Category Archives: General Public

Online Education and Digital Storytelling

Mercedes Bell, a researcher for, shared an article The Art of Digital Storytelling.

The article makes several good points and provides numerous examples graphed below. When digital storytelling is used for education, a new challenge today is keeping the reader engaged, without clicking away, wandering through so many loosely related topics, its easy to get lost, and forget where a digital pathway started, or where it is heading.

The objective of digital storytelling, online education, large scale digitization and information projects needs to be spending more time with better information.


Places & Spaces Mapping Science Workshop

Katy Borner organized a workshop for the Places & Spaces Mapping Science Advisory Board. We met for two days at the School of Library and Information Sciences to figure out the remaining iterations of the 10 year exhibit. See the Schedule and try to visit an exhibit in person, or order the Atlas of Science to read at your leisure. Pictures from the brainstorming session belowBonnie DeVarco, Michael Stamper, and Vincent Lariviere

Kevin Boyack, Deb MacPherson, Andre Skupin, Peter Hook

Bonnie DeVarco, Stephen Uzzo, Michael Stamper


Katy Borner, Kevin Boyack, Debbie MacPherson, Andre Skupin

Kevin Boyack, Bonnie DeVarco, Debbie MacPherson


Emergent versus Imposed Boundaries

When organizing large quantities of resources and information in the digital world… putting things into groups, determining what goes where and assigning boundaries, it can be helpful to look at the real world for lessons learned.  Imposing boundaries in unnatural locations is bound to fail sooner or later, the results can be disastrous taking generations to overcome.

Take for example Southern Africa. Oceans, mountains, deserts, vegetation and other natural features determined where people lived and worked.


Physical Geography and Natural Vegetation
from Exploring Africa at Michigan State University 

Over time, people settled in various areas surrounded by their culture. Learning the best ways to be productive based on the conditions in their area – whether it was a jungle with vast resources or a desert with very few. 

From Africa Expat

Ancient people such as the Shona in modern day Zimbabwe congregated and stuck together in different areas.  Many of these languages and traditions continue today. But these curving, natural, and emergent boundaries don’t match boundaries imposed from outside cultures.

From Wikimedia Commons

Occasionally, an imposed boundary may coincide with a natural boundary such as a river.  More often though, imposed boundaries are designed to work within larger more global schemes, without paying enough attention to the local impact.

From Wikimedia Commons

Anyone can see where arbitrarily drawing lines has gotten us today.  What can be learned from history to avoid similar situations in the fresh, clean, brand new digital world where ideas and information are still patterning out and have no where in particular to belong except where they are emerging as “next to something else” or arranged for convenient, all encompassing, upper level views

Linked Open Data, Colored, as of March 2009

What about situations where digital terrain and intellectual data boundaries are being purposefully laid out. For example Master Web of Science, and Places & Spaces where navigating the data is like exploring uncharted territory, and Katy Borner and collaborators seek to enable the discovery of new worlds while also marking territories inhabited by unknown monsters.

The difference in the semantic world versus the physical world should be that the digital world has no constraints like rivers or mountains. Eventually all of the layout can be determined.  Attention does need to be paid to where cultures are emerging, and how this can benefit everyone both globally and locally.

 Not only watch how the semantic web is emerging, but to direct it’s flow in productive ways, geared for people in different areas that may vary widely in their density and resources, rather than as one empire. Because that only causes trouble in the long run.

Layout Algorithm, NYU

Data Mining at Information and Visualization

Random Layout Algorithm at Cell System Markup Language (CSML) an XML format for modeling, visualizing and simulating biopathways.

The advantage of paying attention to this is, reaching an appropriate balance between random emergence and directed flow will ultimately serve end users and programmers better than any other option, and the solutions will last for a long time.

Communities of Practice at NASA


Time Based Analysis of US Healthcare Reforms

Below is a time based analysis of the US Healthcare Reforms created by Frank Snyder, a physicist who worked in thinking machines and computer vision and now spends his time traveling the world and thinking about anthropology and religion. Image below see the link for the Google Doc.

Whole Building Design Guide, Clinical Relationships.

A few visualizations on Manyeyes are not showing up there at this moment, the visualizations are


IT Graffiti in Public Buildings

The interface between Information Technology and the real world is not always seamless. Below are images provided by Frank and Jane Snyder on their trip across the United States visiting state capitols and presidential libraries. Where unfortunately, architectural beauty can be blunted by shocking displays of IT graffiti in the form of out-of-place computer/video/audio equipment and wiring. Most buildings have controlled this but the exceptions are glaring. Their conclusion is each building (public and private) should have a qualified person responsible to maintain the architectural beauty of the building by reviewing changes that violate the buildings visual appeal. That is, keep the IT graffiti out of public view.


Recycled Glamour and Artomatic

Images from Artomatic 2009. Our entry, Recycled Glamour, was created in collaboration with Sophie, Elena, Edie, Sarah, Rebecca, Becky, Cathy, Deb, Richard, Mark, Bruce, Phil.  Images at the bottom of this post. Visitors can exchange sunglasses, purses, dress up clothes, and sign the wall.

Over 1500 artists exhibited work, the energy is amazing. Some highlights below, tried to capture artists names where possible. Located near the new baseball stadium in DC, runs through the end of June.




Matrix Loops Black and White, Available at the BigRugStore

On the scale of everything that people have ever done and will ever do, multiple view points are always there.

Tomorrow, Barack Obama will give a speech he wrote himself.  This is the opposite of the last president.

Maybe the ability to play opposites against each other ~ to see what is going on ~ will be possible now.

