Math B-Day: Folding Papers and The Mathematics Behind It

Today in class our professor Henk were unable to present until mid-afternoon, and to keep us busy, he threw us a math problem that we have to solve in groups. This assignment opened me to another insight of how Mathematics (and the Education in general) is much more developed, cared about and well, cool, here in Netherlands than in Indonesia. 

Mathematics B-Day
 

If you are thinking this is somehow related to birthdays, then our thoughts run on the same track *highfive*

But this is not in any way correlated to someone’s birthday though. Mathematics B-Day (or Wiskunde B-Dag) is an annual mathematics competition organized by The Freudenthal Institute of Utrecht University. It proposes very open-ended problems meant to be solved by a team of 3 or 4 students. As opposite to the timed test often associated with math/science contest, this one in particular can take all day. In the end, they have to write the report paper which in turn will be assessed on national level.

Further investigation on my part reveals that apparently the Dutch split Math courses in upper secondary education into two categories: Math A and Math B. Students make their choice based on majors they plan to take in college; Math A is mean for students preparing for social sciences, while Math B is meant for student interested to take mathematics and natural sciences. Somewhere along the way, they require the assessment to include process skill and timed tests are no longer fit. That’s why Mathematics B-Day is developed. 

Most participating schools use the result of the test as part of the final grade, although the task itself is not necessarily related to the Math-B curriculum. The best papers are then sent in and ranked by teachers in four regional groups. The final best papers are then ranked by national jury.

The Distinction: Why I think this is great
 

In Indonesia we have OSN (National Science Olympiad). This is probably the most prestigious science competition I can think of. Some high-profile universities hold their own Science competition, mostly a way to steal start in finding new talents. Those are also very popular. Recently there was the PISA – a worldwide test conducted by EOCD to measure 15 yo students’ performance on mathematics, science and readings. 

Mathematics B-Day itself offers problem that put a lot of emphasis in problem solving, conjecturing and proving. Students are challenged to show process skills in developing strategies, making conjectures and try to prove or reject them, logical reasoning, critically reviewing models and adjust them.

I think this is what makes them jump out of the page, at least in my book. In term of not related to the curriculum, it is closely related to Olympiad. But in term of problem solving and open-ended problem, it is closely related to the PISA. But the ‘challenging students to make conjecture and proving it’ part, there is no contest alike in Indonesia, not that I am aware of. Maybe there is one for university students, but not children in compulsory education. I think it is a good idea to start this so early. Logical thinking and mathematical reasoning is important even if you don’t study or work in mathematics or science related field. By offering them an interesting yet challenging problems, coupled with children’ natural enthusiasm and curiosity, this can help to nourish scientific mindset in children. 

A Brief Overview
 

Just as a quick glance to what the problems in Math B-Day are like, this is the problems we worked on today. 

This is the problem from Math-B-Day 2012, and yep, it is a strip of paper. We are supposed to fold that. Sounds boring, isn’t it, but in mathematics, we call it beautiful. How from such a simple thing, complicated yet captivating problems can arise. Just wait for it. 

Oh, and they also give a very cute and fitting name for the task: (Cr)easy. It is not easy, let me tell ya, but it is so damn worth it. By the time you finish this problem you will be very, very, in awe. But it does give you a lot of creasy strips of paper to clean to, though.

The basic idea is that different way in folding the paper results in different pattern once the paper is unfolded.  We are provided a strip of paper. To mark the start of the strip, we put a mark on the left side of the paper, facing us.

Suppose we fold it to the left, and then to the right, and to the right one more time. Then unfold the paper.  This is what we are going to get.

 

 By tracing the paper from the starting mark towards the end, we obtain a path where we turn right, right, left, left, right, left, left. It is easy to see that there is a causal relation between the way we fold the paper and the resulted paths. But to discover the mathematics in it, that is the challenge.

