Dancing in Euclidean Space

I invite you to watch an excerpt of Seventh Sense by the Anarchy Dance Theatre from Taiwan.



There is a somewhat longer excerpt here:


See also previous posts on mathematics and dance:
- Maths and Ballet (2)
- Maths and Ballet (1)
- Music inspired by mathematics ( has item on choreagrapher Crystal Pite )

Prediksi Ujian Nasional Berdasarkan Kisi-Kisi Soal

Berikut Prediksi soal Ujian Nasional Berdasarkan Kisi-Kisi Soal :


PREDIKSI SOAL UJIAN NASIONAL


Untuk Bapak/Ibu Guru yang mau share lewat Blog ini silahkan kirim file ke : matematika.tim@gmail.com


Terima kasih..

If you need a personal Super Computer...

#computing

They say that the smartphones of today are more powerful than the mainframes of the 1970s. That's only partially true of course, in fact it is ridiculous, i don't see anyone managing a corporate database on a phone, not even with 70s software. Phones use all that power they have to facilitate the silly games they have on them.

To the point. Super computing.

The Met Office in the UK still has a warehouse sized computer room packed with computer power. ( See BBC Horizon, about Global Weirding ). They need all that power to run their weather forecasting models which are continuously fed with massive amounts of real-time data from data collection points all over the world.

IBM supercomputer at the UK Met Office

Personal computers, from phones to your home rack may have some power but it could still take -weeks-, if not -months- to do a calculation, or the rendering of an image. As from a certain point you need that upgrade that goes beyond your budget, or simply beyond the available space you have at a certain temperature. And as you might know cooling is still an issue.

If you are into rendering computing intensive 3D images, then vSwarm might be a solution for you. vSwarm is a community based free render farm for your 3D animations and images.

Link:
- vSwarm

April 6, 2012

Interactive version of problem and solution.

Register now for MAA MathFest 2012!

The Teaching Gap

The Teaching Gap by James Stigler and James Hiebert is one of the foundational books in math education. It grew out of research done in response to the Third International Mathematics and Science Study, more commonly called TIMMS. TIMSS, now Trends in International Mathematics and Science Study makes much of their data, materials and resources available for free at timss.org. It's really about systemically improving any kind of teaching, but lucky for us, it's in the context of mathematics teaching. Google Books has a pretty extensive preview.

We ask our student teachers to read The Teaching Gap and have tried various ways to have them read and discuss it. This semester, instead of using BlackBoard, I made a Facebook page for the course. BlackBoard is... okay. Lots of structure. But the discussion threads have never gotten much reading from other students. In the fall I gave Edmodo a try, and it was more functional. I wasn't using the assessment tools there, though, and had no other colleagues using it to share with. So the best features of it were the parts that were like Facebook. Except the students only checked it when they were posting their responses. Facebook has worked pretty well. I use links to Google docs instead of attaching files. Primarily, though, the TAs interacted with it more, had more comments on others' posts and recommended/shared more stuff than they ever did with Blackboard. A lot of our discussion of the Teaching Gap was on Facebook, so I thought I would share the highlights. All of their comments are on Google docs, if you're interested in the whole schmegagy. Dave Coffey, Rebecca Walker and I have developed these assignments over many semesters of working with our novice teachers.

Introduction and Chapters 1 and 2
Focus: Questioning to Make Connection

• Effective readers ask questions that will activate relevant, prior knowledge before, during, and after reading text.
• For example, as you read The Teaching Gap you might ask:

1. How does this reading remind me of my personal experiences related to assessment?
2. How does this reading relate to other things I’ve read regarding assessment?
3. How will this reading connect with my efforts to be an effective teacher?

• Use these questions or develop your own in order to actively engage with the content of The Teaching Gap as it relates to the concept of assessment.

Activity: The Teaching Gap

• Read the preface and chapters one and two in text.
• Keep track of examples in the text where you make connections to your experience, other readings, and your vision of effective teaching as it relates to the concept of assessment.

Reflection: Facebook: post your quick impression of the reading, and your thoughts on how you can assess teaching (your own in particular).

• Jill Beauchamp:I loved the way the "The Teaching Gap" set out to examine teaching across various cultures. It surprised me to find out that teaching varied little within a culture and drastically between cultures. The text spoke about how Japan focuses so much on conceptual understanding and solving challenging problems opposed to spending time practicing procedural steps. This reminded me of what I learned in my COE seminar. We focus a lot on making a distinction between "what are the students going to do" verses "what are the students going to learn."

