السلام عليكم ورحمة الله وبركاته باسم الله الرحمن الرحيم الله مفتح لنا فتو العرفين وفقنا طفق صالحين يا رحم الراهيمين لا إله الا أنت سبحانك أني كنت من الضالمين رب الشحي صدري وصل لي أمر وحل الأقتة من الإساني يفق القولي وصلى الله وسلم وبارك على سيدنا محمد وعلى آله وصح فيه سلم السلام عليكم ورحمة الله وبركاته I hope you all are doing well so we are continuing these virtual Friday Juma reminders given that the times we're in we're not able to actually have Juma prayer and we ask that Allah make this time easy for all of us and allow us to congregate in the massage again soon فهي جنور رمياندر ونحن نتبع this talk about twenty minutes ونحن نحن بحاجة الهراء to pray our doher prayer afterwards this does not take the place of the جمع فتبة it's simply just a virtual جمع رمياندر so today we are going to be talking about patience and trying to understand what exactly patience means in the time that we are living in الحمد لله الله has really honored the rank of the patient ones in the Quran He has given them an immense rank He has encouraged us to be patientHe has told us of the virtues of patients, and the Prophet ﷺ has outlined in various hadith the different ways that the Muslim can try to To what what we can do to implement this virtue of patients how we can go about acquiring this virtue of patients. But let's start with just the fact that Allah honors the patient ones. And encourages us to be patient By telling them that his love هو for the people of patience. الله says in the Qur'an, الله يُحِبُوا صابرين. Another special trait that Allah defines the patient ones with is that Allah is with those people who are patient. He says in Allah هماء صابرين. That Allah is with the people of patience. And so we see in this specific example and we see in these specific ayahs that it's a category of people that has been selected out. Allah selects out a portion of people, with different types of traits that people may have for His love. And then it's also we see that Allah says that I'm also with those people who are patient. That yes I love them and I'm also with them in assisting them regularly in being patient because it's not easy to be patient in the times of difficulty. It's not something that's easy to do. And so when is patience necessary? When is it applied? Well Allah mentions in the Qur'an that one of the main reasons that He created us is to test us. He says in the Qur'an in various surahs that He created life and death in order to test you. To test you to see which one of you would be best indeed. And He mentions in Surah Al-Baqara that He created that He is going to test you and I. Right?  وَبَشْرِسَ سَابِرِينَ So the patient people, they have Allah's love. Allah is with them. And Allah is sending glad tidings to them. And then Allah mentions in other parts of the Qur'an that He is giving them a special type of mercy for the people who are patient. But again He's linking here His tests with the response that He wants us to have. Which is the response of patients. And so in the Qur'an when Allah speaks about the different challenges that are going to that the human being is going to face He is trying to help us shift our framework of this life. That our framework for this life should not be that this life is going to go by easily and then we're just going to easily attain Jannah. That's not the framework that we are supposed to have with regards to this life. The framework that we're supposed to have is You know what? This life is going to be filled with tests. And insha'Allah Allah makes the test easy for us and that He makes these times of luthf and ease and gentleness but we are going to be tested. It's a guarantee from Allah but He also gives us the response that He wants us to have. And it's almost you could think that one of the main reasons why He tests us is to help cultivate this response. That if you and I are not even given the opportunities to quote-unquote shine to spiritually shine then how are we going to attain the reward for spiritually shining? Right? It's kind of like you know you have in the workplace if you don't give somebody the opportunity to prove that they can do the next level of role and then eventually you promote them how are they going to be able to do it if you just keep them in one specific capacity for their entire duration of their career. No, it's about growing. It's about progressing.  But they're given the opportunity. You have to be afforded the opportunity to do so. And then what happens? You show your organization yeah, I'm capable of this. And then they say okay, you had that trait. Now I'm going to promote you. I'm going to give you more responsibility. I'm going to give you more oversight, right? I'm going to trust you more. It's very similar with spirituality in that the more and more we grow okay, we got the basics down. Insha'Allah. Then Allah says okay, now let's see how you do with this. I eventually is going to see okay, now let's see how you do with these challenges. Now I'm going to send somebody in your life to push your buttons and see can you be patient with them because all of my messengers were patient and you want to be somebody who follows my messenger you claim to be somebody who follows the sunnah of my messengers and so if all of my messengers were patient then let's see if you can be patient in these times. So he's giving us opportunities spiritual promotion and spiritual progress is about ascending in the ranks of virtue. That's what spiritual progress is about. The more virtuous we become the more we progress spiritually and that's very much linked to the idea of our nafs. We have a nafs our lower self and it's supposed to progress there are stations of the nafs right and the more our nafs goes from what's known as a nafs the evil commanding soul to the nafs to the self-blaming soul to the nafs to the tranquil soul right