Our Nordplus proposal: 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 help 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 for this thesis "Symmetric Functions of the Eigenvalues of a Matrix".

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 period.

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 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 from English into Lithuanian, Latvian and Estonian and publish and promote electronic versions.

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

Description of partnership ("who does what")

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

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. This work is 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.

Pispalan kulttuuriyhdistys ry (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 from Jēkabpils, Latvia, that is working towards improving the possibilities of education for children and young people in Latvia, thus helping create an educated, ethical and responsible society. It was founded in 2007, and its founding members have been active in other NGOs since 1997. Ūdenszīmes 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 plan to publish books with free licences. 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 Domain.

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 aim for at least one of them to achieve a success that affects or inspires at least 100,000 people.

We will jumpstart an online help room www.helproom.org In our first year we will personally 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 in English, Estonian, Latvian or Lithuanian. 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 improve.

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 fields.

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.

AboutThisPage

• ProposalSummary=Creating math learning materials in the Public Domain with deep ideas and practical illustrations relevant to understanding global realities.
• ProposalStatus=Proposals due March 2, 2009
• ToDo=Write up the proposal
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