• Zack Weber: I have heard from other professors that studies of this sort cannot be trusted because the US has the only true random sample of students while the other countries put forth their best students, it makes it difficult to know then if the study really drives these recommendations or not. But I think with them using the video research they have a more solid case for their ideas.
  
  And how can we assess teaching? I think the best way is to have someone assess you. Either have your CT, another TA, or a professor observe your lesson and keep track of what you did, said, explained, etc. I think if you then have a good discussion you will see things you like about your own teaching and things you don’t like about it, and that is from someone else’s viewpoint. I also think a good way to evaluate is by student’s work. Do they seem to understand or are they constantly questioning? Have you changed your class to fit their learning styles or are you using the same teaching style with no changes? I think answering simple questions like this can also help you assess your teaching because you have to provide for the students and unless you adapt then they will always be behind and stuck.

• Abbey Foster: There is constant talk about the good and bad ways of teaching in the classroom, but there never seems to be a consensis about it. I am hoping from this book I learn new ways of what works and what doesn't. The first couple of chapters have talked a lot about how the methods are so different, but I hope they give specific examples of how the US is lagging behind the other countries. The books talks about how important it is to have quality teachers in the classroom. This is interesting to me as I look back on the past professors and teachers I have had. Most of the time, there is some sort of an evaluation, but are these 'quality' teachers really taking into consideration our feedback?

• Allison Behr:  I was a little apprehensive about reading this book because I was under the impression that the book would undermine the teaching profession. However, I was pleasantly surprised when the book's preface spelled out the lack of recognition and the hard work that is involved with teaching. I also agree that the problem with education is how it is being taught. Using the same techniques that were used 75 years ago fails to address the current needs and capabilities of our students and ourselves as teachers.

Chapters 3 and 4
Activity: The Teaching Gap

• Read chapters three and four.  Keep notes on your reading, in a journal, in the book or on stickies.
• Bring your notes to seminar to discuss.

Reflection: Post to Facebook your reaction to these chapters. Is there something you want to know more about? Did it give you language to describe your experience or goals? Was there something useful to apply this semester? Share your thinking on one of these questions or one of your own. In addition, comment on someone else’s post.

• Steve Suzio: Based on the reading, I found that the typical U.S. classroom of defining and demonstrating rules and procedures is exactly the scenario in my classroom. The students are given a worksheet and the teacher will go over a few demonstrated problems with them and at the top of that worksheet there is a suggested solution for them to look at if they are stuck. Then after about 15 minutes of lecture, they are given the rest of the time to work and ask questions. Any teaching the teacher does, requires very little thinking on the students part and they can give answers they have no clue to based on the tone and guidance of the teacher. This is not true learning, but more can you memorize a procedure and rule. The Japanese and German classrooms develop the mathematical ideas that are being presented, and students are asked to discover these concepts on their own. The teacher facilitates and lets them know what is important in their discoveries and then provides them with the challenging question.
  
  Thinking about how I can assess my own teaching, I would definitely try using video to record my lesson so I can go back and see what my tone is like asking questions, as well as what questions I asked. I could also review my lessons and see what types of problems I am giving students and how I am going about teaching those to students. If they are struggling, how am I helping them to solve it? Am I guiding them through it? or am I asking challenging questions. Anything that will get me to reflect and see what I am teaching and how I am teaching it will help me assess myself.
  • Kevin Squire: Great connection back to our classroom, Steve. I agree, the students aren't engaged during lessons. I hope you see that this is what I was attempting when I made the intro worksheet for Ratios (candy mix). I just wanted them to be doing something, too; instead of just watching me talk about math. And the tone thing...so true, man; so true. I catch myself doing this too often. It's pretty funny (in a sad way) when I am aware of this, though; the kids sit there waiting for something else. I think you do a pretty good job of staying aware of this. Probably why you thought to put it in the response, lol. Thanks for the insight, man.

• Becky Marie: Chapters 3 and 4 of the Teaching Gap compare and contrast the teaching methods used within the Japanese, German, and United State’s classrooms. Personally, I found the most interesting contrast to be the amount of time that is spent on in depth, challenging problems in the Japanese classroom and how much time is spend in the US classroom working on definitions and procedures. In my current placement I find that this is very much the case. Much of the day is spent working on procedures, doing problems over and over again. When students take tests, however, their scores are show that they do not really understand the concepts. I am wondering that if more classroom time was spent on meaningful, explorative problems is they would be more apt to grasp a deeper meaning.
  
