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Nordplus proposal: Classic Math Problems for Changing Realities

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  • Andrius Kulikauskas
    I finished writing my proposal below. If all goes well, I will get letters of intent from our partners and submit my proposal tomorrow. Next I hope to write a
    Message 1 of 1 , Mar 1, 2009
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      I finished writing my proposal below. If all goes well, I will get
      letters of intent from our partners and submit my proposal tomorrow.
      Next I hope to write a proposal to the Lithuanian Foreign Ministry that
      we organize a Sneakernet for Ghor province in Afghanistan. Thank you,
      Ricardo, for your encouraging letter! Peace, Andrius Kulikauskas, ms@...

      Classic Math Problems for Changing Realities

      We will provide activists with self-standing lessons and online support
      so they can apply and share mathematical thinking to address
      globalization and its consequences, notably climate change.

      We will create a set of 30 self-standing math lessons for self-learners
      . Each lesson will present a classic math problem and a deep idea which
      it illustrates. We will organize an online support center for tutoring
      and consulting, but especially for supporting "math in action" for
      analysis and communication of challenges and solutions in our changing
      world, focusing on climate change. We will publish a paperback,
      worksheets, a wiki and YouTube videos, all in the Public Domain.

      Background/motivation for the project

      Our age of globalization is propagating rapid changes and dramatic
      instabilities. Will we match this with an ability to think and talk and
      act decisively and independently? We need to appreciate the connection
      between our local choices and the global picture. Mathematics is a
      language for talking about the subtle but profound distinctions of the
      models that may be at play. It helps us care about each other's
      situation around the world. We're all potential climate refugees. Math
      helps us learn to share with each other. It helps us exchange our wisdom
      as climate patterns shift and disrupt our agriculture, our water supply,
      our built environment. We need to think deeply and learn rapidly. We
      need ideas and problems that are to the point and can be spread freely.
      We need math lessons on-demand!

      Andrius Kulikauskas is since childhood a lifelong learner on a quest to
      know everything and apply that knowledge usefully. At the University of
      California at San Diego, he studied mathematics as a tool for conceptual
      thinking. He was appointed senior teaching assistant, responsible for
      training the first year teaching assistants. He earned his Ph.D. in 1993.

      Andrius taught a Precalculus class at UCSD for students who were ill
      prepared for Calculus. He knew the dismal state of mathematics teaching.
      High school teachers generally don't think mathematically. Truly,
      mathematics should be a tool for thinking, where the point is first to
      understand the relevance of various models, and only then to calculate.
      Unfortunately, textbooks are full of contrived, irrelevant problems
      which hinder mathematical intuition. Andrius taught from his own notes:
      http://www.helproom.org/precalculus.pdf He identified the key ideas
      leading up to Calculus, and surveyed them all in thirty one-hour
      lessons. His students did very well!

      In 2008, Andrius taught algebra as a Professor at American University in
      Bosnia and Herzegovina. He taught 90 business students, many of whom
      were unmotivated because they thought math was irrelevant, and yet they
      rated him an outstanding teacher. He concentrated on teaching them a few
      dozen classic problems which were difficult but insightful. For example,
      suppose that the price of a barrel of oil goes up by one-third this
      week, but then goes down by one-third next week. What is the overall
      change in price? Many people suppose that the two changes cancel out and
      the price is the same. But actually, if the barrel of oil costs $90,
      then it goes up to $120, but down to $80! And, in general, it goes up
      from X to 4/3 X and then down to 8/9 X. This is a very thoughtful
      problem and it illustrates a very deep idea, which is that algebra is
      the study of thinking step-by-step. If you don't think step-by-step, you
      can't solve this problem, because you won't know what "one-third" means.
      Most books and teachers don't and can't teach step-by-step thinking
      because it's a lot of work to grade. But if the problem is truly
      relevant, then the effort is worth it!

      Here are some of Andrius's favorite problems:

      * The world's population is doubling every thirty years. Suppose that
      was always true. When was Adam created? and Eve? It may be shocking to
      learn that they appeared only 1,000 years ago! This shows the power of
      exponential growth, but especially, is a great illustration of how a
      model (and perhaps every model) breaks down at a certain point.
      * What is 10 + 4? The answer is 2! At least the clock says it is! Ten
      o'clock plus four o'clock is two o'clock. This problem shows that there
      is more than one mathematical system, but also suggests that we can't
      write down everything we need to know about a system.
      * All parabolas have the same shape! Some may look skinny and others
      fat. Yet by zooming in and out, flipping them upside down, moving left
      or right or up or down, we can see that they have the same shape. This
      teaches us the basics of transforming any graph.
      * "A right triangle is half a rectangle". Thus the shape of a right
      triangle is given by the ratio of the two sides of the rectangle. But
      you also know the shape if you know one of the right triangle's acute
      angles. We can switch back and forth between these two ways of looking
      at the shape. This "bijection" is the basis for trigonometry!
      * "Four times a right triangle is the difference of two squares." This
      geometric fact makes for a quick proof of the Pythagorean theorem, but
      also shows the theorem's relevance for switching coordinate systems,
      which is to say, points of view.