The way to fold the paper is called the recipe, and it is denoted by lower case l and r. So in this case the recipe is lrr. The resulted path is called the walking pattern, and it is denoted by uppercase L and R. Therefore the path we got in this is RRLLRLL. Three-letter recipe results in 7-letter walking pattern. Imagine the walking pattern of 8 or 9-letter recipe. Can you predict how many bends you will get if you fold it 10 times? Can you predict to which direction a particular bend will be? Can you guess the change in the walking pattern if you change only 1 letter in the recipe?

Turns out, you can.

The task itself is organized in two parts: Part A and Part B. Part A is the exploration, where we are guided to do several exploratory questions regarding the recipe and the accompanying walking pattern. Lots, lots of folding and students screaming “LEFT, no, RIGHT, wait no, LEFT”. Part B is where we analyze our finding, do research, make conjectures and test it. 

It is mentally exhausting, yet satisfying. I believe it also burns calories because I felt mighty hungry after that. Try it. 

This is the download links for the problem: 

http://www.google.nl/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCoQFjAA&url=http%3A%2F%2Fwww.fi.uu.nl%2Fwisbdag%2Fopdrachten%2Fassignment2012.pdf&ei=za7oUpy1DYHO0AWYsIGgBQ&usg=AFQjCNGQyaVijeOpuDJWM1rPA4ZpbAyjIQ&sig2=Eb8Nr4uIllo-k5_QORYHmA&bvm=bv.60157871,d.d2k

This is the applet that can help you to test your conjecture:

         http://www.fi.uu.nl/wisbdag/opdrachten/sliderappletNL/eenvouwdigNL.html

This is the link if you are interested in the previous years' assignment:

http://www.fi.uu.nl/wisbdag/opdrachten/

More on Utrecht University and Math B-Day(or Wiskunde B-Dag) :

http://www.fisme.science.uu.nl/wisbdag/

It is not available in English though. I really want to know the winners and read their paper. But it is probably in Dutch.

MY LIFE IS REALLY WEIRD

I'm living in Utrecht, Netherland now.




This is me near that famous canal, whose name I still don't find out (ignore my roomate).
I have access to all European Union country, visaless.
I get to experience the biting cold winter that leave me with chattering teeth and chapped lips (hopefully with snow later on).
I have to purchase everything in Euro and got a headache everytime because I can't stop converting everything to Rupiah.
I have faster-than-you-can-imagine internet access.
And all that jazz.

Life is good.
Goede morgen, everyone.

PISA 2012

Sebagai mahasiswa kependidikan, jadi tentunya hasil PISA 2012 tidak luput dari hasil pengamatan saya. Namun sebagai seseorang yang masih belajar, saya tahu hasil analisa dangkal saya mungkin tidak mumpuni jika dibandingkan dengan para ahli pendidikan di negeri ini. Namun orang lain ternyata tidak berpikiran sama, dan saya entah kenapa tiba-tiba saja marah begitu membaca artikel yang terang-terangan berkata, 

Maka memang sebaiknya kita tak memperdebatkan hasil PISA, karena arah pendidikan kita memang beda. Beda arah dan beda jalur. Tidak akan nyambung. Kitapun  tak perlu berkecil hati karena berada di peringkat 64 dari 65 negara yang disurvey. Bisa juga tahun - tahun berikutnya kita tak perlu ikut jika yang diuji bidang - bidang itu. Kita baru ikut jika yang akan diukur tentang keberimanan dan ketaqwaan siswa. Karena itu yang sejalan dan searah yang membuat kita bisa bersaing.  Bisa jadi kita akan menjadi yang terbaik. Jadi … gak perlulah kita ribut dan galau oleh hasil PISA tersebut. toh tujuan pendidikan kita berbeda. Bahasa gaulnya nyantai aja cooyy!

Sekarang saya paham mengapa Kurikulum 2013 dicemooh sebagai Kurikulum Jalan Ke Surga. Dan maaf, ocehan diatas terdengar seperti sesuatu yang dikatakan oleh orang yang selalu dapat nilai jelek dan ingin mencari pembenaran.