  • Kevin Squire: This whole "Quantity over Quality" mindset seems to get a bad reputation in many other areas. Why not in Americas classrooms?
  • Amy Lee Pickell: Agreed. In every other aspect of what is taught to American students it seems to me like it is quality over quantity except in math
  • Kevin Squire: I think that it is a problem of all subjects. I'll have to ponder whether or not this is most prevalent in math classes. i.e. there are A LOT of topics to cover in a typical science class. How many of those concepts are taught deeply, and how many are taught as memorization of facts. Thanks, Amy!
  • Brienne Tingley: I agree with this but the problem is how do we get the students to really engage and change their attitudes to wanting to learn to explore it? I feel like as soon as the answer is not given to them, they don't want to even try.

Chapters 5 and 6 
Activity: The Teaching Gap

• Read chapters five and six.  Keep notes on your reading, in a journal, in the book or on stickies.
• Bring your notes to seminar to discuss.

Reflection: Post to Facebook your reaction to these chapters. Did this reading matter to you? Help you understand anything you have seen in the classroom? Make you wonder about anything yet to come?

• Stephanie Petersen: While reading these chapters I would find myself often agreeing with the observations being made and the things that need changing. I also found myself continually wondering how it is even possible to make these sort of changes. I hope that the coming chapters dive more into this! I really liked how the book described schools as systems and how we cannot change the whole system just by changing one part such as the way class is taught. The issue is much larger than just changing the way teachers present information because education is directly related to culture. Students have certain expectations for what will happen in school and how they will learn which is something very hard to change. I know that many of my students have a hard time with change in the classroom and they perform better when there is more structured, guided time. As I read this book, I find myself wanting to step out and make a difference or make a change but I feel that I wouldn't know where to start. How can we make changes in our educational system that might actually be effective? I also wonder why this type of information seems to be ignored or easily disregarded by our society because we have known for a long time that we are behind other countries in terms of education. I know changes are being made, but we need to really find a way to make an effective change that sticks rather than just trying small things that may make a difference for a little while and then just return to old habits.

• Laura Todd: Chapters 5 and 6 in the Teaching Gap covered many questions that I had from the previous chapters, and from our in class discussion. The different ways that Japan and the US use visuals may seem unimportant, but these ways add to the culture differences between the two countries. In Japan students are scripted to be able to answer these complex questions because that is how they have been taught. The example of the teacher that tried introducing a complex problem, but students unable to solve this problem is a good example of of how both students and teachers need to work together to make cultural changes. As a teacher adopting some of the Japanese scripts of teaching can backfire on you because of the US culture and the way students have previously been taught. The survey on the “main thing” teachers wanted their students to get from a lesson was somewhat appalling. In the US teachers said they wanted their students to learn skills, whereas in Japan teachers wanted their students to think about math in a new way to see relationships. I think that younger teachers including our class would have a different view, than wanting students to learn skills.

Chapters 7 and 8
Activity: read the chapter, with an eye for what you can do personally, or what could be done at an individual school. Both should be practical and sustainable.

Reflection: Do you agree with the principles in Chapter 8? Post to Facebook whether you found anything that you think you could do yourself, once you’re teaching. If you were to recommend PD to principal, what would you recommend?

• Brittney Mohnke: I agree with the principles presented in Chapter 8, but it is still hard to picture changes such as this actually happening in our society. If we focus on gradual improvement over time, I think we would eventually see very positive outcomes. However, would people actually act upon these principles? I agree that the most effective place to improve teaching is in the context of a classroom lesson. I think it makes a lot of sense for teachers to become more involved in the reform effort. Although educational researchers provide many good ideas, teachers are the ones who actually know what goes on in the classroom. I also believe that teacher collaboration and the formation of more professional-development groups would be a great idea. This is something I hope to focus on in my future teaching. I hope to improve and reflect on lessons with other teachers. I do not think that keeping the door shut and keeping teaching private is very beneficial. If I were to recommend PD to a principal, I would recommend maintaining a focus on student learning goals for reform. These learning goals should be shared across districts and focused on student learning in the classroom.

• Steven Runkle: The US has been on a path of gradual improvement since the 80's (probably even early if you talk to some of the old timers). Several sets of standards and more and more HS drop outs later, we're farther behind than when we started. The problem with this idea is that people's opinions about education also change over time, and because of this, we reform our educational policies every 15 years or so.
  
  Say we "adopt" this idea of gradual change (and it wouldn't be the first time) and we set a goal to have a brand new curriculum implemented by 2020. I'm certain our goals and opinions about how to "fix the system" will change by then. I'm of the opinion that if we want to implement real curricular change, it has to be within 5 years. That is more than enough time for ed programs and current teachers to adjust.
  
