 for ideas pertaining to mathematical modeling. Mashul, do you want to go to full screen? Just a second. Just a second, let me. So as I said, it is not about teaching some advanced mathematical modeling techniques or programming language, et cetera. The goal was to kind of create a transition from what they are currently teaching. That is, we know in a typical undergraduate Indian physics classroom, what they basically teach is derivations. And after that, solving problems, the problems that are there in the typical textbooks. So our idea was to create a transition from those things that they are currently teaching. From there, if we can create a bridge or a transition to novel approaches to modeling and computational modeling simulations, et cetera, how to create that pedagogical transition. Now, the motivation of this whole workshop came from policy documents that are nowadays coming across the world, wherein the relevance and the significance of approaches like interdisciplinary thinking, computational modeling, et cetera, is becoming more and more evident. And all policy documents are explicitly advocating that students should be given training in these regards. So our national education policy 2020 is having similar recommendations. Prior to that, the US next generation science standards, where they're considering modeling, computational modeling, other novel approaches to modeling, et cetera, that has to be there, even from the school level, that is the recommendations. So there is a futuristic vision that is being put forward. And it's increasingly nobody is disputing or nobody is questioning the goals and the necessity for these goals and things to be part of the education and the curriculum. But overall, across the globe, there is a challenge on how a transition can be facilitated from the existing scenario to these novel things. So that is the overall motivation for this workshop. The second obvious thing is, of course, there is a dismal reality of physics education, existing classroom scenario. We know that the situation is not very good. So coming back to what is the policy, I will go into these motivations step by step. The first one, as I said, is the policy recommendation where they are envisaging a radical shift towards interdisciplinary thinking, not just integrating science and social science, but not just integrating sciences, but that is happening in the ISIS, et cetera. To some extent, one can debate how effective that is, but some integration between the science disciplines is already happening at some parts of our country. But the advocacy is beyond that to integrate, not just with science discipline, but science and social science, along with the collaborative learning, et cetera. So the COVID, the pandemic provides an example of the need for it, where if we want to have a model of a pandemic or something like that, which we saw in our newspapers regularly in the last couple of years. So in order for something like that to be taken up, we need insights from multiple disciplines. We need insights from disease epidemiology. We need from sociology, psychology. Insights from multiple disciplines should come together to make a meaningful model of such complex phenomena such as epidemics, climate change, et cetera. So this is the overall larger relevance of the issue. And I hope that is more or less self-obvious taking into account the last couple of years and the events that have been going on, including the recent Nobel Prize, et cetera. The second point, the second motivation, was I said, is the dismal reality of physics education in our physics classroom, where often students are passive recipients sitting idly and noting down things. And from there, we want them to increase their agency and make them active participants in knowledge construction, actually make sense of what is going on, understand things deeply, et cetera, and nudge them towards the practices and proficiencies that expert scientists in the field possess. So this is not true to science education in general. And I don't think this needs much elaboration. We all know about the dismal reality, where what remains at the end of three years or five years of physics education is a heap of terms, equations, and packs all jumbled together with the students struggling, even with the basics, even after MSc. So this is a kind of a, some of you might have seen this I have shared with some of you and given an IUS talk where I also, our expectation is that after five years or seven years of physics education, if we consider each brick as a derivation or a problem that is being thrown at the student, our expectation is that they will nicely and neatly arrange and create a knowledge structure upon which further, if they are going to advance studies, they will further build on it. But with the reality is the second figure. Now the solution that we are suggesting is to re-envision physics education with an emphasis on modeling. So by that, what we mean is teach derivations and problem-solving as an activity in mathematical modeling. Now let me, I will elaborate on what I mean by that using with the help of a derivation of the wave equation of a string fixed at both ends, how that derivation can be recasted as an activity in mathematical modeling. So that is our first strategy to give teachers and teachers an experience of, OK, take some derivations that they're teaching in their, as part of their course, in their classroom, and how to recast that derivations from the perspective of a mathematical modeling. Basically, rather than conceiving or perceiving it as a series of mathematical manipulation, they should be able to change the perspective towards derivation. OK, there is something in the real world. There is a physical phenomena that has to be modeled. How are we going to model that? What are the process and steps that needs to be undertaken in order