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+370 699 30003
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:
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
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
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
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
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.