? So that is actually I think the kind of kind of questions Danis love and I are discussing. So uh we would like to use this kind of uh format to get into discussion with you as our audience uh and as the readers of SETM in order to move forward the content related to discourse and of course to move forward as a worldleading journal.
Yeah. Thank you very much Gabriela and uh yeah thank Oh, participants. Uh, so see you. Yeah, see you at one of the upcoming conferences. There are enough around.