Saya disini bukan mendiskreditkan agama. Bukankah kalau dipikir-pikir, mengukur keberimanan dan ketaqwaan itu yang justru merendahkan agama? Maksudnya, bagaimana caranya mengukur intensitas keyakinan dan ketakwaan seseorang terhadap Penciptanya? Hapal tidaknya kitab suci? Siapa yang paling taat beribadah dalam sehari? Lalu kalaupun ketakwaan bisa diukur (dengan judge manusia), apa impact nyata yang diberikannya terhadap dunia? Dan bagaiamana dengan orang yang tak beragama, yang menjalankan hidupnya sepenuhnya atas penalaran rasional dan altruisme universal? Karena akui saja, dan pedih saya mengakui ini, lebih banyak hal baik datang di dunia dari pihak yang tidak mengusung agama tertentu, ketimbang sebaliknya.

Tapi saya disini nggak ngomongin itu. 

Beberapa waktu lalu, Finlandia sempat menjadi primadona karena hasil PISA yang mencengangkan. Praktisi pendidikan dari seluruh dunia seketika menaruh sistem pendidikan Finlandia di bawah mikroskop, berusaha mencari tahu seperti apa Negara Skandinavia ini mendidik anak-anak mereka. Bagi yang update gossip dunia pendidikan, mungkin aware tentang tidak adanya tes standar, PR yang sedikit – karakteristik pendidikan Finlandia yang banyak disebut-sebut.  Namun satu hal yang luput dari perhatian – karena biasa bagi mereka dan tidak biasa bagi kita – tidak adanya Agama dalam kurikulum mereka. Atau mungkin lebih tepatnya, tidak adanya Agama resmi yang mengatur setiap aspek kehidupan bernegara disana. 

Ya,Finlandia adalah negara yang mayoritas penduduknya unbeliever alias tidak beragama. Negara-negara Skandinavia lainnya (plus Jerman dan Belanda) juga unbeliever. Singapura juga adalah Negara sekuler. Jepang dan Cina kuat memegang tradisinya, namun agama tidak pernah dicampurkan dalam urusan Negara.  

Saat membayangkan Negara tak beragama, kita tentu membayangkan Negara yang rusak, korup, penuh prostitusi, penduduknya calon penghuni neraka semua. Namun kenyataannya, Negara-negara diatas merupakan Negara-negara dengan standar hidup tertinggi di dunia dan perekonomian yang kuat, dengan sumber daya manusia yang mampu bersaing di kancah dunia internasional.  Oh, dan mereka juga Negara-negara yang anak-anaknya meraih skor tertinggi di PISA, yang berarti kalau tujuan tes ini berhasil, merekalah Negara yang mampu mendidik anak-anak yang mampu berpartisipasi secara maksimal di masyarakat modern.

Jujur, saya bangga dengan Negara kita yang memegang teguh tradisi dan Ketuhanannya.  Namun mungkin sudah waktunya kita berhenti menjadikan itu sebagai justifikasi kekurangan kita dalam mendidik anak bangsa yang mampu bersaing. Banyak orangtua yang lebih memilih anaknya hafal alquran atau bahasa daerah ketimbang bahasa Inggris, beralasan bahwa hidup di dunia hanya sesaat dan akhirat yang selamanya. Tapi masalahnya sebelum ke akhirat, kita harus tinggal di dunia yang fana ini dan menghadapi segala yang ada disini. Sudahkah kita bisa menghadapinya? Kita mengeluh tentang Freeport. Kita mengeluh tentang bule yang jadi manajer di negeri sendiri sementara pribuminya jadi bellboy. Kita mengeluh soal dibohongi koruptor dan para penggerak koruptor. Kita mengeluh soal inflasi, UMR dan kurangnya lapangan kerja. 

See where I’m going?

