okay new start and let's have another taken for bending hello welcome everyone to this uh summer school the online edition uh usually we have 20 people who come to the netherlands and enjoy uh utrecht you can see a beautiful picture here of utrecht and people would go on a pedalo and see the rachten the canals that go through it but this time things are completely different and i'm very happy you're joining us here in this online session and it will be a bit shorter than usual we'll have two days today we'll have from two to five and tomorrow another day of three hours from two to five and uh well as i said i'm very happy you are all all here and to our big surprise there are a lot of you normally we have about 30 maybe maximum 50 participants and this year at least the people who subscribed add up to a total 479 from 36 different countries so i i decided not to say good afternoon because some of you will have a good morning some of you will be have a good night anyway i'll won't talk too long i'll go through some practicalities of you as far as you don't already know them and then i'll give the word to professor paul drivers so you can just have a look here which countries are represented we're very happy that you're all here and we hope you'll have the opportunity to be interactive with us using the live chat screen in the bottom of your own screen okay so uh all information i fortunately don't have to repeat because it's on the website for you you've had enough mails containing the location of this website so please go there if you want to know something about the program if you want to know what research pitches there are and you want to see them and if you want to know what to do to prepare for a workshop or a talk um all right tomorrow we'll tell you more about the certificates because if you are an active participant then you have the right to a certificate i want to say one thing that just a very recent change is in the second channel that we use for broadcasting the talks so i've updated the links on the website just 15 minutes ago to a new channel that's channel number two and it will be the well different from the one we had half an hour ago so just that you know i saw some of you already subscribed to the second channel as well and so that's not really necessary the program will have kickoff with uh paul drivers in about two minutes on this channel then later today at three o'clock there will be parallel session one will be me and the level of this one will be upper secondary so if you're interested in the tactics of mathematics upper secondary this is your talk i suppose but you could also go to case hochland who has a wider scope actually both primary and secondary school level and he will talk about numeracy so that will start at three o'clock then at four o'clock we invite you to go to the first channel and watch the short pitches that participants have recorded about their own research and please leave questions and comments for these researchers which they will happily answer today and tomorrow so that there's some form of interaction because unfortunately because of the large numbers of participants this is by far not as interactive as we usually have our summer schools but please make it as interactive as you can by leaving these questions and comments during talks and for pitches and we end the day with a short closing in which we'll maybe discuss some of these comments and questions and definitely do a short reflection on the day so that's it from me for now i'm very happy to introduce to you professor paul drivers who will talk about realistic mathematics education he's a full professor of mathematical education at our institutes the freudian tile institutes that's the inter that's the institute that actually organizes this summer school and uh i think further introduction i'll leave to him what he wants to say a bit more about himself so here he is thank you oh there's a five to ten minute break between each part of the program so you can get yourself a drink and refresh and then we can also set up the new technical parts of the next part okay see you thank you very much for here um for the introduction rohit boss my colleague at the freudian dal institute it's a great pleasure to speak to you it's a bit strange i don't see you but we are really excited as what he already said by this huge number of participants and a big interest in the work of our institute at utrecht university so my talk will be a kind of so to say crash course in realistic mass education i hope you had the opportunity to have a look at the the preliminary tasks that rohil already distributed and which we will discuss later on so a crash course in realistic math education rme as we abbreviate it it's essentially an old theory in a sense that the big developers of it were hans freudenthal and adri trevos in the previous century he received two very seminal books of the the two professors but it is still alive as you can see here two very recent books edited by my colleague maya vanderhoff of bandhausen and interestingly enough they are open access available so you can really download the complete books at the links that you see below and you will not have the time to copy the links but the slides will be available so it's old and it's still alive and i will explain to you like i said in a very brief notice some key aspects of the rme theory i will set up a kind of shared vocabulary and i will reflect with you on rme task design so these are the three main aims first an introduction to rme what do we mean by realistic math education well it is a domain specific namely for mathematics a domain-specific instruction theory on the teaching and learning and it has been elaborated into a number of what we call local instruction and these local instruction series on the didactics of algebra calculus whatever these local instruction theories also contribute to the whole picture of the overarching rme series here you see um some uh well what should i say a snapshot from a recent paper by maya van der nervopaners and myself this is a 2014 version there is an update 2020. and the red sideline illustrates a quote realistic situations are given a prominent position in the learning process these situations serve as a source for initiating the development of mathematical concept tools and procedures so this is probably the most common view on rme that people