  Like Kevin said, I think we could do this much quicker than people think. But, teachers and administrators have to be committed 100%. If schools can completely implement a completely new special education program within a year, I'm certain they can do the same with general education within 5 years. But everyone needs to be on the same page.

• Luke Hagan: I fully support all of the principles outlines in Chapter 8 except for principle #5. Teachers are most often thought of as the only person in charge of a classroom. The principle seems to be a means to an end for principle #4 but I doubt that the implication can be made.
  
  As a counter example; A developmental psychologist could sit in on the classes of every teacher. This is an ensured in context type of PD and while highly theoretical, still serves as a justification for why teachers need not be straddled with the responsibility of improving the whole of education. It is a nice way to think about a teacher but some will not take to it.
  
  The Initiatives laid out are also completely understandable as well.

Chapters 9 and 10.
Post a discussion question to Facebook.  What do you want to know about what other people thought about this? Alternatively, answer someone else’s question by replying to it.

Write a paragraph for your teaching philosophy about how you will improve as a teacher, or how you feel like you can contribute to the profession, or both! (If you already have such a paragraph, edit it.)

• Brittney Mohnke: Chapters 9 and 10: These chapters stressed the importance of teacher collaboration in improving lessons and subsequent student learning. I completely agree that improving teaching should lie in the hands of teachers, not educational researchers, since teachers are the ones who have experiences in actual classrooms. Thinking about teacher collaboration, though, made me think about the situation many of us are in this semester. Many of us are placed in a classroom with another teacher assistant where we have to team-teach and collaborate almost every day. Have you guys seen this as beneficial? Does it connect with what the Teaching Gap is proposing in terms of teacher collaboration? Also, can the time be found for teachers with such hectic schedules to collaborate and work on lessons together during the school week?
  
  • Jess Alexander: I really feel like having another TA in the classroom has been beneficial for me. Allison and I do collaborate and discuss everyday. I think that it could be connected to what the Teaching Gap says about lesson studies, but it would be a smaller version of that. After most lessons, we usually talk about what whether it went well or we give input on what could have been better. I find it very helpful to have a peer there to talk about my teaching and planning with. 
  • Abbey Foster: I am not placed with another TA in my placement, but I am constantly collaborating with my CT. She’s wonderful and so helpful! We are always bouncing ideas off of each other and trying new things. Time can be an issue, but this is our job and I feel in order to put our students first, we have to give them all of our efforts. If we don’t, I feel we are only holding our students back from reaching their full potential.

Summary
Hopefully you can see why we have found the book valuable. At one point we were going to stop (probably for variety's sake as much as anything else) and the previous students said we should definitely keep it. I also hope you can see the value of Facebook as a discussion forum, and are interested in the book if you haven't read it. Sorry the post was sooo long! Short compared to all the responses, but I probably could have consolidated more.

April 5, 2012

Interactive version of problem and solution.

Register now for MAA MathFest 2012!

What is the difference between digital image processing and computer graphics?

#mathematica

Although digital image processing and computer graphics are similar in the sense that they rely heavily on ( advanced ) mathematics and that they work with computer imagery they are in essence quite different technologies. So, what is the difference between digital image processing and computer graphics?

Computer graphics creates new digital images from geometrical descriptions, such as 3D-object models or (scene-)graphs, developers of computer games, special effect programmers in the movie industry all use ( primarily ) computer graphics.

Example: Computer Graphics - Click to enlarge

Digital image processing strips an image down to its core: an array of numbers and can thus be manipulated in any way possible, i.e. rotating, resizing, morphing, etc.

 Example: Digital Image Processing - Click to enlarge 

In certain applications the two fields meet, for example when 3D models are (re-)created from image data. An interesting project is for example the creation of a 3D model showing the distribution of dark matter in the universe.

Both Digital Image Processing and Computer Graphics are playgrounds to show off your math skills. Most, if not all mathematics software have extensive support for computer graphics as well as digital image processing.

April 4, 2012

Interactive version of problem and solution.

Register now for MAA MathFest 2012!

Donald Duck in Mathmagic land

#disney# #donaldduck#

Although I am a math geek and a great fan of Donald Duck I had never seen the movie Donald Duck in Mathmagic land.

I knew vaguely of its existence but somehow I never went out to get it. I think I have seen all other movies with a strong link to mathematics though. See my other posts about that. Sol Lederman's Wild About Math blog had a link to it on YouTube. Here it is.



Enjoy the movie!

April 3, 2012

Interactive version of problem and solution.