and then all the way up eventually to the station insha'Allah of nafs the perfected soul and then there's the station the contented soul there are different stations in between but our progress is about how we are progressing spiritually and virtue is the main way to exemplify our spiritual progress how do you know if you're progressing spiritually okay are you exemplifying more and more virtuous traits if so Alhamdulillah that's a good sign if not okay we got to keep working on it right and so tests then are ways for us to progress spiritually or they're ways to progress spiritually we pick right wherever a response that we want to have but Allah says He will test you to see how you will respond and then He gives you here's the answer I'm giving you the answer of how you are supposed to respond usually when a teacher gives us a test they don't give away the answer but Allah says here's the answer I'm going to give you the answer I'm going to give you a cheat sheet I'm going to tell you I sent the best of teachers the Prophet ﷺ said in a hadith that I was only sent as a teacher Allah sent the best of teachers to give us the whole playbook this is how you're supposed to do here's a study guide on how you get through this life and how you get through these tests Alhamdulillah we have that but then what happens right do we apply it or not a teacher can give you the outline they can give you the study guide they can give you everything but do you and I implement it and then when we go and take our final exam or we go and take a midterm if we studied and if we implemented it and if we actually used it Insha'Allah we're going to get a good grade on the midterm if not how can we expect to right in the same way we have the roadmap and we have more we have the answer already we already know what the answer is that the problem becomes and this is the problem this is the one of the most difficult parts for the spiritual traveler that we understand it intellectually but do we get it pragmatically how we implement it so many of us we know we know that there's a day of judgment we know that we're going to die we know that the angels are going to question us we know all of these things intellectually but have they moved us and become solidified in us in a strong enough way to where we're actually going to take action and change our life that is the focus of the believer that does that knowledge actually turn into or does that information turn into true knowledge which moves the limbs and the heart into action that okay now I know what I have to do I am in a battle in this life against shaitan against my nafs and I am in a battle regularly against the forces of evil so and I have to progress I have to push and I have to fight that is the way we're supposed to actualize the material actualize the knowledge and the information that we are learning so if we know all of that we have to take a step back do we actually implement it and that goes back to all of the actions that we do on a day-to-day basis they will help us answer the question of are we implementing the knowledge that we have or not are we praying are we taking this religion seriously are we careful and we speak about others are we trying to be patient are we just going in the opposite direction and being lazy and complaining all the time and seeing this life as one big we're being let down in some way or another you can have either a response depending on where we're at or in between type of response on that spectrum so we will start to think though when the tests happen like what's going on why is this happening to us why is this happening to me why is this happening to my family all of these situations these answers will come up when the tests happen but Allah again already gives us examples He gives us examples in order to help us understand look if I'm testing you it doesn't mean I'm upset at you necessarily right tests can descend as a form of punishment we know that it's in the Quran and they can test they can descend as a form of us trying to turn repentance towards Allah but they can also descend as a form of elevation for some people one test could elevate them and for others it could cleanse their sins and for others it could drive them towards Toba and for others it could be a a punishment at the same time for something that they should have been doing to try but to try to wake them up right so tests can descend for any reason and Allah tells us who we are with when we are tested He says in the Quran gives us examples of different messengers and He's telling us you are joining the club of these messengers that I had one messenger Sayyidina Nuh and the Prophet Noah that Allah gave him a difficult test that he called his people for 950 years and they regularly rejected him every single day week month they're rejecting him they're turning away from him they're physically harming him they're doing all sorts of difficult things to our beloved Prophet Noah and yet he remained patient Allah says that he remained patient such that he attained the Resolute among the messengers Subhanallah but what was the signifying quality that if he's a messenger and he is so close to Allah and he's among the mighty messengers and he regularly mentioned in the Quran you would think well maybe life is supposed to be easy for him maybe he just goes out and he has a beautiful way of calling people and speaking to people and he knows how to do all these things shouldn't people just listen to him not necessarily no that's it one of his tests and of course the messengers have many tests he was tested with his own family as well that some of his family members did not make it on to the ark when the great flood came so how does that work well if the test comes if the response was to be patient say in the Noah of course he's our teacher he of course