have and my hidden agenda to be honest is to kind of nuance this view it all started out with hans freudenthal who was a famous mathematician but also he spoke like nine languages he was in contact with many scientists in different domains worldwide he was really a very well known scientist and he said mathematics is not like the abstract body of inaccessible knowledge out there or in heaven no it is something that we together develop we created mathematics is human activity and in the heart of that is the process of mathematization which means that we make mathematics out of it out of what out of situations in our lives and maybe out of mathematics itself so why did floyd and dan come up with those ideas well friedendorf said well on the one hand usually in teaching mathematics we present the things upside down compared to in the ways they were invented and this is what he called anti-didactical inversion we as mathematicians did a lot of work and once it's finished we tell it in another way to our students and also as a second point freudian dust said well we have this mechanistic and structuralistic approaches to education and on the right hand side you see an example of this in an old-fashioned textbook and through this you learn to carry out the procedures but the type of knowledge that you will acquire and skills is not flexible and not applicable and in the end not very useful and to illustrate this human activity idea the iceberg metaphor came up which says that if you want kids to be able to add five plus two and to know that the outcome is seven this is observable behavior you can see kids do it you can assess it you can grade it but this is only the top of the iceberg the ability the skill to perform this addition floats on a lot of previous experience and knowledge that kids have they have been throwing dice they have been counting on their fingers they have been using some abacus they have worked with the number lines and all these experiences are like the the foundations for the observable skill of adding five and two now if you consider this as an iceberg you only see the top of the iceberg above the water level but if you say well this is what i want and i can reduce on what's below sea level and cut off the experiences that are the foundations for the procedural skill then the iceberg will go down if you cut the bottom part of the iceberg it will sink a little bit and this your skill the procedural skill of adding will also get less well so this is a nice picture to illustrate a bit um here on this slide you see a lot of um well literally um reviews that you can consult if you want to know more about it so far for the introduction and now in this like i said crash course i'm going to probably overwhelm you with some vocabulary that we use and four key terms that i would like to briefly explain before we will revisit the tasks that you might have been working on already these key concepts are mathematization didactical phenomenology the most impressive expression to pronounce at least use of models and guided reinvents now first mathematization i already used the word and it relates to um what we call the activity principle principle meaning that mathematics is a human activity mathematics is something that kids should do now mathematization very bluntly speaking comes down to doing mathematics making mathematics making mathematics out of situations around you or out of situations that you encounter in one way or another and our colleague adri travis made the distinction already a while ago between horizontal and vertical mathematization and to explain this i use this type of figure by horizontal mathematization we mean going back and forth translating between realistic context realistic problem situations and mathematics so you encounter a problem and you phrase it in mathematical terms and you create a mathematical model for it and that's horizontal mathematization from the left to the right and from the right to the left means that if you have a method from mathematical model and you made some calculations or solutions you can translate them back to the meaningful situation that you started with so horizontal mathematization corresponds to connecting the world within mathematics and the world without outside mathematics and this is what rb is most well known a vertical mathematician means that you build within the world of mathematics your structures your objects your methods there's more mathematics within mathematics abstraction for example and a vertical mathematization is something that is a bit underexposed in the theory of rme i think well maybe not in the theory but in the view that people have worldwide so mathematization in short means making mathematics out of the situations that you encounter and these situations can be realized which refers to the horizontal or can be already mathematical which refers to the verb as a short example i'm not sure if you can read it this is part of a poster that 14 year old students in the netherlands made and it was about a situation with fixed costs and variable costs and at the top you see then they are performing calculations they're really like very close they use the numbers of the problem situation but on the bottom right hand side you see the word formula and the line and they are trying to set up some general rules which are no longer so much attached to the problem situation so they start getting their own life and they are like moving from the world of the problem situation into the world of mathematics so in my viewer in this poster i can see some elements of horizontal mathematization and of vertical mathematization i'll come back to this in a minute so mathematization means like making mathematics out of it and the out of it is out of problem situations around you or maybe problem situations within mathematics oh there's a question yes has the iceberg been applied outside the context of mathematics and stem not as far as i know the iceberg i'm not sure if you could hear it the question was has the iceberg being used also outside the context of mathematics education or stem education as far as i know not but i'm not sure and at least it would be an interesting thing to do it would be a nice challenge to see if you could apply it elsewhere so open for input on that thanks for the question the second key word is a didactical phenomenology and that relates to what