Saya kira itu karena kita gampang dibodohi, karena kita tidak siap menjadi warga dunia dan karenanya sama sekali buta akan bagaimana caranya menempatkan dan membela harkat bangsa di mata dunia. Siapa yang melarang kita menjadi bos di Negara kita sendiri? Tidak ada. Satu-satunya alasan kita tidak menjadi bos karena kita tidak bisa, titik. Saya pikir kita harus berhenti bersikap seperti korban dan mulainya mengakui bahwa untuk bisa menang di permainan ini, kita harus mengikuti aturan permainan. Bukannya membuat peraturan sendiri dimana kita bisa menang. 

Menurut saya, keadaan idealnya adalah masyarakat yang sadar agama dan tradisi namun bisa menjadi warga dunia, mengerti peraturannya dan bisa memenangkannya. Kenyataannya? Kenyataanya adalah masyarakat yang ribut soal Miss World tapi minim respons soal pengerukan sumber daya alam besar-besaran di Negara mereka. Ada gap yang sangat lebar antara keadaan ideal dan kenyataan, dan entah bagaimana kita harus bisa menjebatani gap itu. 

Anies Baswedan mengatakan bahwa yang kita perlukan saat ini adalah kesadaran diluar Indonesia (beyond Indonesia), bahwa salah satu janji kemerdekaan adalah janji berperan dalam tingkat global. Sir Ken Robinson juga berkata bahwa arah revolusi pendidikan ada dua, yaitu ekonomi dan cultural. Bagaimana mendidik anak bangsa yang mampu menempatkan diri di pertarungan global dunia ekonomi 10 tahun lagi (padahal memprediksi bagaimana ekonomi minggu depan saja susahnya minta ampun), namun tetap memiliki sense of identity; tahu siapa mereka, mereka datang dari mana dan apa yang mereka bela. 

See? Ini debat lama yang sudah menjadi perhatian dan diperjuangkan banyak pihak selama bertahun-tahun. Sekarang masalahnya, kita mau membantu perjuangan ini atau tidak. Kalau tidak, kalau dunia memang tidak penting, kalau yang penting memang ketakwaan dan tidak yang lain, ya tidak apa-apa. Tapi jangan mengeluh kalau nantinya kalah di pertempuran dimana anda memang tidak berjuang untuk menang. Kalau iya, kalau anda tidak bisa tidak peduli melihat bangsa sendiri diinjak-injak, kalau memang mau berjuang, get back in the game. Belajar, berinteraksi, perkuat  global awareness. Dalam kepercayaan saya, membela Negara juga salah satu bentuk ibadah kok :)

WESTLIFE : The Nostalgic Charm of Dying Boyband

I was watching TV earlier today with my roommate, we were flipping over the channels when something interesting came up – Westlife concert. It’s not an ordinary concert too; it’s their last tour before retiring. Needless to say I was about to piss my pants seeing those faces I fell in love head over heels years ago. We stayed up longer than we usually do only for the show, and when it began, it was … woah. I haven’t been listening to them for years, I don’t even remember their faces anymore, but I still can remember every word of their lyrics. 

 This is what late 90's boyboand look like

For you who don’t know, Westlife is (was?) a boyband from England. Think N*SYNC and Backstreet Boys, only with less squeal-inducing dance moves and way, WAY, more suits. They were not as internationally famous as N*SYNC or BSB though; they were mainly popular in Europe and Asia but never made it in USA. They rose to their peak of popularity in late 90’s, before one of their members quit and went solo. Their popularity has been declining since then; they made several comeback attempt but none are successful enough to catapult them back to what used to be their throne. The last time I heard of them was in 2010, I think.

Now, I’m not a fan of Westlife, but then again no one is. We are all former fan. I bet all those women crowding the arena also haven’t been listening to Westlife for quite a while, but they used to be one of those little girls singing to Flying Without Wings while fawning over Mark or Nicky, more than a decade ago. I remember N’SYNC, their comeback at the Grammy and how the now-huge celebrities like Lady Gaga and Katy Perry went crazy over them. I think that is the selling point of these senior, yet dying boybands; nostalgia. Their songs are no longer selling, they are also not as cute as they used to be, and better competition arose here and there, yet their shows will always be crowded.  It is because everyone wants to live off those years once again, when you are just a little girl and everything is so simple. It’s like time machine; it’s like having a nice date with a dear, forgotten part of your life. 