to model that? So the content of the derivation remains same. What we are advocating or an emphasis is a change in perspective. I will elaborate, as I said, with a more concrete example of the derivation of the wave equation. After that, the workshop, the design of the workshop is to stress the importance of numerical solution. So nowadays, if we look into it, typical BSE classrooms, the 95% of what the emphasis is on, like once the differential equation is arrived or achieved it, the emphasis then the 95% of the times the emphasis is on analytical solution. Even though there are some universities have courses on numerical methods, et cetera, that's often a separate course, not very much interlinked or connected with the other regular course in mechanics or electrodynamics courses, et cetera. So give students and teachers a more deeper understanding of the conceptual aspects of numerical solutions. How? Oh, Professor Borowski has joined. So then let me let me. I'm a shoot. Hi, hi. Go on up. Are you are you all right? Are you feeling OK? I'm feeling OK, yes. And you? OK, because I tried to call you in your office and then I tried to call Amitabh and he said, you may not be feeling well, so. Yes, in the beginning of the week, that was a little, I had a little flu. So but today it's OK. I think it's a half an hour problem. Oh, there's a contue. I think, yeah, there was a confusion lately. So we were OK. While we were waiting for you, we just thought we would make Mashu do some practice talk. So OK. So all right, but I think we're all set. So Mashu, I think you can take over and introduce the speaker. And yeah, let's not waste. So I will directly. Oh, sorry. I am too late. So it's beginning at 12 o'clock. German time? 3.30 Mumbai time, yeah. OK, sorry. OK, yes. Yeah, sorry for the delay. OK, so I will quickly introduce you and then you can take over. OK, so good afternoon, everyone. Good afternoon, Professor Borowski. Welcome to yet another HBCC seminar. Professor Borowski will be talking to us at HBCC today on an interesting and extremely relevant question. What kind of knowledge distinguishes a teacher from a scientist? Just PCK pedagogical content knowledge. A question all of us had in some form or the other at some point of our mind. The talk will be premised on the fact that a teacher's knowledge is central to the teaching learning process in school. The question that arises is what kind of knowledge does a teacher need for teaching? Professor Borowski will walk us through a brief history of the research in this regard. This question has been investigated for many years and the basis of many research projects is the construct of PCK, postulated by Lee Shulman in 1980s. The talk will briefly discuss the development of different models of the PCK by drawing on insights from individual studies in the German-wide projects Pro-Win and Profile-P. These studies prove parts of the models that has been out there but also questions certain other parts. So based on the studies conducted by the group headed by Professor Borowski and his collaborators, the question of the role of physical knowledge in the development of the PCK will be discussed. Also results will be shown how the physics knowledge of student teachers changes during these studies. Coming to the speaker, Andreas Borowski is a professor of physics education at the University of Forzdam, Germany. Dr. Borowski finalized his doctoral thesis in the field of multimedia learning in 2004 at the University of Dortmund. From 2005 to 2008, he worked as a teacher for secondary and upper secondary classes at Alpertprop Schul in Essen. Andreas did his postdoctoral research at the research group Teaching and Learning of Science at the University of Duisburg, Essen. He got a professorship at RWTH Aiken University. Since 2013, he's the chair of physics education at the University of Forzdam, Germany. His research interests are the professional knowledge of teachers and the competence of students in the upper secondary school and at the university. To investigate the research fields, he develops paper and pencil tests as well as coding schemes to analyze lessons and interviews. Dr. Borowski's main interests are the connection between the knowledge of teachers, their quality of instruction and student outcome. Over to Andreas. Thank you very much for the introduce of mine. And yeah, sorry for the delay. I make a wrong time call. So I, in my time table, it sends 12, 30. So it's a delay of three hours, but not three and a half. So that's the explaining. Okay, I will begin with my talk. It's about, yes, my research about the last, I think 10 years, 12 years. And I will begin before that, I will probably begin in the time of Shulman in the 90s, 80s and then come to now and what is about PCK and kind of knowledge from a teacher what we think that a teacher must have now. But I would like to start my presentation with a quote because I think the quote says a lot about the research on PCK. The quote is from a time before Shulman published his articles on PCK. Does anyone know the author of the citation? It's very hard, but I think no one, but I expected that. The quote was from an article of Dark Matter. Why I bring Dark Matter in the lecture of PCK or in the talk about PCK. For me, it shows the universal approach of researchers. We can't explain something such as the expansion of the universe or even more difficult why some teachers are successful at teaching and other teachers are not very successful. As researchers, we develop hypothesis to address these problems in a systematic and focused way. Even if we postulate something like Dark Matters to do so, I can imagine that the idea that teachers should have a special knowledge was unusual in the beginning. But they had to be something to explain the difference so that the postulate of kind of knowledge. On this side, it's not a quote from the