passed the test with the best of grades he passed that test because he was patient Allah says that he is from the patient from the Sabaidi that he is from those people who are patient he remained patient we can't even remain patient for a few days let alone a few weeks he remained patient for 950 years our lesson we take from that is sometimes the answer is to keep trying what we need to do but to wait in this situation we have to wait it out in this quarantine situation that we're in we have to try to let ourselves and our families not get perturbed internally of and get this anxiety of when is this going to end when is this going to stop we just have to be patient through it just like say in the Noah of Islam he waited it out and that is one of the main responses that we need to have is to essentially wait out the situation say in the Abraham of Islam and we've mentioned this in the past conversation say in the Abraham of Islam had immense tests but he remained patient through all of the tests that he went through say in the Yusuf of Islam the Prophet Yusuf of Islam he went he exemplifies patients and again his example is being used in the Quran that he exemplifies patients because he was patient when he was thrown into the well by his brother he was patient when he was again thrown into jail and falsely accused he was patient in being in a land with no family and nobody but he always had a lot and keep in mind then from this story that you and I might have to be patient alone sometimes nobody else will get what we're going through sometimes nobody else will hear us or feel us or kind of understand it but God always understands your problems of course he does and he is your best friend through the problems part of this being patient is in the Allah that Allah is with the people of patients that when you and I are patient he's trying to tell you very colloquially like I got your back I'm with you don't worry I'm going to help you through this I'm I'm assisting you without you even realizing I'm going to create the traits of patients in you but you have to rely on me you need to put in the effort right that if you and I put in the effort Allah is going to give us immense assistance immense spiritual madad immense spiritual assistance through the difficulties and he was with he told the prophets that he's with you right that he told Sayyidina Abu Bakr and he told the Prophet ﷺ and Sayyidina Abu Bakr right in the famous story of them being in the cave look at this amazing story when they were in the cave and they were running from the Quraish and the Prophet ﷺ is with Sayyidina Abu Bakr and they see that the Quraish are right there they're in the cave and the cave was such that had in the narration had the Quraish looked down they would have seen the feet of the of the blessed Prophet ﷺ of Sayyidina Abu Bakr صديق رضي الله عنه but they didn't that Allah gave them a way out but he tells he reveals this that he says to the Prophet ﷺ tell your your companion your صحبي لا تحزن إن الله محمد لا تحزن إن الله معنى that don't worry don't grieve don't don't be in a state of of anxiety because Allah is with you with the إن الله معنى Allah is with us سبحان الله that that was the station of the Prophet ﷺ but of Sayyidina Abu Bakr صديق that an ayah was revealed to console him that Allah is with us because look at the patience you have to have internally to just maintain right like you have to just be hiding because people are chasing me look in this situation حمد الله we're generally most of us are in safe circumstance so we have to be patient just to kind of ride it out wait till it ends we don't have to be patient through trying to figure out somebody gonna get me and God forbid is my life under threat but the Prophet ﷺ Sayyidina Abu Bakr صديق in this situation they had to be patient through all of that but Allah told them that he's with them and that his being with them removed that anxiety and that worry and that kind of that comes with the waiting at time from time to time and so we see that all the prophets have this these different stories Prophet أيوب ﷺ right the Prophet جاب ﷺ that he has to be patient for an immense period of his life because of a sickness that he that he was afflicted with but he achieved this station and he is mentioned he is mentioned in the Qur'an as being from among Allah's most excellent servants and his patient servants right it's we could go story by story of different prophets but all of them were tested immensely and we know there's a Hadith that the prophets are tested the most and then those closest to them and those closest to them so if we're in tests we should be in a state of patience and that Allah is giving us a chance now to show him that we can respond with virtue so our response then in these specific situations should be one where first we just accept intellectually that I have to be patient through these times and then we have to figure out what does that practically mean right we can say be patient be patient be patient all we want but what does it mean or you see that in patience is when the difficulty first happens and the Hadith of the Prophet ﷺ he mentions there's a story of a woman who had lost she had lost one of her children and she was at the grave of that child and the Prophet ﷺ walked up in the cemetery and he told her he consoled her to try to be patient and she without looking said you don't know what it's like what I've been through and that she is expressing that emotion that she's feeling at the time and the Prophet ﷺ walked away and eventually the Sahaba came up to her and they told her do you not know that that was the messenger of God and she immediately she runs to his house and I'm paraphrasing here she immediately runs to his house she says I'm sorry I didn't realize that was you and he mentions to her that patience is