From the MAA Books Blog: 
MAA Launches Online Store Powered by Amazon
 (10% Coupon Code)

April 2, 2012 #MathAwarenessMonth!

Interactive version of problem and solution.

From the MAA Books Blog: 
MAA Launches Online Store Powered by Amazon
 (10% Coupon Code)

Lupakan Rumus Matematika SMA & SMK

Biarkan rumus itu menari di ujung jarimu!

Salah satu yang acapkali menjadi persoalan ketika mengerjakan soal-soal matematika adalah lupa rumus. Dan seringkali ketika lupa rumus, kita tidak bisa apa-apa lagi, terpaksa menyerah! Melayanglah ...impian untuk memper-oleh hasil belajar matematika yang optimal nan membanggakan. Mengapa kita mudah sekali lupa dengan rumus matematika? Jawabannya sederhana, sebab kita tidak sungguh-sungguh mengenal rumus itu dengan baik. Kita tidak cukup memahami konsep yang mendasari rumus tersebut secara mendalam.

Suatu waktu kamu berkenalan dengan seseorang di suatu tempat. Dan setelah perkenalan itu kamu tidak pernah berjumpa lagi dengannya atau sekedar berbagi kabar melalui sms atau sekedar say hello by phone. Apa yang terjadi ketika kamu secara tak sengaja berjumpa lagi dengannya selang beberapa lama? Kemungkinan kamu sudah tidak mengenali dia lagi atau mengenalinya tapi samar-samar dan butuh banyak waktu untuk mengingat-ingat kira-kira siapa dia. Demikian halnya rumus matematika yang kamu kenal tetapi tidak secara sungguh-sungguh. Pasti kamu akan mudah sekali lupa dengan rumus itu atau setidaknya membutuhkan waktu cukup lama untuk mengingatnya kembali.
Bandingkan dengan ketika kamu pertama kali bertemu dengan seseorang yang kemudian menjadi kekasih hatimu, apalagi jika dia adalah cinta pertamamu. Jelas setelah perkenalan pertama itu kamu pasti menjalin komunikasi berikutnya dan berikutnya lagi secara intens. Tidak hanya itu saja, kamu pasti juga sering bertemu, pergi bersama dan melakukan berbagai aktivitas bersama lainnya. Kamupun mengenalnya lebih dekat dan mendalam, mengenal watak, sifat dan karakternya, hingga impian-impian hidupnya. Sampai akhirnya kamu harus berpisah dengan kekasihmu karena berbagai sebab. Nah, ketika tak sengaja kamu berjumpa dengannya di suatu tempat setelah perpisahan itu, kamu pasti akan tetap mengenalinya, bahkan dari kejauhan saja kamu sudah tahu bahwa itu adalah dia. Jangankan bertemu, bahkan ketika menolak bertemu atau dengan sengaja berusaha melupakannya, dia masih tetap sering mengusik pikiranmu – kerap hadir di ujung galaumu sekuat apapun kamu ingin melupakannya. Dan percaya atau tidak jika dia cinta pertamamu, dia akan selalu ada di ujung hatimu, tidak peduli kamu sudah berkeluarga, kenangan akan dia akan selalu bisa dihadirkan. Begitu juga bila kamu mengenal rumus matematika secara mendalam dan secara intens bersentuhan dengan rumus-rumus itu, entah lewat membacanya, menggunakannya dalam mengerjakan soal-soal matematika, atau berlatih matematika dengan teman-temanmu, rumus itu akan dengan cepat hadir di pikiranmu ketika kamu memanggilnya.
Oleh sebab itu, untuk bisa menguasai rumus-rumus matematika dengan baik kamu mesti sampai pada tahapan bisa melupakan rumus matematika itu. Bisa melupakan (tidak sama dengan lupa!) mengandaikan kamu sungguh mengenal dengan baik, mengerti dan memahaminya secara mendalam. Dan seperti halnya cinta pertamamu, sekuat apapun kamu ingin melupakannya, dia akan tetap ada di ujung hatimu. Demikian juga semestinya kamu melupakan rumus matematika! Biarkan rumus itu hadir sendiri dan menari di ujung jarimu ketika kamu mengerjakan soal-soal matematika. So, Lupakan Rumus Matematika!

Lupakan Rumus Matematika

Biarkan rumus itu menari di ujung jarimu!