natural science, but it described another important event. It was about the discovery of the planet Neptune. Before Neptune was discovered, the planet Uranus was known. However, the orbits of the planet did not agree with the prediction of classical mechanics. The conclusion of the Frenchman, Lee Ferrier, was that there must be another planet. He calculate its position and John Gottfried Gull and Heinrich-Louis de Rest discovered the planet. To relate this discovery to the development of PCK, it's not my idea. The comparison comes from Lee Schulman. I heard the example during the first PCK summit, who was interested, the video is already available on YouTube. Schulman saw the knowledge of Uranus and the discovery of Neptune as a analogone to the knowledge of CK, the content knowledge and the PK and pedagogical knowledge. So the knowledge about these forms of knowledge and his discovery of PCK. CK and PK were not enough. They had to be something else that could additional describe the abilities of teachers. I don't want to strain the comparison, but the contribution of Matthias Steinmetz in astrophysics, another point to address, which is very important for researchers from my point of view. Through the discovery of Neptune, the method of theoretical prediction based on a model established itself as an other fundamental pillar in the equation of knowledge. From my point of view, this is also true for educational research. In this lecture, I would like to take you to a journey in which we get to know our Neptune that is PCK better. I will try to make the lecture not too special. I will also try not to hide the problems I see with the construct of PCK. And in the end, I would like to discuss wherever teachers do not, could not, have a special expertise beside the knowledge of PCK, probably in CK. If you read the literature on PCK, you simply cannot avoid reading two articles by Lee Shun. In the article, those who understand knowledge, Growth in Teaching, which was published in 1986, Shulman discuss the missing paradigm in teacher education. I really liked the article that it discuss teacher expertise well, to which I will return later. Many skin constructs and ideas are already though of there. Also the term pedagogical content knowledge is already used here. Here, however, it is described as a second kind of content knowledge, it's pedagogical content knowledge, which goes beyond knowledge of subject matter per se, to the dimension of subject matter knowledge for teaching. Beside PCK, Shulman postulate other special kind of knowledge of teachers, the subject knowledge and the general pedagogical knowledge. However, Shulman say the knowledge about curriculum and learning, as well as knowledge about educational system or even attitudes towards learning are important areas of knowledge for a teacher. So that's not only PCK, we have other areas of knowledge that's very important for a teacher. In the German speaking research on professional knowledge, the model of Baumart and Kuntas become established. See it here on the slide. In addition to the beliefs and the motivation, the self-regulation and other skills, the professional knowledge, it's the central important in this model. This knowledge is subdivided again into five knowledge areas in which three knowledge areas are the pedagogical knowledge, professional knowledge and the pedagogical content knowledge, the PCK. There are the central. Perhaps the model is only so popular in our country because it reflects the structure of our education system. In Germany, the teacher training is divided into subject specific content knowledge, subject didactic, the pedagogical content knowledge and pedagogical components. The model therefore reflects the status quo of the education system in Germany and was not developed exclusively from a teacher learning theoretical perspective. That's probably the strength and sometimes also the weaknessness of this model. So what's mine, this particular amalgam, this particular combination of content and pedagogical knowledge look like. In history, various models have been developed for this purpose. In a contribution by Julia's News in 1999, she compare different models. Here, she distinguished two main categories, the integrative model on the left side and the transformative models on the right side. In the integrative models, PCK emerges as an overlap from other areas of knowledge. In this case, the progression of knowledge, pedagogical knowledge and the conceptual knowledge. So it is enough that you have knowledge in the other areas and the PCK is co-developed. Probably you would know this models or these kind of models as the TPAC models. It's very popular in the field of computer or technical PCK. In the case of the transformative model, it is not enough to have knowledge in other types of these. The knowledge still needs to be transferred into the particular type of the teacher knowledge, the PCK. On this transformative model, Magnuson-Metal does not deal with the relationship of PCK. He established a model with different knowledge domains. Rather, he developed not a model. What is PCK? He operates. What is PCK? The statement of the model is that knowledge from the areas science curricula, students understanding, instructional strategies and assessment of scientific literacy contribute to an orientation of science teaching. Here we try to identify individual areas of the PCK, but they are rather unconnected to each other. The model of Park and Oliver goes one step further. Here, the PCK is not at the end or the top of the model. Rather, PCK is the center around which the various areas of knowledge are arranged. In addition, he has an interaction between the individual knowledge areas. Thus, they're no longer just next to each other. Otherwise, the individual aspects of PCK are here the same as in the Magnuson model. A further change is that in