IC16: Discovering The Art Of Mathematics

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IC16: Discovering The Art Of Mathematics
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Christine von Renesse will present the efforts of the project “Discovering the Art of Mathematics” (DAoM) to teach a final course in mathematics to students at the college level using inquiry-based learning. The connection between photography and mathematics will be used to showcase how inquiry can connect art and mathematics while developing deep mathematical content. All teaching materials produced by DAoM are freely available online at www.artofmathematics.org.
Mathematics Heat transfer Imaginary number
Mathematics Mathematics Process (computing) Right angle Maxima and minima Numerical analysis
Mathematics Mathematics 1 (number) Mass Euler angles Social class
Rotation State of matter Multiplication sign 1 (number) Modulform Line (geometry) Multilateration Student's t-test Food energy Position operator Social class
Group representation Multiplication sign Social class
Moment (mathematics)
Mathematics Lie group Multiplication sign Mathematician Mereology
Mathematics Different (Kate Ryan album) Connectivity (graph theory) Projective plane Energy level
Mathematics Elementary arithmetic Projective plane Right angle
Mathematics Elementary arithmetic Lie group Weight Universe (mathematics) Materialization (paranormal) Circle Game theory
Different (Kate Ryan album) Lie group Universe (mathematics) Student's t-test Social class
Point (geometry) Group action Projective plane Student's t-test Line (geometry) Sphere Sphere Connected space Mathematics Group representation Mathematics Circle Social class
Computer programming Stereographic projection Mathematics Different (Kate Ryan album) Multiplication sign Projective plane Mathematician Axonometric projection Surjective function Social class Physical system
Angle Inference Student's t-test Free group Mereology Imaginary number Connected space
Cube Free group Distance Set theory Social class
Geometry Block (periodic table) Gradient Student's t-test Mortality rate Mereology Sequence Different (Kate Ryan album) Term (mathematics) Cube Queue (abstract data type) Free group Algebra Set theory Social class
Statistical hypothesis testing Pairwise comparison Multiplication Confidence interval Euler angles Connectivity (graph theory) Sheaf (mathematics) Content (media) Archaeological field survey Student's t-test Calculus Function (mathematics) Mathematics Mathematics Cube Right angle Free group Mathematician Imaginary number Resultant Position operator Social class
and the whole thing in the year the work of
the thank you you and so what I'm interested in
is less doing exhibits as I can hear a lot of people doing I'm more interested in how to teach mathematics in a different way there are lots of intersections tho as was mentioned in the beginning it's really interesting to see how everything is connected to them as a can you by max and I am German originally but I teach in the US no and my passion about teaching mathematics is the number of a lecture to doing this right now feels really awkward and I will give you a
job soon so I can get out of this situation the so the overlap
that I can see you with exhibits with math exhibits is the kind of audience that idea with that you guys and what does my audience usually think about mathematics they hated their afraid of said they don't wanna do it anything you can name but they have to be in the math class in college because our college requires to math masses exact well if you have a STEM majors so math major assigns major you have your own classes but all the other ones English majors the the majors whatever tortured with 2 more math class so the question is what are you doing there how do you the do deep mathematics and how do you show them that mathematics is called but um OK and to show you dance I will show you this small video
clip from my own class what I want you to do is to look at what it is
that I'm doing and what it is that the students are doing and after will still have some time to talk to your neighbor about that so instead of me telling you what it is that's happening in my classes I want you to find out the OK you know the internet you don't but 1 of the things that you to be a guest of trying to think of things like this and they'll back at that but if you are a really really only 1 of the things that go to the the variance and and so on so I think we have that form that it looks like a position in which you do have more and I only know of the act and was 9 0 and 1 does a list of some of which 1 is the 1 for the energy rotation we are of the actors life that was later ones and that's something here and you have to be acquainted yeah I think the last 1 we have 1 can you like that because they did not come in at the time it a willingness in the room have these intermediate states that once you have the match at on the line of the ones I would think that the main so it's these ones are way of doing it this so that that was the very high and we give in this time using that have left in the play now 1 of the 1st half of the size of the whole way yeah yeah I know and I know that I mentioned at the beginning of this the the what happened thank you and it is
in you
and the the end of the 2 and in and you need to be thinking about the and the OK let's get back together please since