we call the reality principle but what do we mean by reality anyway um and freudian tile wrote about that um reality refers to what you experience as real the highlighting is from me because this is the most important word you as a student or as a pupil or as a teacher should experience the problem situation as real and andre trevor said um reality is the world of the child and means that we try to identify the appearances of mathematical phenomena that fit the world of the child and that means to which the child can attach meaning so reality realistic refers to meaningful this is what ari says here in my opinion so realistic can mean different things it can mean feasible doable it can mean related to real life but it can also mean meaningful sense making or in dutch referring to realizing namely to be aware of to imagine and in fact it's the latter two meanings that i found far more important than for example the real life so maybe the main point i want to make today is that realistic mathematics education does not necessarily refer to real life but it refers to making sense being meaningful to students okay now the didactical phenomenology this means this connects to the previous because the phenomenology directive of endomonology is in fact like the art of a teacher to [Music] identify phenomena situations contexts that are suitable to make sense to students your target group and to invite them to develop and understand the mathematics you want to teach you want them to understand so it's the art of identifying phenomena that are suitable and that beg to be organized by the mathematical means that you want to teach so to put it bluntly didactic often phenomenology means that you identify situations or tasks contexts that really invite the mathematics that you want them to to think about in a natural logical meaningful way [Music] and this phenomena this is the final line of this slide they can come from real life but probably the main thing is that they are experienced as real by your target group and what your target group experiences as real of course is very dependent on student age student level country culture language whatever so this is a subtle question how to identify these phenomena but the main point is take care of this this is really the art of a designer and a teacher to pick out sense making phenomena for those students for this mathematics at that you have time for another moment sure uh the question is uh is the horizontal mathematical lesson mathematician the elaboration of the mathematical model and the practical one is working in and with the mathematical horizontal mathematization means involves setting up the model these are yeah setting up the model creating the model that's the one-way direction but also once you have the model and you work to in it going back from the mathematical results to the problem situation so it's going back and forth but essentially yeah makes sense and one more question that really fits what you just said how real must the real phenomenon to study in primary school yeah good point how real should the phenomena be um if you don't mind i will postpone this question because i'll come back to this in uh well in a few minutes okay and remember if i forget it but i will not well this is an example how maybe this is already part of the answer this is an example of a primary school textbook series on division and you have 18 nails as you can see and my father who is a tinkerer has this nice box with drawers and he wants to clean up his uh his desk and to put the nails into the drawers and the first task is i want to divide them i want to put them in three upper drawers how do i do this now the idea is then that um you open the three drawers and you do the nails one two three four five six etc so in the end you will end up with six nails in each of the three drawers right this is what the designers have in mind however if you have ever been as a child with your father in his tinkerer cabin and you saw him dealing with nails you might know that he does this quite differently he puts the big nails with the big nails in one drawer the small ones the small ones maybe um different colors or different materials so he has quite different ways of sorting them out than just fair division so if as a child you know about this you might be hindered by this problem situation to get into the idea of division so um this is real life but not real real life in the sense that the real tinkerer would not do it like this so how real should real life be at least it should not hinder and in this case if i know more about the tinkerer and how he deals with nails [Music] right um okay so i consider this not as an excellent example and the main point of this talk is take care of the examples you use because well there are dangers very easily models is important in realistic math education and this relates to what we call the level principle and maya van der hoeverpanizer wrote already in 2003 models are representations of problem situations which reflect essential aspects of the mathematical concepts and i think this is quite share this idea and as an example you see some models here for example at the lower uh at the bottom you see a chocolate bar which can serve as a model for ratios i take there are one two three four five parts and i take one half of one part so one tenth etc um the middle right hand side you see a ratio table uh one before it connects to nine two to eighteen etc so then the ratio table is a model for me to think about ratios to operate on the upper right corner you see a number line on which we can jump and this is clearly a model for calculations arithmetic calculations and the middle top is a more complicated model that's a tree model for algebraic formulas or expressions i should say and we implemented this in a digital tool in our digital math environment so we have all kind of didactical models that should help students to understand what they are doing or maybe support their operations this is one way of looking at models but there's another way and that's the way by les mistres van der hoevel the model of model 4 distinction which is called immersion modeling and this connects a bit to this horizontal and vertical mathematization because the idea is as follows um when you start working on a problem a meaningful problem you're often your thinking is very much connected to this problem