Salah satu yang acapkali menjadi persoalan ketika mengerjakan soal-soal matematika adalah lupa rumus. Dan seringkali ketika lupa rumus, kita tidak bisa apa-apa lagi, terpaksa menyerah! Melayanglah... impian untuk memperoleh hasil belajar matematika yang optimal nan membanggakan. Mengapa kita mudah sekali lupa dengan rumus matematika? Jawabannya sederhana, s...ebab kita tidak sungguh-sungguh mengenal rumus itu dengan baik. Kita tidak cukup memahami konsep yang mendasari rumus tersebut secara mendalam.

Buku Lupakan Rumus Matematika ini akan membantu kamu mengenal, memahami dan menguasai rumus matematika secara mendalam, sbelum kemudian kamu harus melupakannya. Mengapa melupakan? Sebab untuk bisa mengerjakan soal-soal tes matematika dengan cepat dan tepat kamu harus bisa melupakan rumus dan membiarkan rumus itu menari di ujung jarimu. Jika kamu masih berkutat dengan rumus dan terus mengingat-ingat rumus saat ujian, maka Teeeeetttttt! Waktu habis!

Apa yang ada dalam buku "Lupakan Rumus Matematika Versi SMP/MTs" ini?
* Rumus Matematika LENGKAP dan konsep yang melatarbelakangi rumus itu
* METODE CEPAT Mengerjakan soal matematika plus bonus RUMUS CEPAT
* Contoh Soal & Pembahasan yang lengkap dan variatif
* 1001 plus SOAL-SOAL Standar Nasional yang dilengkapi kunci jawaban

Buku ini ditulis oleh HJ Sriyanto [Penulis buku Matematika yang produktif, menulis lebih dari 30 judul buku matematika dan 7 buku Matematika Kontekstual SMA lolos penilaian BNSP]
So, buku ini dijamin berkualitas dan beda dari yang lain!

Untuk pemesanan hubungi Penerbit Selingkar Rumah Idea Pustaka
email: sri.pustaka@yahoo.com

'യൂ ട്യൂബ്' പോലെ 'ജിയോജെബ്ര ട്യൂബ്'

കോഴിക്കോട് സ്വദേശിയും എറണാകുളത്തെ മാസ്റ്റര്‍ട്രെയിനറുമായ സുരേഷ്ബാബുസാര്‍, ഞാന്‍ കണ്ടതില്‍വെച്ച് ഏറ്റവും സൗമ്യനും മിതഭാഷികളിലൊരാളുമാണ്. മൂന്നുകൊല്ലങ്ങള്‍ക്കുമുമ്പ് മലപ്പുറത്തുവെച്ചുനടന്ന ദ്വിദിന ഐസിടി ഗണിത വര്‍ക്ക്ഷോപ്പില്‍വെച്ചാണ് അദ്ദേഹത്തെ പരിചയപ്പെടുന്നത്. ജിയോജെബ്രയുടെ അത്ഭുതലോകം പാലക്കാട്ടെ മുരളീകൃഷ്ണന്‍സാര്‍ ഞങ്ങള്‍ക്കൊന്നിച്ചാണ് അനാവരണം ചെയ്തുതന്നത്. പിന്നീട് ഈ മനുഷ്യന്റെ ഊണിലും ഉറക്കത്തിലും ജിയോജെബ്രതന്നെയായിരുന്നു. അഞ്ചുപാഠങ്ങള്‍ ഇതുവരെ നമ്മുടെ ബ്ലോഗില്‍ പ്രസിദ്ധീകരിച്ചു. കൃത്യമായി ഓരോപാഠവും തയ്യാറാക്കി മെയില്‍ ചെയ്യും. തിരക്കിനിടയില്‍ മിക്കതും ഞാന്‍ കാണാതെ പോകും. തമ്മില്‍ കാണുമ്പോഴൊന്നും അതേക്കുറിച്ച് ഒരക്ഷരം മിണ്ടില്ല. ഒരിടവേളയ്ക്കുശേഷം വീണ്ടുമത് മെയില്‍ ചെയ്യും, യാതൊരു പരാതിയും കൂടാതെ!
ആറാം പാഠത്തിലേക്ക്....ജിയോജിബ്രയില്‍ തയ്യാറാക്കിയ നിര്‍മ്മിതികള്‍ ജിയോജെബ്രട്യൂബ് എന്ന സൈറ്റില്‍ സൗജന്യമായി അപ്‌ലോഡ് ചെയ്യാം.അപ്‌ലോഡ് ചെയ്യാന്‍ ജിയോജിബ്രയില്‍ തയ്യാറാക്കിയ നിര്‍മ്മിതി (.ggb file) മാത്രം മതി. എക്സ്പോര്‍ട്ടു ചെയ്ത .html file ആവശ്യമില്ല.തയ്യാറാക്കിയ ഒരു നിര്‍മ്മിതി(.ggb file) അപ്‌ലോഡ് ചെയ്യുന്നതെങ്ങനെയെന്നു നോക്കാം.
ഇവിടെ ക്ലിക്ക് ചെയ്ത് ജിയോജിബ്രട്യൂബ് സൈറ്റിലേക്ക് പ്രവേശിക്കുക. തുറന്നുവരുന്ന ജാലകം നിരീക്ഷിക്കുക.