this model, reflection is assigned a special meaning. The distinction is made between reflection in action and reflection on action. That is, once of reflection during teaching and once after teaching. Those characteristics are extremely important for a teacher. On the other hand, I have to be able to react spontaneously to problems during the lesson. Here, it would be good if it could fall back on my knowledge, but I also have to be able to analyze what happens during the lesson with my knowledge after the lesson. And based on this analysis to plan the next new lesson. You'll see we have very, very many models. Building on these different models, different studio studies have accentuated the aspects of PCK differently. And the figure based on analysis of Park and Oliver, my colleague, my colleague, Sophie Kirschner, it is listed with studies considered which aspects can be seen that in all studies, students understanding and instructional strategy and representation is a part of PCK. So probably you can say it's a heart of PCK. Even though the analysis was done in 2016, nothing had changed yet. Those two knowledge areas are actionally always considered central. It can also be seen that in some studies, expertise or the content knowledge was considered as a part of PCK, but sometimes there is not a part of PCK. There is still a discussion about this to this one day, but I will come to the end of the talk. The question is wherever the content knowledge is needed for the teaching process, is something special? For example, should it be assigned to PCK or wherever the content knowledge is something normal that is scientists also have this specialized content, this knowledge? In the second column, you can see that the studies can be divided into two categories. The lower category, the PCK of individuals or groups are described. So it is about finding out what specific knowledge teachers have. The second type of studies try to measure the knowledge in the field of PCK. The studies then they try to determine among other things, connection of PCK to other knowledge dimension or to teaching. I would like to continue in this direction in this talk. With this purpose, I will show you sample facts that we used in other studies. Here you see two open-ended questions on the slide. The first question is about the egotism of experiments in the classroom. The second is about misconceptions of students. Most types are identical in that they ask about general aspects. It is a test on the meta level, so it's big. The task you hear, see is more concrete. In a situation, it's refused here, so you go in one classroom situation. At the top, the possible task in a school examination is given below. It's a student solution. The question here is not whether the task was answered correctly or incorrectly, rather the aim here is to diagnose what can be deducted from this incorrect task. In other words, what possible misconception the student had. Here as we are here, the quote from Schumann. We used this and similar test items in different groups. We wanted to find out whether our task really test the special knowledge of teacher because PCK is the special knowledge of teacher. But perhaps each of you can briefly consider what the result of the examination might be. All right, let me clear it up. It is difficult and not entirely clear what we measure. The table above, you can see that different groups we compared. The first group is physics teachers, which we have further subdivided into physics teacher for higher education and those for basic education. In addition, we survived non-physics teachers, pre-service teachers and physicists. Hello, you can see the individual comparison in the diagrams. Since the data come from a Russia analysis, the value of the YX is without any unit and reflects only the difference in the ability of the groups. Overall, it can be seen that physics teachers and especially physics teachers for higher education perform better than the other groups. If one examinized these difference more closely, the difference also became significant with the significant effect sounds. Okay. But it can also be seen that the other groups can also solve tasks from the PCK domain. So our tasks do not ask something that only physics teachers can do. Our tasks are something that physics teacher can do better. Come here up to the PCK models at the beginning of my talk. It seems that both models should be right. PCK could have emerged into griffility from the other knowledge domains. This is supported by the fact that the other groups also had PCK. However, this PCK was worse than that from the physics teachers. The transformative model can speak for this. On our research results, then we developed the following model from our results. In the middle here, it is a continuum from the content knowledge to PCK, the pedagogical content knowledge to PK, the pedagogical knowledge. Tasks that we develop can be answered partly with the help of different knowledge dimension or only one dimension. Purple technique question, for example, one news third law would be in the CK domain. But the above question, for example, about the justification of exams in physics class would be in the transition area between CK and PK. As described from physics at the beginning of the lecture, the dectic research is more than just description. The developed model should be used to make predictions. If the predictions are correct, then the model could be confirmed. If, however, the predictions are not correct, then it must be considered whether the model or the measurement or both were failed. At the first PCK summit, a model was developed and then published by Julius Neusen. The PCK is included in the model of teacher's professional knowledge and skills. To explain the whole model would be take here too long. I just want briefly say how we used the model to a situation in our