when the calamity first strikes is when you have to be patient that is when we expect things to go smoothly and then immediately boom everything is turned upside down in a minor way or in today's world in a major way our job plan and our plan for this and our social plans and our financial plans and all the different planning that we did turned upside down now patience is when the blow first strikes so in this situation it's already happened but as things continue to change and develop and inshallah they get easier but if God forbid they get they turn in a direction than the one that maybe we hope for okay we have to know we have to be patient our first response has to be okay inshallah Allah knows what he's doing Allah has a plan okay if Ramadan is not the same this year if we're not able to congregate in Tarawee and all these things our response should be one of okay at the heart level we're saddened but we should not be in a state of of being upset this is Allah's decree he knows what he's doing so we be we're patient through it and practically how do we implement this first we understand that the time we're is one where we're used to immediate instant gratification okay I need this I can order it right online immediately and alhamdulillah these are good things in general but as soon as I need this fast food fast everything as soon as I need something I can get it or I want something more so I can get it right so we patience is about waiting it doesn't happen immediately so the first step is to train ourselves to realize that the cure and the result does not immediately but it doesn't mean it's not coming we make a dua and then 5 minutes later or 10 minutes later we're like why is the dua not accepted we have to be patient with the answer we have to be patient with the time and the circumstance and the situation that we are in the second response then is to see this as okay it's coming from Allah what does Allah want me to do how does He want me to behave in this situation that I need to internally maintain a state of composure when you and I complain we can leave the station of patience if we're trying to attain the station where Allah loves the sabidin he loves the people of fortitude and patience and subar is more than just patience it's like perseverance it's putting in the effort it's a struggle it's active struggle with ourselves that's when we're talking about this idea of subar but just to kind of use a word that easily like an easy word in lexicon but it includes patience and perseverance in this constant struggle okay so we see this is from Allah reminding ourselves then not complaining about it right and then we have to try our best to have the response that God would want us to respond with so if we have let's say time and we have time to do things we use that time for good or at the very least not for bad something neutral or good ideally and that now we're starting to get to the essence of being patient with the situation right if we start to use the time that we had in the opposite of what we should be doing or to engage in more sin or something of that nature it's hard to actually then say we're being patient and you and I just there is a a hadith that into Dar al-Faraj waiting for relief is part of ibadah it's part of worship so just sitting in our homes trying to do good trying to spend time with our family and just waiting for this situation to get better is we're getting ibadah it's ibadah if our intention is correct all of us should make the intention that we want to be in a state of ibadah as we wait for this situation inshallah to get better and to remember that practical things that we can do to fill our time with good right we should have a portion of time where we spend learning order some books whether it's religious books or other types of knowledge right but we should spend learning the more we thrive internally and that's important we should have a portion of our time where we are physically taking care of ourselves exercising if we can portion of our time where we're spending with family portion of our time where we're trying to work on some type of good project or something that we want right we have time right now and many of us say if only I had the time to do such and such Alhamdulillah now we have the time and so if we spend the time then inshallah we will be able to if we spend the time doing good to attain this state of not only are we being patient through the time but we're also being patient in the best of ways not complaining and doing things fulfilling our time with what Allah appreciates us doing right and lastly just remember that this might be difficult to do but it's totally doable so use this time now Allah has given us a chance to show okay ya Allah I am weak yes I am not very capable but with your help inshallah I can attain this state I want to be among the people you love I want to be among the people you have who you are present with I want to attain these stations so we turn to Allah and we turn to Him and help and we turn to Him in assistance and inshallah we are going to get through the time we are going to get through the difficulty and we ask that Allah grant us and all of you and all of this community and all of our loved ones and this entire global community immense patients through these times and lastly just to mention that this coming Wednesday night inshallah will be a very very famous night in our tradition known as ليلة النسة شعبان that known or شبب برات in some cultures that is known as the night of the fifteenth of شعبان it is generally accepted through by the majority of the ulama in our community as a night that we should spend in worship in a famous hadith of the Prophet ﷺ he said that Allah gazes at His creation on the fifteenth of شعبان and He asks and He says is anyone seeking forgiveness from Me