situation like the nails in the drawers or whatever and your phrasing your your language is often related connected to the situation um and this is really then you are really into the situation and a bit less maybe in the abstract mathematics which is no point because this is how you usually start i would say next level [Music] would be the referential level which means that you're still manipulating the mathematics and operating in the original situation or context but you're not so much involved in the problem situation itself because you feel like okay this is my example this is my situation but in fact i'm working a bit more in general and i'm referring to the problem situation but i start doing the mathematics more on its own however if a student has problems at this level you as a teacher refer to the problem situation the third level then is the more general level in which the focus is on the in situation independence mathematical objects and solutions and so the mathematic the meaning is more derived from the mathematics itself rather than from the original problem situation or contexts again if students have difficulties at this level you immediately fall back or go back to the to the lower levels because then they need that the lower levels to attach meaning to the situation they are in roughly speaking the situational and referential might fit better to the horizontal mathematization and the general level fits more to the vertical and finally we have the formal level which means that um [Music] in fact you're uh you're also using more formal mathematical and conventional mathematical notation and terminology to express your mathematical ideas so the idea of immersion modeling is that while learning mathematics you usually go from a very concrete situational level to a more referential general and formal level and as a teacher you might take this into account if you want to recognize where students are and where their problems are of course not at every moment and not with every student you want to reach for the formal level that's depend depends on your goals okay um there are two questions paul do you have time sure it depends on your but these fit one question is what can we say about relation between mathematical modeling mathematical models and the way it's used in rme and the second question uh how do you deal a realistic means relates to what students can imagine what if students imagine different things okay indeed the word modeling has really different meanings and i just briefly addressed two of them one is the use of what we call didactical models like the ratio table of the number line the other one is modeling in the sense of immersion modeling like layers of understanding that students build and indeed a third meaning is mathematical modeling which [Music] yeah refers a bit to this horizontal mathematization i would say and maybe to the lower levels in the four level model that just presented um yeah but i did not pay attention to that because again it's also again a slightly different meaning of the world of the word modeling and the other question was um of course students will attach different meanings to to the same situation or the same task um that's a very general issue in teaching of course to in whole class teaching for example because not all your students are at the same point so this is the very general issue of differentiation [Music] which is hard to deal with which i'm not going to address in this talk but very generally speaking the idea of rme is that the student is the starting point of the learning so as a teacher you would like to try to understand where the student is and what the things mean to him or her or don't mean or what's meaningful to this student to build upon for the further learning and that's of course quite a challenge for for a teacher especially if you have like 30 or 40 kids in front of you um again i'm going a bit quick in this crash course but in the light with the time i will just continue for the moment for the fourth and final concept guided reinvention that's a relatively short one refers to the guidance principle sometimes [Music] people say that okay if you want students to discover the mathematics themselves in a meaningful way what's the role of the teacher well freudian tile had this claim coined this expression guided reinvention reinvention is that indeed we do like students to create their mathematics in a meaningful way and in a natural way which clearly outlines with a kind of constructivist view on learning still we have to acknowledge to admit that not all of our students are as clever and bright as oiler newton and archimedes and pythagoras together and if we want them to master the mathematics methods all these genius scientists have developed they might need some guidance so students do need guidance from textbooks online resources peers the teacher because we don't in the end want each students to follow their own idiosyncratic learning trajectory we also want them to end up with a kind of mathematical knowledge that they can communicate to others and that is has converged to common mathematical standards so guided reinvention is a nice expression in my opinion because it highlights on the one hand the aim of students reinventing their meaningful mathematics and on the other hand the role of a teacher amongst others to guide them to help them and to make sure that we will in a way end up with with common mathematical knowledge so how do you do this well there are different ways my my phd supervisor conochrachemia said well what might be a helpful heuristic is think how you might have figured it out yourself and another heuristic is have a look at the historical development of a mathematical concept and these are two ways to think about ways how you can guide students but a very important starting point is listen to the students how they express themselves where they are what is meaningful to them and try to connect to that so um like i said apologizes for this uh this quick amount of jargon um but now we spoke briefly about four key concepts in rme mathematization like making and doing mathematics didactical phenomenology like identifying nice problem situations and phenomena that invite specific mathematical development the use of models didactical models and this layer model to know where students are and the idea of guidance reinvention to express the