study. In a video study, we collected the CK, the PCK and the PK from about 40 teachers using questionnaires. Then we videotaped two lessons from 40 teachers to introduce the false. We elevate these videos in terms of interconnectedness. This involved how well the individual statement were incorrect in the class. Additional, we survived the students experience before the lessons and after the lessons with the questionnaire. The goal was to find different predicted connections. Here we can see our results. Unfortunately, there is no continued power. The CK has an impact on the PCK and the PK on the interconnectedness. The interconnectedness in turn to the students outcome. Here it's also a correlation between the student outcome and the PK. So something is not so good. It's our model or it's our measurement. We also elevate these videos in terms of cognitive activation. The results remain stable. With our study, we were thus able to confirm parts of the model. However, we are unable to prove some correlation that should exist according to the model. This is something at odds with studies from other subjects in which, for example, a correlation between PCK and teaching and students performance was found. At the second PCK summit, the model presented earlier was further developed. It is now called the refined consensus model of PCK or RCM of PCK. This model consists of different levels, which I would like to introduce very, very briefly. In the middle of the model is the teaching process. The teachers had mapped the pedagogical reasoning about planning, teaching and the reflectional teaching. This area is referred to the inactive PCK. Thus, it's about the knowledge that is directly related to the concrete teaching. The personal PCK maps the knowledge a teacher has in general about teaching and learning, which is therefore rather unexpected to a situation. A teacher's knowledge has always been gained in a specific context and it's determined by specific amplifiers and filters. This reason, the collective PCK, that is what we as a community know about teaching and learning physics, cannot be taught directly. On the very outside, there are other knowledge dimensions. This knowledge base as an indicated by too many arrows in the model influence the different types of PCK, but also vice versa. What is important about the models of PCK are now viewed differently. On the one hand, for example, as a disposition that can be queried with the help of the test, but it's also directly observable on the teaching process. We also attempt to test sections of this model in a study, the student's teachers. With this purpose, we collected the CK, the PCK, the self-efficacy experience and the beliefs about teaching and learning using paper and pencil test. In addition, we developed a performance test for explaining. This would allow us to measure the internal domains of the model individually and then relate them to each other using the path analysis. The result is that we were able to trace very nicely the path from CK to PCK to the amplifiers and filters and to the explaining performance. The result also confirmed in other studies. Here again, the ability to explain well were analyzed with a professional knowledge of a teacher in a cross-legged panel design. Here too, the results are similar and confirm to the model. The question that arrives is how this PCK develops during the course in the university. For this purpose, we have survived the knowledge of more than 250 students in the Bachelor programs on 11 universities in Germany and the master program of four new universities in a longitudinal section. The left diagram shows the development in the Bachelor program, the right diagram in the master program. The master's program, the development before and after the internship of one semester is shown. The Y-axis, the personality which comes out of the rush analysis is plotted. It can be seen that the students add PCK over the courses of their entire studies. In this regard, it should be noted that pedagogical training in Germany often begins in the first semester. With this previous results, we could therefore show that our students are actually quite well prepared for the later profession as a teacher with our training. In the title of the lecture, I had asked what kind of knowledge distinguished a teacher from a scientist. Provided I already asked only PCK. In the list thing of studies on PCK, we went that CK is partly considered as a part of PCK, but there are also studies to do not see PCK as a part of PCK. They still say that a teacher's CK is different from a scientist. The teacher's subject knowledge must have been entered to connect to the lesson in such a way that he or she can prepare the essential aspects for the lessons in a technical correct way. However, the content must always be adapted to the students so that they are not over texted or unchallenged. In our profile P study mentioned above, we survived not only this PCK, but also the CK. We operationalized the expertise in three areas. Here you only at first see two of these areas. Here you can see the areas of the school knowledge and the university knowledge. Since physics cannot already be divided in this way and since the university, we also repeated many things we are already taught in school. We decided to use the degree of matemization on the progress as an indicator that allowed us to short the task objectively. The third category we have called it's the category in-depth school knowledge. This is a theoretical developed category of knowledge. The content on this category is about the limitation of models, the differentiation of solution strategies and the identification of similar differences in physics. The discussion around this deviation could fill a lecture alone. Therefore, I mentioned it only here briefly. More important for me is now that results we have obtained. On