so that I may forgive them is anyone seeking provision from Me so that I may provide for them and is there anyone suffering so I may relieve their suffering and so many of us are in one of these categories and we should make an intention to get the special gaze of Allah on this coming night and spend the night of نسة شعبان I believe MCC inshallah will be doing a program on نسة شعبان via live stream to help encourage us and teach us what we should be doing how we can spend the night in worship but we should make a niyah spend that night in دعاء spend part of that night in the hadjud prayer or the very least extra prayer after Isha and ask Allah for assistance for all your worldly and other worldly needs and ask Allah for immense relief from the suffering that humanity is going through this is a very very honored night and some of the ألم I say after ليلة القدر this is one of the best nights of the year for the Muslim and so we should keep that in mind try to bring this night to life and ask Allah to elevate you to increase you to give you and make you among the people of patient among the category and in sha Allah don't we should try not to worry that Allah is is the best of planners he is all wise he knows exactly what he's doing and he's going to take care of us in this situation and in all the situations that we will face in our life وصلى الله وسلم وبركة لسيدنا محمد وعلى آلي وصحبي وسلم شاء الله جزاكم الله خير thank you for joining us we will have another talk Sunday night in sha Allah 8 pm we're going to regularly be doing these we're going to be talking about how to manage faith in these trying times and and these regular Friday reminders in sha Allah we'll continue wishing everybody the best please stay safe please stay healthy happy Friday جمال مبارك in sha Allah and please again remember that this does not take the place of the Friday sermon we still have to pray our 4 أقات الضهر وصلى الله وسلم وبركة لسيدنا محمد وعلى آلي وصحبي وسلم و الحمد لله رب العالمين


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.  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.  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.  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.


What's up everybody takedown here welcome back to the channel today. I'm gonna be doing a nether munchpack video My fourth munchpack today I've decided to do another mini munchpack is to me There are better chance of getting some good stuff out of it And if you guys want to get your own munchpack visit munchpack.com and use promo code Real takedown to get $3 off your order, but let's just get into today's munchpack and show you what we have Let's get into it. We're gonna try everything in here and rate it from best to worst Okay, so they added this this is new and it is stickers on every item that you get in munchpack And it tells you where it's from and what it tastes like so if you have allergies It's really good and for me and anybody else that makes videos It's really good because we now know where it is from. Let's try the first item I can't really pronounce it delus la lake. It looks like wafer chocolate wafer snacks And it is from Argentina. Okay, so here we go It doesn't look kind of like it does on the packaging on the packaging the wafer looks darker and it looks like chocolate But it ooh It has a really good scent though It's probably like hazelnut or something like that. So I love it. Let's give it a quick try here Not bad. I do have a complaint though The wafer kind of tastes stale on this, I don't know if Maybe this one was just close to expiry something like that, but The wafer on it does taste Not as crunchy. It tastes like it's almost stale, but the flavor to me is like hazelnut It is good still let's put it in the middle for now it can move up and down the line anywhere, but These ones here are from turkey. I don't know if they're called mood. They are milk chocolate It's almost like those to be the Japan snacks I had before the koala ones So we're just gonna open it up They look exactly like those koala ones I had before I think it was one of the first munchback I had pretty same Idea has a little image on the front and it looks like a cookie. Let's give it a try whoa Those are really good All of them have different images Holy hell It's gonna be gone by the end of the day, let me see if I can get a cross section for you guys Kind of falls apart chocolate in the middle They are delicious Honestly, this might be the best thing I've ever had from munchback They're pretty similar to the Japanese koala ones I had before Koala Marsh, I think they were called but These are a lot better The chocolate is real milk chocolate is really creamy the cookie tastes excellent and It's a lot better than the koala Marsh to be honest with you those ones there. We're not the greatest I expected a lot out of them, but these are perfect. These are first place right now I'm gonna have first place on this side. These are first place. They are perfect and they are delicious Next up we have green apple candy. I thought it was Something else at first, but they are from China. This should be pretty cool. They look really good Let's give it a try Here's what they are. They are really small Give you that there. You can't really see it, but it's supposed to be green apple. They are the tiny tasty chewy candies So let's just try one here whoa, I Wasn't expecting it to be like really a chewy I was expecting more like nerds in a way the consistency of that but they are Soft, let's have a few we're gonna have to these are amazing to holy hell. These are Perfect. I'm not into candy Never have really been into candy. I'm usually like chocolates and other stuff like that, but For the candy these are perfect. These are one of the best candy I've ever had Best part is they come in strawberry watermelon and blue