they only give me 15 minutes and not an hour and a half which I would have preferred to have em so I would love to hear 1 of 2 things from the audience what you know this and that but so and by the way this is what class looks like all the time I don't ever stand up in front so this is class anything but in others no and in the the end of the day right so they had worksheets with questions that they can work through a Honda had vocabulary they came up with their own representations that so they have a lot of paperwork that's what I heard you guys notice to great what else the the
right I don't debate that basically I watch them faIl over and over again here you know
the only use of and what's 1 of the things that I did in the
moment of this you most frustrated and failing so what something that I did I didn't me I didn't just walk away and say whatever if you have take
it somewhat some motivation now now what I ask you right there and so I ask why they gave up and I also acknowledge this is really hard hard and at
other times you might see me acknowledge like mathematicians have to fail they have to make mistakes so that's that's part of what we're supposed to be doing OK so there's a whole lot pose on this there's
also a video about the success is not just a few years of you it is that you can go look at that on our website which is the art of mathematics of or M. now and I didn't really say anything
about my project that maybe I'll do that later
so teaching using incre for me it has a lot of different components the most as I am the coach I'm not supposed to tell them in mathematics I'm there to help them rediscover mathematical ideas so i infuse them with just enough so that they can get to the next step depending on the level where that
and if you can do that math majors you can do that with the majors that I'm not interested in math and I'm sure you can do that with people come visit in exhibits so the ideas of learning mathematics that way I think a very general and I've also done at an elementary school and high school I really feel like it goes all the way through them OK so our
project we have some funding from the National Science Foundation beyond the 4th grand right now but eventually they're probably 1 to give us any money anymore will have to see how it goes we wrote 11 books they be 2 semesters worth of mathematics 1 of them is
about games and puzzles and the Rubik's cube is an activity from that 1 and they're all freely available
on the net so unfortunately don't make any money without the good news is anyone can download them and use them as universities are using them but also with elementary schools middle schools and high schools by now have been downloading materials and playing with them in math circles math workshops infusing the curriculum of ideas the 1 1 of the things that we notice is that it's not enough to
give people the questions that we ask for the activities that you need to know how to run a class from that way if you have only ever lecture and suddenly you're supposed to do this increase stuff you need a lot of different tools you have just as
much control but the control knobs look very different and so we started to write blog posts about the different tricks that we do but grouping students getting the attention they cut to ask questions how to run a discussion any of those things and that was enough either so now we're doing traveling workshops so we actually go to university and we work with the professors of the local universities and help them experience what it feels like as a
student to be meaningfully classroom and and practice some of the tools so that someone of the current project that we're working on is doing the workshops only in the US style um and
then I wanted to give you guys 1 are connection examples of because I thought it fits in well that I've done with my class so we were wondering if I want to take the whole room and say this inside of the theater plays and I want to have a 2 D representation how could we possibly do that and so the students were 1st thinking about if they were in sitting inside a bubble how could they map every point from the outside onto that viewing sphere around them and even doing that has a lot of very interesting mathematical questions that come up by themselves like the lines of parallel like the top lines on the ceiling here what kind of things would they be on my spheres would baby lines with baby well then alliance within the sphere maybe circles but what kind of circles and how do I know for sure so there's a lot of mathematics happening right there um and this was the manipulative reuse so that so respectable house in front of them and it but the i in the middle and actually started drawings so had some some way to make a conjecture about what they think it is and then they have to prove it afterward and then regret we let the students think about how to project so not everything is on a sphere great but I wanted in on a piece of paper so how do you get stuff from a C on a piece of paper those are not math majors they don't know anything about projections and so the different groups developed their own projections and is really cool every
time someone invents a stereographic projection every time someone invents a rectangular projection I don't need to introduce them they just pop up and then I have them too long the classroom in their projections so we have a 2 9 different classroom drawings into hand-drawn with their own projections an afterwards I tell them about the