the left hand diagram, the three measurement points in the Bachelor program are entered on the X axis, first, third and fifth semester. On the right diagram, the measurement time points before and after the long-term internship of one semester in the master. On the Y axis, the person ability is plotted. It can be seen that recognized that students are learning the CK well in all these areas through the studies. So we could also actually be proud of our education but we looked on the development of knowledge also in extreme groups. We grouped the best third, the middle third and the worst third together. On the top left of the slide, you can see development of school knowledge, the top right, the development of the in-depth school knowledge and at the bottom, the development of university knowledge. All the diagrams actually look very similar but it's striking about all the graphs that the mean of the worth group even at the last point is lower than the meaning of the middle group at the first measurement point. That means that we have not provided good enough support for students who already have great difficulties at the beginning. Here we need to develop new and target support programs. So we have investigated something else and have some across a new area. I think there's always the exciting thing about research like the discovery of the Neptune. I start with the question of what the skin distinguished the knowledge of a teacher from the scientists. It is certainly the PC, the CK, but also the subject meta knowledge. In addition, it is also the pedagogical knowledge and probably contact knowledge. I have not presented these two in details here but yet conceptually answered the interplay of the individual knowledge categories. As well as the question of error, there are perhaps not yet knowledge areas discovered or postulated areas of knowledge that play a special role. So we don't know that till now. It is also unclear how this knowledge is on the reflection in the classroom. So how can these knowledge areas can help to improve student learning? I would like to close again with an example that does not come from physics. In the US basketball games were exterminated for a long time around the quality of a play for a long time, wrong and little meaningful values were used for it. That's just seen on the left side. Only gradually one understood on which is dependent then on the right side. My question is, and which I want to close my lecture, what is our wrong assumption in the area of the professional knowledge of the teacher or in other words, how should we change our constructs if necessary so that we recognize the essential variables? Thank you for your attention. Thank you, Andreas for a nice and interesting talk. We will open up for questions. Please raise your hands or type in your questions in the chat and we can take it up. So one thing that came to my mind, you indicated that the nature of PCK changes as we go, as the grades changes. As the grades go higher, definitely the content knowledge becomes more complicated and involved. So I'm assuming that there is a corresponding change in PCK as well. So can we say that the complications involved in PCK decreases as we go like to higher grades or what is the kind of change in PCK that happens as we go from say lower grade school to university? So you characterized in terms of degree of mathematician but can you throw a little more details into what exactly you meant by that? Okay, at first, I think the first complication is what is a CK and what is the connection to PCK? And then for your question on CK, we have lower mathematics like only equations or simply routines in school. When you go to the university, you have integrals and differential functions to use and to understand and you have vector analysis probably. So you have not two dimension or one dimension description of physics formula. You have a third dimension description probably. So that's different. And also when you go to mechanics, you have not only the classical mechanics, you go to Lagrange function to describe mechanics on a more detailed way in the university. So you have force and you can with some assumptions in the beginning, you can describe with force many phenomenons. The different in our mathematics X. Your question is, or I understand your question in that way, is there another PCK about the learning process in school or in the university? Is that right? Yeah, like what is that? For example, if you are training a school teacher and compare that with we are training a university teacher. So what is the nature of the chain? I'm assuming that the pedagogical content knowledge is going to be different. Okay, we don't measure the content knowledge about the teachers who teach student teachers. We only look at what the knowledge of student teachers are. But to answer your question, yes, that's another PCK. I think at the university, you must teach the why you must teach some contents. So why is the third law important or why is Ohm's law important? Because in many phenomena, Ohm's law is a good assumption, but it's wrong because the temperature probably is not constant. But you can learn from this law many ideas about the nature of science. It is how probably linearization or it's only to variant one variable you can use on Ohm's law. So in school, you can learn on physics what's important in science. So your PCK in this is you must know about the why, why you teach this point in the university, you must on the meter level, you must have the knowledge about what must I teach a teacher that he can come to a reflected practitioner, that he can teach in a way that he know that it's not only the content he must teach that he must teach the why behind the content. So that's different in the pedagogical way. And also in the content way, student teacher must have much more content knowledge than the