raspberry. So if you don't like green apple You can get them in whatever flavor you guys like honestly They could tie for first place, but I'm gonna have to put them in second place as of right now next up we have a Belgian waffle From Belgium it looks pretty good. It looks like a waffle. It's I was expecting it to be hard, but it's pretty soft Let's give it a try. Okay, so I'm just gonna open it up a little bit here Look at that it honestly is a waffle. That's really cool Let's see if I can get a little piece out Just like that And it's a whoa that smells really good Almost like French toast in a way like the cinnamon scent in that Let's give it a quick try here Really soft. This is amazing. I wish you got more in with it, but this is Perfect. Holy crap so soft so delicious If you had a little bit of butter it'd make it perfect, but it is amazing on its own as well I'm gonna have to give this third place right now. It honestly could tie with the other two snacks next up. We have Walkers this is cheddar and onion chips. They're from the United Kingdom And I've been trying to get these for a while. I really wanted to try them They do have different flavors and I really wanted to get a variety pack But nowhere online sells it that I've seen so if you guys know of anywhere that sells the Walker chips in a variety pack That could ship to Canada. Let me know. I really want to try them, but let's get into these ones here and give them a taste It looks just like a basic chip Not too much seasoning on it But it smells like there's a lot of seasoning. So that's a good thing. They're light on the seasoning But the scent is there. Let's give it a try They're good. Holy crap If I wanted to I could eat the whole bag Pretty small, but The flavors there now as somebody that does not like onion you don't taste too much of the onion which for me I'm a fan of that these chips get second place right now Everything I got today was amazing Everything I got today was delicious Usually whenever you get munchpack you might get depending on the size you purchase One to two items that you just don't like and you consider gross today. That did not happen Thank you guys at munchpack. You guys are awesome This is the best thing I've had so far from you guys And it will be getting another one in the future for my fifth munchpack video Hope you guys did enjoy if you guys do want to get your own munchpack and at least try it out Like I do use the code real takedown for three dollars off your order But I'm gonna end this video here. Hope you guys did enjoy if you did Please leave a like and I will see you guys in the next video. Please take care. Peace


In this last one line hypothesis test we're actually going to get in to a difference of proportions. And so here our null hypothesis is that there's no difference between the proportion of gas that was below capacity and the proportion of wind that was below capacity. And our alternative is that it was greater than zero. And so here, before we can actually get into the one line test we do need to do some prep work. And so I'm going to create a new column called below capacity for final gen. And this is essentially just going to be equal to the deficit, but we're going to use a special function called an apply function to quickly apply a conditional statement to the deficit. So we say dot apply. And then we give it this keyword lambda, which effectively tells Python that we're about to create an inline function. And we say x colon true. If x is less than zero, else false. And so what this is doing is it's x is just a placeholder, so it just needs to be the same cross both values. And it's saying set x set below capacity to true, if x, x being deficit is less than zero. Otherwise, if x is greater than or equal to zero set below capacity equal to false. And so, so if we print out the first five rows of our data set. We can see that we have our date time column, we have our fuel generation capacity deficit percent deficit that we've seen before. And now we have a below capacity, which will be true anytime the deficit is negative and false anytime the deficit is positive. So then, once we have our data as it needs to be, we need to actually calculate all of our samples, similar to our difference of means we needed to calculate the sample mean. Now we need to calculate the sample portions. And so in this case we can see sample wind prop. It's just final gen loc. And it's where final gen dot fuel equals wind below capacity. So we're only interested in in the below capacity column. So we're just going to leave it at that. So we're essentially going to just extract the below capacity column for wind. I'm going to copy this paste it and change the instance of wind to gas. And here when to gas. So that we just pull out the natural gassy. And then we're actually going to calculate the proportion. So our P wind of our sample is the length of which sample wind prop. And we are only interested in where sample wind prop equals true. And then we divide that by the total length of sample wind prop. And I'm going to copy that and change this to gas here, gas here, gas, and finally, gas. So these will give us the actual portion of when the wind and natural gas was below capacity. And then I'm going to get diff prop, which is following our alternative hypothesis up here is gas minus wind. So it's P gas sample minus P wind sample. So we can run all of that and see that the difference in proportion was point three five. So then we can move on to the one line test so we won't actually do a randomization procedure for the proportion. But in theory you could follow the procedure or a difference of means and just substitute in your difference of portions. In order to do this one line test we need a new library so we're going to import stats models dot stats dot proportion. And we're