aim of making students reinvent mathematics but i mean in the meantime guide him as a teacher so this is nice but how does this apply to specific tasks and this is um why i presented you with three tasks from dutch textbook series this task on the lawn was for like 14 to 15 year old students 14 i guess um about a lawn in a garden extending it i should tell you that in the netherlands we have a lot of gardens and a lot of lawns 15 by 20 is a big garden that's true most are smaller but could could happen the second task about melting eyes was first like 16 year old students um who just had a graphing calculator to graph functions and that's why there's the word plot in task c plot means use your graphing calculator to sketch the graph and the third task is from a booklet which we edited already a while ago and the picture that you see on the left hand side was made in geogebra i prepared a nice animation but we added some technical issues i'm not going to show it to you but there's this line which intersects the parabola in two points and you draw the midpoint of these two intersection points and then you start moving the line up and down and um you see what happens with this midpoint and it seems to move vertically and the question is is this really the case those are the three tasks and in the preparation that rohir sent you the question was could you well first work on the task yourself and then could you tell us what you think about the realistic qualities of the context and the tasks and there were some very nice comments thank you very much for the all the input on the youtube channel and some very helpful insights also for me interesting to read your opinions i cannot react to all of them so i would like to get a kind of summary through a poll which we're going to do now if you consider the first task of this loan which is extended i ask you two questions do you consider the task realistic and do you consider the problem situation realistic for the moment i just stick to one single task do you consider the task realistic and my question is if you could go to on your maybe you have a smartphone or on your computer to menti.com and use the code that you see there above and could you then please give us your votes if you think about the loan task do you consider the task realistic and now i hope that i will have some votes coming in if not i will look at how here desperately yeah there's one vote okay good do you have time for a question while people know sure what does that mean i don't know if you have voted you can listen to me what's the question some people want to know about rme and multicultural classrooms is there anything you can say how army could help in a multiple classroom okay in the meantime please enter your votes right we have 20 now but i would like to go up a lot we have 185 people watching okay great so this is our ambition for the moment um so how about rme in multicultural classrooms um again that's a challenge because if we take the point starting point of problem situations and mathematical activity being being meaningful then the question is how does this meaning refer to these different cultures i remember a very blunt example we had a national examination here in the netherlands on ice i something with snow and a lot of snow was in the task and in in suriname and grasau they had the same examination which is in the well a region where they don't have any snow so this was quite a difficult task to imagine and to make sense of for the students there so problem situations and context can be culturally biased and if you teach rm in an rme way in a multicultural classroom this is definitely something you should take care about okay um maybe um this this shows a clear image that people consider the long task as realistic roughly speaking i have the same question for the next task so let's go on and please answer the same question for the ice cube task you remember do i need to do anything uh i hope that you can answer now the ice cube task whether you consider it realistic at the bottom i see copy to your account oh here what does that should i press it i think i should is there anybody who can vote for the ice cube task i hope you can okay and here's the third one does that work probably not either okay then i will uh well we had some votes for the first task but now i will drop it for the moment and i will just uh continue this is not what we want right i will just continue um for this first task um many people considered it realistic and um if i may be a bit provocative i am i don't agree at all because the situation in the netherlands of having rectangular in your garden this situation is realistic in a sense that it happens often and kids can imagine it in the netherlands at least might be different in other cultures but if you want to extend your lawn of course you make a plan your garden is not well has clear borders i guess so you cannot do whatever you want so you make a plan beforehand it's not that you do something and then afterwards see what you've been doing also if you add a strip to your lawn you have to carry those rolls of lawn and you you do it you it's a lot of work heavy work so of course you have an idea of the width of the strip that you are adding so it would be very artificial to to not knowing this and in the unlikely situation that you don't know it it's also very unlikely that you think oh okay but i had a mathematics teacher and then and he said something about x so let me set up an equation and even in the very very artificial situation that you would set up an equation here then in task b it comes up with a 374 square meters but how can one ever know the 300 374 there's only one way to know it that is to measure the new extended long but if you measure the new extended loan why not and then multiply the two dimensions and get 374 why not immediately mention the unknown value of x that you would like to know so in short the problem situation is meaningful to students but the elaboration into a task is really very artificial and not natural at all so if this is what we mean by rme i'm afraid that rme comes down to teaching to students okay we have a silly tasks it's not realistic at all but please do what you what i ask you to do and this is not at all what we want of course i may be exaggerating a little bit at the moment but the point i want to make is that a nice picture and a nice