students ever have. But why he must have this deeper knowledge? He must have this deeper knowledge that he understand the connection in the subject and student teacher are not scientists in one field that is an expert probably in the field of electricity or particle physics or something like that. Physics teacher must understand the subject as a whole that he know what's important of the subject and how I have interconnectedness between different aspects of the field. So how I feel connection between force and motion and electricity or how in this field are the energy so that he has a very good connection in the mind. So the content knowledge is not only very deep but it's to confirm very connection between other concepts. Okay. So the other thing is in Germany even those who are teaching at the university or higher levels do they have to go a mandatory training in PCK, et cetera. Because in India only those who are teaching up to grade 12 has to grade 10 or 12 has to like have a degree in for example bachelor of education. It is not required for those who are teaching at college or university. They're a master's degree in physics or PhD in physics that is enough. They don't have to undergo like as formal training in aspects related to education or like where some of these issues are discussed explicitly like the PCK, pedagogies, et cetera. What is the comparison? What is the like situation in Germany? I think it's probably the same as in India. For school, everybody must have an exam in pedagogy. So we have for primary school and secondary and upper secondary school, different study programs. And in each study program, they study the subject, the pedagogical content knowledge and the pedagogical knowledge. And for the university level, there is no education needed. So there are good researchers and when you're a good researcher, you come in position at the university and then you can teach other students. I think that's a problem. And in the interview, you must create a concept about what you think is a good teaching. And in the interview, you must hold one seminar that some people look how good your teaching is, but in the end, only or nearly only the research is the main point if you get the position or you got not the position. So the assumption behind this system, which is what you're saying is the same in India and Germany is that at the higher levels, people will pick up these things on the fly. Like as they practice, they will automatically pick this up. But at the school level, that won't happen and it has to be explicitly taught to them. So do you agree that this is a, like do you agree with this assumptions or is there a problem with the fundamental problem with that? I agree that you need a PCK or you need a pedagogy how you must teach, how you can teach in school. And I think you must need it also in the university. But in our system, it's not that you need it. Perhaps it's true, like in most of the countries, I don't know whether any countries have this US also, I think, in here. I see there's a question. Yeah, yeah, that's a question from Karen. Karen, you want to unmute and speak? Yeah, I think the question was already kind of answered because I was confused as to whether you're just teaching teachers who will go into teaching school children, not university and not at the university level. That's you've clarified. But still I wonder if you think that there are some fundamental differences between how you would teach teachers to teach physics at the school level compared to how you would teach teachers to teach physics at the university level. Yeah, I think that is the fundamental different. Probably it's in the system of Germany but in Germany, the idea is that a teacher not only reproduce some receipts or some ways, some algorithm that he or she had learned in the university or what you can read in books. The idea of a teacher training in Germany is that a teacher learn many things many methods and many content and ideas about teaching. And then he used this knowledge and prepare an own lesson that is specific for each class he taught. And so you can say that the teaching process is the same because on the one hand it's the process of what can I learn about physics and what can I learn about nature of science with this physics content. And in the university, I learn on a meter level. So how is the concept of physics? How is the connectiveness of different concepts? How are different methods connected to some concepts or some pedagogical methods connected to the learning process to boys or girls and to the beginning when you look at the experimental circle for example, you have different aspects you can learn the experimental circle you can learn about hypothesis and why it's good to learn about hypothesis. You can learn about the process of during the measurement you can learn something about the analysis and the discussion. So you learn on a meter level how the research process is going on and you learn why it's necessary to do the research process in such a way probably that's objective or something like that and that you have an theory that's every time going on. So research is when you give some piece more of theory after the process that you have before. So I think that is on a higher level at the university and sometimes on a different level than in school. It's also for this the PCK or the idea of teaching is different in school and in the university. But I think that could be also in German aspect. I know other teacher training systems and in this systems teacher learn in the education that they can use books and in the books are some ideas of teaching and they can use the books in the classroom but it's another thinking about what a good teaching process is it's not using a book or using an algorithm that it's giving from the book in the process that is one way and probably in the German way. I don't