program that you can actually use that does that all that which you've probably seen on your phones already you know you take pictures all around you the programs stitches them together and then you get a nice projection this 1 done by the program call tiny plants so afterwards systems could go out and do their own piece of art by picking is at the place that they liked and and using the out to do that and then we had a little exhibit in our class about that but it felt really important to 1st do with the mathematics themselves because I really want them to be mathematicians and not start with the app because then I feel like all long out then they think they're drawing it themselves is kind of boring cheap compared to what the program can do so I had to be really careful not to give away that this is all figured out and that their programs to do this but to really approach is that something new and get to that in the end of yes that's about that I project and
their tons of more like we we use a lot of connections with art because that's what motivates the students so whenever possible we try to get through that angle to get to an interesting mathematical idea and that's the
main part oriented tool books 2 of our books dance book and the art and sculpture book out in the hallway you might have seen that and also some of our flyers if you just look at the book please don't take it you can download it for free because I'm going to take me conference after this and I
wanna bring us to the and so that's at any questions
and the the no the the the I don't I do have distance by their own Rubik's Cube because often that's the only thing they'll take home for the weekend as homework they get very attached to them but I also have a set of Rubik's cube that I brings so that no 1 has an excuse of not participating because they sick therefore got conveniently the cube at home so I do a bit of both but the 1st thing they have to do when they come to class as they have to take the beautifully perfect Cuban enough to mess it up and that's very hard enough to take a deep breath and then it will take 2 months before they can get back the I don't know if that answered your questions about the set of cubism about you so you mean like a cube that's perfectly
solved well what what we figured out last semester is that there's an app that solves the cube for you so you type into the Arab public for the cube looks like and the app tells you how to solve it and so we actually use that because it sometimes much easier to explore what specific moves to you if you start with a nice Q so I allowed them to use that out but then they still had to figure out how to do with the final exam was that they had to meet one-on-one with me and explain to me how this solving the queue so in the end it had to do it that would be there in all the questions that I ask in the book that a whole set of questions about that the 1st layer we let them do themselves without any help and all of them get there and then for the other parts we use the corners 1st method just because is mathematically more interesting it's less procedural you have to always think you can just apply and they have to use the method where I know they will have to do some thinking and I will the yes some of them already know how to solve the cube so then I would help them with a different method but there's
still a surprising amount of thinking that needs to happen that of the by the way the I personally don't like I really think you can do everything without a lecture i teachable Kiko the sequence without a lecture I teach algebra geometry without like I teach whatever that's just my personal Krasnov everybody has to do that but that's why Matt I it if in doubt I cover this material but the mature that I do I do in discovery mode but I haven't tried everything so I can't actually promise working that this party you grade the students during or at the end of the term we have a whole block on assessment ideas a lot of participation rates so I have a good chunk of a class of 40 per cent of the classes participation so if they come to class and they don't do anything that already fail the so they work during class they have to and then after that there lots of
writing assignments and some other components why it has to be friend you're right if your goal so different and teaching method is different your assessment has to be completely different you know what the last class size where this would work so I don't know know I teach up to 36 students I have a friend who teaches up to 100 students in this way if you would give me 500 would try identify would succeed so now guess the best I can do about them losing 1 more so OK a lot of multi so the goal is to really do mathematics so I don't care much as much about memorizing or induced classes that aren't that all care about memorizing I care about inventing creating problem-solving and I create about like I care about a positive attitude towards mathematics I care about so that the matter Goals higher confidence less anxiety more engagement so we have a whole list on our website you can look at it like I'm that's all to understanding what mathematics is about understanding that they are living mathematicians in this world we're not all that right so so those kinds of roles that are not really connected to the content all part of that this it's a little hard to measure so we have a lot of surveys about beliefs and attitudes and have very positive results in those and we have brought about the output of another blog about those results the content is a little bit harder to measure to compare so in calculus I can say that I do as well in that funding Freebase style as I would do with a lecture style but for the classes with the Rubik's cube it is not really a comparison there not a whole lot of math classes out that to the Rubik's cube in the 1st place so what exactly are you looking for so it's tricky to measure the and I think the pulling of sections thank you it