going to call it prop. So this is a new library that is specifically used for a difference of proportions. To use the test that we're going to do, we need to define our success number, which is very similar to what we did for a single proportion where we determined our success rate. In this case we need to determine the number of successes for our first data set stamp gas, and the number of successes for our second data set stamp wind. So we're going to do that within square brackets. So, again, the key here is to follow the, follow the order that you went in for your hypotheses. So we want sample the length of sample gas prop where sample gas prop equals true. The exact same thing that we did up here to calculate this P wind or P gas. And then I'm going to copy this, everything from the link command, comma, and then paste. And I'm going to edit this so that we have instances of gas equal to change those two instances of wind. So these are are the number of successes for both gas and wind. And then we also need to define sample size, which is just the length of sample gas prop. And then the length of sample wind prop. And so this is an effect the denominator of our proportion up here. And so once we have these values, we can actually implement the command which from the prop library that we defined up here. So it's prop dot portions underscore z test. This is the command, we need to give it a variable called count, which is our success number. And we need to give it a variable called n ops, which is our sample size. And then we need to give it the alternative. And in this case we follow a slightly different form of alternative. We're using a right tail test so it's a greater than sign, but for this particular command, we need to say, larger. So instead of saying greater or less, we say larger. And in particular we want the first value that's going to print to results. And so here we can see this p value is very close to zero, much less than our significance level. We can reject the null hypothesis in favor that the proportion, the difference in proportions is greater than zero.


So by all points are pretty important within this game. They allow you to not only buy some amazing abilities for your setup but also at the same time they allow you to apply resistances to your build so you can enter certain areas within the game unharmed. Today within this video I'll show you how you can get easily 40 to 50 by all points in literally 20 minutes. How's it going guys my name is DPJ and if you enjoyed the video leaving a like really helps out and if you like what you see and want to see more by all mutant be sure to subscribe. So yes by all points are pretty important. You can see how many I have here and I've used quite a lot, not going to lie, but a few abilities, applied a few resistances as you do but I've still got what 40 plus. Now there are three certain points within the map where you can earn tons of by all points in literally minutes and it's how I've got so many. Now like I said there's three places but it's probably more I don't know like I said I'll just showcase you guys are through today and this will give you all the by all points you need. So the places you do want to check out you can see on the screen now the first one is within the dead zone and it's called the by all nucleus 8c. Within this small by all plant there are an absolute ton of by all creep enemies all giving you one by all point each I think there's literally up to what I think 12 maybe 15 but I will state to enter these areas you will need a resistance to by all hazard obviously but this can be received very easily via gear even if you have to use by all points you already have to make up the difference you will still receive way more than you spend either way so you're going to be up. So yes this first by all plant is within the dead zone if you just circle this area you will come across at least three to four sets of by all creeps throughout time kill these and then you go underground through the couple of routes and you will find within the center of this place even more by all creeps sometimes by all containers which also give you those by all points you also get a by all bus which when you kill you get another by all point there's also a by all pool at every location today which allows you for one by all points to edit your appearance and the second plan which is a lot like this one is located at the very top of the map within clumpy dunes the plant is called bio nucleus 10k the plant like i said a lot like the first is home to many by all creeps and again a by all bus located again underneath circle the area kill all the by all creeps then go down below kill the other by all creeps kill the bus and you are good people from here guys the third plant is actually probably the first one you'll come across and one you might have already gotten to this is the biggest of the three today and it's almost center of the entire map and it's called by all nucleus 60 again this place is home to many by all creeps and that by all bus but there are just as many by all points to be earned here people yes guys use these three locations and you should see a total of 45 plus by all points easy and if you got the right setup you shouldn't have a problem killing these at all now if you're in need of any armor or great weapons check out my channel i've posted quite a few guides on this game so far and you're bound to find something that will help you out but yes the end of the video has arrived if you enjoyed it leaving a like really helps me out if you're new around here and want to see more by all mutant be sure to subscribe and if you never want to miss a video i upload you can turn notifications on by hitting that bell button but guys thanks as always for stopping by and hopefully i will see you on that next one