ജാലകത്തിലെ Register ബട്ടണില്‍ ക്ലിക്ക് ചെയ്യുക.തുറന്നുവരുന്ന GeoGebra User Forum – Registration വായിച്ചതിനു ശേഷം താഴെയുള്ള I agree to these terms എന്ന ബട്ടണില്‍ ക്ലിക്കചെയ്യുക.അടുത്തതായി വരുന്ന Registration ഫോമില്‍ ആവശ്യമായ എല്ലാ വിവരങ്ങളും (e-mail വിലാസം ഉള്‍പ്പടെ) നല്കി Submit ബട്ടണില്‍ ക്ലിക്കുചെയ്യുക.(User Name / e-mail address ഉം Password ഉം ഓര്‍ത്തിരിക്കണം.)
താഴെ കാണുന്ന ഇന്‍ഫര്‍മേഷനോടുകൂടിയ ജാലകം പ്രത്യക്ഷമാകും.
“Your account has been created, However this board requires account activation, an activation key has been sent to the e-mail address you provided. Please check your e-mail for further information.”

തുടര്‍ന്ന് നമ്മുടെ e-mail തുറന്ന് Welcome to “ Geogebra User Forum” എന്ന പേജ് തുറക്കുക.

ഇതിലെ Please visit the following link in order to activate your account എന്ന ലിങ്കില്‍ ക്ലിക്ക് ചെയ്യുന്നതിലൂടെ www.geogebratube.org എന്ന സൈറ്റിലേക്കുള്ള രജിസ്ട്രേഷന്‍ നടപടികളെല്ലാം പൂര്‍ത്തിയായി.
നമ്മള്‍ തയ്യാറാക്കുന്ന ജിയോജിബ്ര നിര്‍മ്മിതികള്‍ അപ്‌ലോഡ് ചെയ്യുന്നതിനും, ലോകത്തിന്റെ വിവിധ ഭാഗങ്ങളിലെ വ്യക്തികള്‍ അപ്‌ലോഡ് ചെയ്തവ കാണുന്നതിനും ഡൗണ്‍ലോഡ് ചെയ്തെടുക്കുന്നതിനും ജിയോജെബ്രട്യൂബ് എന്ന സൈറ്റില്‍ User Name ഉം Password ഉം നല്കി Login ചെയ്യാം.
നമ്മള്‍ തയ്യാറാക്കിയ ഒരു ജിയോജിബ്ര നിര്‍മ്മിതി ഈ സൈറ്റിലേക്ക് എങ്ങനെ അപ്‌ലോഡ് ചെയ്യാം എന്നു നോക്കാം.
ജിയോജെബ്രട്യൂബ് എന്ന സൈറ്റില്‍ പ്രവേശിച്ചതിനുശേഷം Login എന്നതില്‍ ക്ലിക്കുചെയ്യുക.അടുത്ത ജാലകത്തില്‍ User name ഉം Password ഉം നല്കി Submit ബട്ടണില്‍ ക്ലിക്കുചെയ്യുക