story does not in itself make a realistic mathematics task or a mathematical activity and in this case the task and the activity asks from our students to put off their common sense and to put their minds in mathematics mode and in trying them to to find out what a mathematics teacher or textbook designer might want them to do now and this is not at all what we would like in mathematics i hope you understand my point the second one the ice cube as somebody in the in the youtube channel already highlighted this is a bit more realistic in a sense there are some physics involved but i guess an ice cube would never melt like this an ice cube would melt and get more round and well a bit messy it will not remain a clear nice cube and also the speed of 0.3 millimeter 30 ml millimeter per uh or whatever now sorry 1.5 millimeter per minute this puzzles me because i could imagine it at the start the surface touching the hot air is big so it might melt quicker or slower i don't know so as soon as you start to know anything from physics you are really confused by these stars so taking a problem situation from physics as a starting point for mathematics is nice but again the model here is well really puzzles me and confuses me and draws my attention away from mathematical tasks so again even if the situation is interesting the elaboration is not realistic in a sense that it's puzzling me as a student if i think about my physics course that i have next next hour finally the parabola task many of you said well this is less realistic but if you think of a target group of like 16 17 year old students high achieving students they've seen parabolas many times in their school career so far so maybe they are quite familiar with parabola and if i make them do the exercise in geogebra they will encounter this phenomenon of the midpoint going vertically so then the question is is really true can be a natural and a meaningful one again depending on the situation on the level on the age and on the way in which the teacher frames it but this context or problem situation has at least the advantage that it doesn't have the limitations or the shortcomings of the previous two so in this sense this can be a very meaningful task in geometry using geogebra or so which invites some algebra and from that perspective can be a very really an rme task so in short because i have to think about the time ah i get some five minutes so let me use them i'm not one i don't want to make a plea by claiming real life situations and contexts or nonsense are not needed not at all i do want to make a plea to take care that you don't use context in a very artificial or confusing way or in a way that they lack opportunities for mathematization and what we sometimes see is that people understand rme as okay i start a task with a story and then i do my regular mathematics with a very weak connection between the story and the mathematics and that's in my opinion not what rme sets out for so we are looking and that's the didactical phenomenology we are looking for situations that are meaningful for students can be real life very nice but in a natural sense-making way in vitro mathematics so rme is much more than a task starts with a real life story so an appropriate problem situation is meaningful to students can be a real life situation that can also emerge from the world of science or the world of mathematics and of course this is largely dependent of the skills competences interests age culture of the students that are in front of you so please unders take him keep in mind that rme is different from real life stories even if for example with young students it can be very important that the starting problem situation is really coming from real life but it should be meaningful recognizable experienced as meaningful to the students so in short to summarize i tried to in this crash course outline rme as a domain-specific instruction theory i try to make clear that reality refers to what students experience as real and meaningful and mathematics is something you do next i try to briefly express four key words namely mathematization doing mathematics making mathematics out of it didactical phenomenology as the art of identifying suitable problem situations or phenomena that invite mathematics the use of models on the one hand didactical models and on the other hand this level of emerging models and guided reinvention as the role of the teacher or the textbook author to offer opportunities for students to reinvent mathematics but in the meantime to offer enough guidance and finally the word of caution that i would like to express is please be critical when you see real life situations in that they should not be artificial or puzzle students but they do invite the mathematics that you want them to work on and real life and that is not the main criterion the main criterion is meaning making sense making and in that sense that students experience the task as meaningful so thank you very much for your attention um thanks for attending the summer school enjoy the rest and if there are any questions i'm not sure if you have time for that at the moment or here please guide me i just promised that you would go to this chat and would answer any questions that are left okay okay nice promise it's a pleasure um thank you for your attention sorry for the density of vocabulary and enjoy the summer school and i will see your questions in the chat window thank you all right i will take over yep there you go [Music] well thank you very much paul uh we will be back very soon on this specific channel i will interrupt the stream for a moment and then come back with a new stream and uh there will be also a workshop on our other channel i'd like to repeat what i said in the beginning for some people will not have heard that i've updated the channel we had a technical glitch 15 minutes before the start which made us change the channel the right channel is now on the website just so just click the link in the program there for the workshop you would like to go to and uh well if that goes wrong you can just search for the freudian tile institute's channel that will be the channel for the talk by kate hoagland on number c and this channel will be the channel for the workshop on a smooth slope the slide is a smooth slide to slope by me thank you for your attention here thank you for your questions and i hope to see you soon