      Imagine if all of math education was organized around such classic
      problems. Andrius will write an essay for every such problem to show why
      and how it's interesting for a mathematician and philosopher. Each
      lesson can include many variants of the problem along with applications
      and exercises. A few dozen problems are enough to survey all of algebra.
      They could fit in a paperback of 150 pages or so.

      Such a paperback would allow parents to master the mathematics which
      they'd like to help their children learn. After reading such a
      paperback, they would feel confident taming the monstrous 500 page
      textbooks used at school.

      Imagine, if people could use such materials without restriction! Ours
      will be in the Public Domain so they might be shared, adapted and
      improved! A teacher in Africa might print out one lesson at a time,
      think up a game that teaches the concept, and then write a letter how it
      went. People could share examples and applications from around the world!

      Indeed, we can set up a wiki to collect classic problems, ideas and
      examples in math and other subjects. A wiki is an online tool with which
      individual problems could be easily edited and linked together into a
      pattern language, as in Christopher Alexander's "A Timeless Way of
      Building". Yet each lesson can also stand on its own.

      We're living in a world with many new issues linking people of very
      different cultures. We need to be able to understand subtle but profound
      implications of our decisions. Activists need math to analyze and
      communicate the choices we have. We can support them online with a chat
      room and related venues. We can help them find the right lesson to apply
      to their challenge and to teach the public and the powers-that-be. They
      can present their lesson with a short video of "math in action".

      We have many opportunities to apply math in our world. We can develop
      math intuition based on real problems, not contrived exercises. We can
      organize an online community to create learning materials in the Public
      Domain that encourage self-learners to understand mathematics in terms
      of its deep ideas and practical applications. As we face global
      challenges, including our current economic crisis, we find social and
      business opportunity in recognizing what is truly worth learning, and
      making that available for all to share freely. We offer a Baltic and
      Nordic team to start up this activist approach to education.

      Project description (including account of planned activities/project plan)

      Our project's activities are ongoing and/or evolving over an 18 month

      Andrius will start by identifying noteworthy math problems from his own
      notes, from websites, from discussion groups, from colleagues online and
      from mathematics textbooks, especially intuitive books such as "Applying
      Arithmetic: A Handbook of Applications of Arithmetic" by Zalman Usiskin
      and Max Bell and "How to Lie with Statistics" by Darrell Huff. He will
      continuously look for new problems and invite others to contribute them.
      He will relate each problem with a deep idea that it illustrates. He
      will select what he thinks are the thirty or so pairs of problems and
      ideas and which most completely and profoundly present mathematics. He
      will write an essay for each problem/idea.

      Andrius will also create a general format for writing up each problem,
      idea and related examples, illustrations, applications and exercises. He
      will adapt the wiki at worknets.org with templates and navigation which
      accomodate the contributing, polishing and organizing of these problems
      for self-learners.

      Early in our project, Andrius will travel to Tampere, Finland to work
      for one month with filmmaker Teemu Takatalo at the Hirvitalo community
      centre. Andrius will work with activists to understand what math ideas
      might be relevant for their campaigns. Teemu will coach them on using
      video to communicate these ideas.

      Andrius will also travel to Latvia to work with open source publisher
      Didzis Veinbergs. Didzis will find one or more designers and/or
      illustrators to help with designing the website and illustrating the
      mathematical ideas. They will also provide images for our video makers
      in Finland.

      Mihkel Pilv and Miksike will find adults who are interested in learning
      mathematics, perhaps in order to help their children learn. Andrius will
      visit them in Estonia for one month and tutor them. He will also
      organize online tutoring at www.helproom.org by chat, email and Skype to
      help them and others around the world.

      Midway into our project, Andrius will start publishing individual
      lessons online. Miksike's adult learners will test the lessons and help
      create related worksheets. Andrius will return to work with them.