Mein gott. Please slap me for being so melancholic. 

But that is true; here I am watching them singing My Love, all the while mouthing the lyrics silently and mulling over my life and how different it was then and now. I bet all those girls crying also feel the same way.

It’s crazy how much things like this can affect you, really.

Temple Grandin: A Review

Yesterday I finally brought myself to watch Temple Grandin. It’s a biographical TV-movie about Temple Grandin, a noted autistic who is a professor of animal science at Colorado State University, a bestselling author, an activist and a consultant to the livestock industry. The movie itself casts Claire Danes as Temple Grandin, who does a really good job although she’s probably too pretty to be Grandin. She’s too pretty to be anyone actually. The movie itself is pretty ordinary for a biographical movie, nothing of the sort of A Beautiful Mind. It’s understandable since this is a TV movie, not for the big screen. 

This movie really opens my mind about autism and the struggle of autistic people. Sure, we all heard about autism, some of us even has them as friend, but probably not a lot of use know what it is like for them back then when Psychology weren’t as developed as today. For the record, Mrs. Grandin grew up in the US at the 60’s, back when black people were still trying to earn their equality, homosexuality was still classified as mental disorder, and fight for LGBT was just begun. Autism was also classified as mental disorder. Autistic kids back then were not expected to develop speech, let alone social life. Have an autistic kid? Well, no other choice than putting your kid in an institution.

Mrs. Grandin (or should I say Miss?) herself is diagnosed with autism at the age of 2. She couldn’t speak until the age of 4 and every psychiatrist her mother took her to offered nothing than life as a mentally disabled. Yet now, she is 66, an accomplished author, a professor, and an activist. Once, she turned up in an autism meet-up with her mother and shocked everyone there with the fact that not only she is able to speak and be aware of her surroundings; she has a B.A, a M.Sc. and was currently studying for her doctorate. 

I also learn a lot about what it is like to be autistic, at least from Mrs. Grandin perspective. As an autistic, she is very sensitive to noise, afraid to be touched by people (her mother was very depressed because Temple refused to be hugged) and unable to understand any form of social interactions (joke, etc.).

But she got one very, very beautiful mind. Boy, and they really know how to present it in the movie. She describes herself as a visual thinker – she thinks in pictures and words are just second language for her. Her mind is like a full-length movie that she can play at will, pausing here and there to notice small details. This, she says, is her number one asset in working with animal. Her incredible alertness to detail eases her to understand how an animal mentally process everything. And you know what else she could do? She only needs a second to look at a French passage, a language she hates the most, and she is able to recite everything, every word, perfectly. She didn't memorize it, she 'read' the book she already copied to her mind. She is also really good in science and math, but only limited to geometry and other branch of Math that needs good visualization. Stuff like Algebra is practically grumbles to her.

This sounds a lot like eidetic memory to me, I don’t understand what the difference and why she doesn’t just say it so if they are actually the same. She talks about this mind too, and other kind, on TED. I got really disappointed that she does not actually talk like Claire does in movie. Sure, she has distinct accent and body language but I think Claire overdoes it. 

She is also very distant emotionally, which in turn makes her very pragmatic. That’s why even though she loves animal and believes that they have to be treated with respect, she is not vegetarian and fully understand the benefit of animal as food. No death ever make her sad, too. She is like very genious, very cold robot.

All in all, I think some credits definitely has to be given to Temple’s mother, for her persistence in proving that her daughter is not less than everyone else, and to Temple’s science teacher. Yes, Temple’s is very interested in science; rocket, planets, planes, etc. She did not do well in school though because her autism got in her way. Her science teacher was the very first person who noticed her talent, her brilliance, her beautiful mind, and nurtured her. 

I know this movie is very old and probably very boring since its biographical and all, but it is definitely recommended, especially if you want something to watch that make your cold soul a little warmer.