ഈ ജാലകത്തിലെ Upload materials എന്ന ബട്ടണില്‍ ക്ലിക്ക് ചെയ്താല്‍ വരുന്ന ജാലകത്തിലെ upload file എന്നതിലുള്ള Browse ബട്ടണില്‍ ക്ലിക്കുചെയ്ത് സിസ്റ്റത്തിലുള്ള നമ്മുടെ ജിയോജിബ്ര ഫയല്‍ കാണിച്ചുകൊടുക്കാം. തുടര്‍ന്ന് Upload ബട്ടണില്‍ ക്ലിക്കുചെയ്യുക.
അടുത്തതായി വരുന്ന ജാലകത്തിലെ Information for Students എന്നതില്‍ ജിയോജിബ്ര നിര്‍മ്മിതിയുമായി ബന്ധപ്പെട്ട വിശദീകരണങ്ങള്‍ നല്കാം.ജിയോജിബ്ര ഫയലിലുണ്ടായിരുന്ന Toolbar, Inputbar, Menubar ഇവയെല്ലാം അപ്‌ലോഡ് ചെയ്യപ്പെടുന്ന ഫയലിലും കാണണമെങ്കില്‍ Show Toolbar, Show Inputbar, Show Menubar തുടങ്ങിയവയുടെ ചെക്ക്ബോക്സുകളില്‍ ടിക്ക് മാര്‍ക്ക് നല്കണം. നമ്മള്‍ അപ്‌ലോഡ് ചെയ്യുന്ന ഫയലുകള്‍ ഉപയോഗപ്പെടുത്തുന്ന വിദ്യാര്‍ത്ഥികള്‍ക്ക് അതുമായി ബന്ധപ്പെട്ട മറ്റു പരിശീലനപ്രശ്‌നങ്ങള്‍ നല്കാനുള്ള സൗകര്യങ്ങളും ഇവിടെയുണ്ട്. അതിനുശേഷം Continue ബട്ടണില്‍ ക്ലിക്കുചെയ്യുക.
തുടര്‍ന്നുവരുന്ന Information for other Teachers എന്നതില്‍ Title, Description, Language, Target group, Tags (ഏതെങ്കിലും ഒരു ടാഗ്) ഇവ നല്കി Save ബട്ടണില്‍ ക്ലിക്കുചെയ്യുന്നതോടെ അപ്‌ലോഡിംഗ് പ്രക്രിയ പൂര്‍ത്തിയാവുകയും താഴെ കാണുന്ന രീതിയിലുള്ള ജാലകം തുറന്നുവരികയും ചെയ്യും . “Your material was successfully created. Thank you for sharing it with the Geogebra community!” എന്ന ഒരു സന്ദേശവും കാണാം.

നമ്മള്‍ അപ്‌ലോഡ് ചെയ്തിരിക്കുന്ന ഫയല്‍ Download ചെയ്യാനും Embedd ചെയ്യാനുമുള്ള സൗകര്യങ്ങള്‍ ഇവിടെ ലഭ്യമാണ്. നമ്മുടേതായ വെബ്സൈറ്റില്‍ നിന്നോ ബ്ലോഗില്‍ നിന്നോ അപ്‌ലോഡ് ചെയ്തിരിക്കുന്ന ഫയല്‍ ഉള്‍ക്കൊള്ളുന്ന പേജിലേക്ക് hyperlink നല്കാനുദ്ദേശിക്കുന്നുണ്ടെങ്കില്‍ ഇപ്പോള്‍ ലഭ്യമായ url.(eg: http://www.geogebratube.org/material/show/id/6053)സൂക്ഷിക്കേണ്ടതാണ്.
ICT അധിഷ്ടിത രീതിയില്‍ ഗണിതശാസ്ത്രം പഠിപ്പിക്കുന്ന എല്ലാ അധ്യാപകരും സന്ദര്‍ശിക്കേണ്ടഒരു സൈറ്റാണിത്..Geogebratube
ഈ പാഠത്തിന്റെ പിഡിഎഫ് രൂപം ഇവിടെനിന്ന് ഡൗണ്‍ലോഡ് ചെയ്തെടുക്കാം.

Playing mathematics

#openuniversity# #m336#

" If it isn't fun it isn't Mathematics. " If any part of mathematics is causing problems make it so that you can play with it. It is easier said than done but it -is- true: mathematics is something you should =DO=. You can't read a mathematics book as if it was just any book in any field, let alone that you can read a maths book as if it was a novel. The mathematics reading protocol has to be applied and that means: verify everything that the author tries to tell you. Mathematics books are notoriously full of errors so you might even find one. If it isn't the best method than it certainly is the method with the most fun involved: study by playing with mathematics. If our brain is the computer then mathematics is a computer game. Really.

Built from scratch with Mathematica

I decorated the cube above with tilings I had to study for M336. Studying tilings is dry, to say the least, so I became 'actively involved' and created tilings myself using Graphics in Mathematica, I put the code I made for Frieze patterns to work on Tilings.

As far as I can remember I have always loved mathematics, except for the darkest two years of my life. I remember myself sitting in the second class of secondary school looking at something I had never seen before: geometric proofs in Euclidean style, i.e.: no algebra, no numbers, no vectors, nothing. The teacher had this gigantic protractor for making drawings on the blackboard. The government dropped this style of math teaching years before but that teacher insisted on Euclid. Looking back I think he just wasn't flexible enough. My grades for math were terrible and so were those of many others. He destroyed the dreams of many children. Although I catched on later, I don't think that I will ever be ready for Euclid.