      As the videos are completed, they will be published online and also made
      available through our wiki. Didzis Veinbergs will promote them and the
      activist's campaigns along with the upcoming book. Andrius Kulikauskas
      will visit him in Latvia and they will publish and promote a short
      paperback of "Classic Math Problems".

      We will adapt the book and translate it into Lithuanian, Latvian and
      Estonian and publish and promote electronic versions.

      All of the materials created for our project will belong to the Public

      Description of partnership ("who does what")

      Our project includes four partners from Lithuania, Estonia, Latvia and

      Minciu Sodas is the coordinator for our project. It is a sole
      proprietorship registered in Vilnius, Lithuania. Andrius Kulikauskas is
      the founder, sole proprietor and Direktorius. Minciu Sodas is an online
      laboratory for serving and organizing independent thinkers around the
      world. We have about 150 active and 1,500 supportive participants. Our
      most spectacular project so far was the Pyramid of Peace
      www.pyramidofpeace.net in 2008 in Kenya. We organized 100 peacemakers
      on-the-ground and 100 online assistants to avert genocide during the
      post-election turmoil. We used our wiki, mailing lists and chat room,
      all in the Public Domain, to coordinate our work.

      Andrius Kulikauskas will select the problems and ideas, author the
      essays, the lessons and the paperback, and code the wiki and help room,
      which are the heart of this project. He will be supported by Minciu
      Sodas's team of online assistants who will collect interesting examples
      and tutor self-learners.

      Miksike is a pioneer in educational crowdsourcing. www.miksike.com More
      than 1,000 volunteers have created 30,000 worksheets used by 120,000
      students, see: lefo.net Miksike is a Private Limited Company based in
      Estonia. Mihkel Pilv is the director. He is an innovative entrepreneur,
      ever discovering new business opportunity. Mihkel and Andrius met on a
      flight to the MIT Media Lab ThinkCycle's Development by Design 2002
      conference in Bangalore, India to which they both won travel awards for
      their papers about their work.

      Miksike will provide adult volunteers to try out the Classic Math
      Problems learning materials, provide feedback and create related worksheets.

      Pispala Cultural Association runs the Hirvitalo center of contemporary
      art in Tampere, Finland. Hirvitalo is a base for artistic and cultural
      activists, including gardens and permaculture. Markus Petz is now the
      European Voluntary Service coordinator there. He first met Andrius on a
      road trip they took together to visit UK independent thinkers. Markus
      organized a video bridge from Hirvitalo in 2008 with Andrius about his
      paper "An Economy for Giving Everything Away".

      Pispala Cultural Association will organize ten activists addressing the
      consequences of globalization, especially climate change. Each activist
      will create a YouTube video illustrating "math in action" in their
      campaigns. Teemu Takatalo will coach them in video skills.

      Ūdenszīmes (Signs of Water) is an NGO in Latvia which will host Didzis
      Veinbergs's work to publish our Classic Math Problems as a paperback in
      the Public Domain. Didzis and Andrius met in 2008 at BarCamp Baltics.
      Andrius invited Didzis to Vilnius for the workshop "Ethical Public
      Domain: Debate of Questionable Practices" which Minciu Sodas organized
      for COMMUNIA, the European Union's thematic network for the Public
      Domain. Didzis spoke there about his dream to publish books in the
      Public Domain. Didzis will publish, promote and distribute Andrius's
      book as well as provide designers and/or illustrators for related websites.

      Minciu Sodas will translate the book into Lithuanian, Ūdenszīmes into
      Latvian and Miksike into Estonian.

      Of our total budget of 82,000 EUR, which includes our co-financing and
      our administrative fee, we ask for 60,000 EUR of which 30,000 EUR is for
      Minciu Sodas, 10,000 EUR for Miksike, 10,000 EUR for Pispala Cultural
      Association and 10,000 EUR for Ūdenszīmes.

      Each of the partners will contribute co-financing in terms of the work
      of their many volunteers who will collect examples and staff our help
      room and translate into Lithuanian (Minciu Sodas), try out our lessons
      and create worksheets (Miksike), apply our math lessons to climate
      change and other global challenges (Pispala Cultural Association) and
      promote and distribute our book (Ūdenszīmes).

      Expected outcome (Please describe the expected results of your project,
      who will be effected and how, directly and/or indirectly)

      Our project will result in a wealth of learning materials in the Public

      We will publish a short, readable, popular book "Classic Math Problems"
      with essays on about 30 math problems and the deep ideas they
      illustrate, along with applications and exercises, and an introduction
      that weaves them all together. There is a chance that our book will
      become a classic. "How to Lie With Statistics" was first published in
      1954 and today ranks in the top 7,000 books at Amazon.com

      We will organize a thriving where such problems are suggested and
      polished by completing a template for them. Our wiki will link together
      the problems by various threads. We will establish a new paradigm for
      creating learning materials.