know it's better or not. It's another way. We say a teacher must have a meter level and then adapted this to the learning process in the classroom. I hope I can answer your question. Yeah, but of course it brings up more questions also. So I'm wondering, I've heard from students in India that it seems to be common for students who pass from high school into university level physics. They will, well, for example, if they're asked how did your school physics help prepare you for the university level? I've heard students say, well, it didn't help me at all. I had to start from zero. It was completely different. They're surprised by, actually it has something to do with maybe their understanding of the nature of science. It only really comes in at the university level because at the school level they have no idea of what science research is and so maybe this is somewhat connected to what you're saying because students at the school level if they don't really have this idea of physics, of research, they have a different conception of the nature of science. And maybe there needs to be more like maybe the two, there shouldn't be such a big jump between school teaching of physics and university teaching. And maybe some of the problems do have to do with the way that teachers are trained for teaching school and the way that they're hardly taught about teaching if they become researchers. I don't know the school system in India. For the German school system, I see the problem you taught in mathematics because in Germany, mathematics in school, it's only a calculation and mathematics in the university it's yes, like mathematics, you have definitions and then you have some evidence for the hypothesis in mathematics. So it's not what calculations. For the physics, we have new standards developed for the upper secondary school. And we have in these standards, basic concepts for basics concept. One of the concept is mathematician. So that in school, they learn that mathematics is the language of the physics and mathematics are a kind of model. So the equation, it's not a formula for a visitor. So it's a model where you can use in different processes but you must understand the variables of the model then you can use it. And also the superposition is one point and the energy conversation, probably the conversation rates are one point of this and probability and determination are the first, the fourth concept. And I think with these concepts, we have not such a big break because it's probably the idea when you solve problems in the first semester of physics, you can use these concepts to solve this task. You have some mathematician, you have probably the conversation rates and other things. And I think the break in physics is not so big as in mathematics in Germany, but I think there's every time a problem because in university, you have another goal then in the school, in school, also in upper secondary school, the goal is knowledge for everybody or deeper knowledge for everybody for the normal life and in the university, you develop the field of what you study. So yes, there is a problem also in Germany and we have high drop-out rates at the university in the physics course in the first semester. I think there's only one-third of the students who begin the course will end the study program. Thank you, Aniket, go ahead. Hi, just this answer which you gave, that brings a question to my mind. So should we say that the PCK for a given learning area is universal or is it specific to the context of where the classroom is situated? I think some of my colleagues will say yes, that is so. When you go to some colleagues from Australia, they say that PCK is specific to one content in one classroom in one situation. So you can only have this small focus. And that was a problem with the first model from Julius Newsom, that when you go to this small model, my idea of PCK is more on an abstractive level. When we teach in the university, we cannot teach for every content in every classroom every time. That's too much. And a teacher teach, I think, 30 years. So how we can prepare a person in so many fields over so long time. So my idea is on a meta level. So what must the teacher know that he can prepare a lesson for specific people in a specific school, for a specific content in a specific time? For that, the second model came, the refined consensus model. In the middle, you see the specific situation. We call it the inactive PCK because it is specific to this only one teaching situation. But you must have the personal PCK, what a teacher have in mind, what a teacher know to create this lesson. And as we as a community, what we think it's a good knowledge to prepare lessons. So the second model allow us as researchers to go to different steps. We as a researcher go to a meta level and say, okay, this knowledge you must have to create lessons. Some people say, okay, we measure with tests the personal PCK. And some says, okay, what in a specific situation with specific students? How we must teach this? So we have different areas. So the question is not so easy to answer, but from my point of view, PCK is more in the meta level, but I think some people says, okay, it's specific. And for us at the university, I think we must develop our students to create the specific situation from a overall knowledge. Okay, thank you. If there are no further questions, let's thank Professor Borowski for such an insightful talk and taking up our questions. Thank you, Professor Borowski for your time and wonderful talk. Thank you for the invitation and thank you for the delay. It was the half hour that's, yes, it was my first time to connect with India and not connection with German people who say, okay, you must have the idea of this half hour. Sorry, it never happened the second time. Yeah, it's 20 minutes actually, so anyway. Okay, thank you once again and bye-bye. Okay.