      We will also include links to 10 videos that show our "math in action".
      We will have helped 10 activists use math to make their case to the
      public and relevant institutions.

      We will jumpstart an online help room www.helproom.org In our first year
      we will help more than 100 people develop their mathematical thinking.

      We will create worksheets for use through Miksike and other venues. In
      particular, we will create one-page worksheets, each dedicated to one
      lesson, so that a teacher can print them out on-demand when they prepare
      for their class.

      We will publish CDs and/or USB flash drives with all of the above
      materials for use in remote areas such as Africa with computers such as
      the One Laptop Per Child XO.

      Our materials will be primarily in English, but also some lessons and
      worksheets in Estonian and possibly other languages.

      All of the content which we create for this project will be in the
      Public Domain.

      We will have a team of enthusiasts in the Nordic and Baltic countries
      and around the world interested in further developing learning materials
      for mathematics but also other subjects.

      Dissemination of results (Please focus on sharing the results with
      individuals, organisations or groups who are not your partners this project)

      We will have electronic versions of the book and associated learning
      materials in English, Lithuanian, Latvian and Estonian.

      We will print at least 1500 copies of the English version of our book.
      We will sell at least 1,000 copies in stores in the Nordic and Baltic
      countries and also by mail.

      We will distribute our printed book to at least 500 people around the
      world who will help promote the printed and/or online versions, bring
      attention to them and open up business opportunity. We're especially
      interested in parents, especially homeschoolers, who would like to learn
      math better so they could teach their children, and also activists who
      might benefit from applying mathematics and thereby raise public
      interest in our classic math problems. We expect at least 7,000 people
      to read or hear lessons from the printed book and that a second printing
      be profitable.

      In the first year that the book is available, we expect at least 10,000
      people in the Nordic and Baltic region to download the electronic book.
      We expect 100,000 people around the world to download the English
      version and another 100,000 people to learn from it through the One
      Laptop Per Child program with which we have links through Edward
      Cherlin's Earth Treasury, a working group of Minciu Sodas.

      We hope to attract media attention to our activists's campaigns in
      Finland and encourage other activists in the Nordic and Baltic countries
      to make use of our math lessons.

      In Estonia, Latvia and Lithuania, and other Mikiske Learning Folder
      countries, we would like our math lessons to be a key resource for
      Miksike's large community of teachers and students.

      We expect that Earth Treasury initiative www.earthtreasury.net will
      organize the creation of open source educational software and animations
      based on lessons in our book.

      We expect our wiki to be a growing repository of math lessons and our
      chat room helproom.org to be the center of lively tutoring and
      consulting services, for free and for pay, in math and other areas.

      Minciu Sodas has many contacts in Africa. We're very excited that they
      might use and share our math learning materials.

      In all of our efforts, our materials will spread more easily and widely
      because they are in the Public Domain for all to freely share, adapt and

      How will you evaluate that your project has met its objectives

      We evaluate our project in terms of the relationships which we create,
      especially the people we include.

      We expect, at the end of our project, to have a thriving wiki system
      with a well structured template, a core team of contributors and a
      growing collection of lessons and applications in math but also other

      We wish to find an eager market for our book so that we can fund a
      second printing of our own resources. We will note any interest that our
      book be translated, republished by others, and printed on-demand.

      We will be excited to see individual lessons being copied and
      circulated. We will note the most popular sites for getting our book and
      note the download statistics.

      We will be delighted if our materials are used by teachers and there are
      students learning math without standard textbooks, but especially in
      poor countries, such as in Africa.

      We would like to see one or more of our lessons receive attention in the
      press thanks to its significance for some activist campaign. We would
      like one or more of our videos to be popular at YouTube. We will make up
      for each lesson a "tag" (like "halfrectangle") which can be used on
      YouTube, Flickr and other sites to note the uses of our classic math
      problems that all are encouraged to share. We would be excited to see
      people using such a tag system.

      We plan for an active online help room with regular tutoring activity
      and potential business opportunity.

      We wish to encourage a growing number of people that math's deep ideas
      and classic problems are truly relevant for thinkers and activists,
      especially for global issues such as climate change. We will know that
      we are having an impact on globalization and climate change if our
      lessons are adapted locally.
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