A grand scale of idea and information exchange may now be able to swing across full spectrums of public opinion.  What a perfect mathematics and art problem.  Solving this problem in meaningful ways would include:

* Incorporating diverse viewpoints, agendas, and business models;

* Opening and strengthening communication channels;


Opposites can look alike – maybe people had to dislike Sarah Palin before being able to laugh with Tina Fey.  Maybe there had to be an economic crisis and two wars to:

* Speed up the pace of innovation about strategic data capture and efficient re-use;

Obama’s brand new speech tomorrow will address the oldest problems where:

* Seeing, being able to work with and fine tune diverse viewpoints in pragmatic, opposite-side-of-the-coin-ways may be able to help really understand what transparent governance looks like and how it functions;

* Public safety is the opposite of paranoia;

* Openess and Reason are the opposite of opaqueness, IE opacity, without the ability to see, compare or study;

* Actually thinking and considering multiple viewpoints are the opposite of rash actions that cost a lot of money and do not actually deliver schools or other locally useful buildings to the people supposedly being helped;

When Barack Obama takes office, the future is a welcome opposite to the past.


Form, Function, Connection, Perspective, Responsibility, Reflection

Sent by John Giunta: When I was teaching at the Rock Creek International School, they used the International Baccalauriate program, there were rubrics in place that were useful in assessing our learning and teaching.  Here is a list that fascinated me, it is part of another little project of mine.

Responsibility: What is our responsibility with this knowledge?

Causality: Why is it this way?

Form: What are the qualities of this?

Connection: How does it relate to other things we know?

Change: Is it changing, and from what to what?

Function: Is this useful, and in what way?

How do we know any of this?


From Instructing Autism: Assessment


Digital Continuity



ABOVE: Nature-2 (rough).jpg @ 50% (Gray)
BELOW: Untitled-1 @ 33.3% (Layer 4, Gray)

Both by Bruce MacPherson, work-in-progress sketches for the MathFactory, for Gallagher & Associates Design Proposal



Below is the introduction from Time & Bits, Managing Digital Continuity edited by Margaret MacLean and Ben H. Davis, an eternity ago in 1998 for the Getty Research Institute.  The Getty Research Institute is dedicated to furthering knowledge and understanding of the visual arts and aesthetic appreciation through the advancement of long term digital preservation and information exchange techniques to protect our common cultural inheritance.  The book is about an early workshop pondering over new problems with obsolete media and machines impact on the cycle of: capturing, preserving, distributing, representing, and unlocking a real understanding of the meaning of stored data. See the Long Now Foundation Projects for follow on work such as the Rosetta Project.


Workshop Figure 1

This was a very unhappy interface. And small wonder. No doubt this entire virtual environment was being encrypted, decrypted, reencrypted, anonymously routed through satellites and cables, emulated on alien machinery through ill-fitting, out-of-date protocols, then displayed through long-dead graphic standards.  Dismembered, piped, compressed, packeted, unpacketed, decompressed, unpiped and re-membered.  Worse yet, the place was old.  Virtual buildings didn’t age like physical ones but they aged in subtle pathways of arcane decline, in much the way that their owner’s did.

Bruce Sterling, in Holy Fire. Science fiction writer and founder of the Dead Media Project.


Workshop Figure 2

Below from the article Storage Knowledge by Doug Carlston, page 28 Time & Bits: Managing Digital Continuity

– process information is everywhere and, with increasing frequency, it will not be possible to perceive the full expression of the content-creator’s intent if the ability to perceive the process information is lost.

Imagine, if you will, that we are talking about process content that represents the instructions for building a virtual space and populating it with still and animated images tied to sounds.  Even if one could disambiguate the various data forms and figure out what was image, what was sound, and what was descriptive code, the author’s expression is virtually impossible to deduce absent its interpretation via his original processing device.  If in the future it becomes common to create digital wire models of complex inventions and other devices in lieu of written words, we will have an entire body of obviously important process data held hostage to its original interpretation device.

Perhaps in these areas we just have to give it time.  We do seem to have some movement towards standards, numerical bits have been translated in a reasonably consistent way into numerals and letters of the Roman alphabet (and others), a necessary first step toward a process Rosetta Stone.  And there appears to be a compelling universal interest in standardizing the operating systems and chief applications of commonly available computers, although these standards themselves continue to evolve at a hazardous rate.  Perhaps this process will not continue indefinitely, in which case we are confronting merely an interim problem while the universal standards are finally worked out.


All of this was written before the explosion of the semantic web, online services, and the large scale development of open standards.  Nevertheless, many early concerns raised at the Time & Bits workshop are still valid.  The documentation of places and buildings together with the public information they generate has only just begun.  When will the process information be mature and standardized enough to tell the story of all these people and places over long periods of time?  There are many arguments on OntologForum regarding the utility, accuracy, and even the possibility of universal standards for such large scale processing. Like buildings in the real world, some digital architectures are better than others, some data deserve to be taken better care of and

“there is no constituency representing that body of information”

Margeret MacLean, Setting the Stage, page 33 in Time & Bits: Managing Digital Continuity.

3 images below are from the central garden at the Getty Center in Los Angeles. You can go anywhere, touch anything, get led in directions you want to go anyway, and have tremendous vistas open up around unexpected angles.  There are curves and corners. Only the best materials are used and they are taken care of.  The combination is gorgeous together.  This level of spatial design, execution, and maintenance is needed for an equivalent level of high quality, long term, takes-forever-to-build, semantic web spaces made expressly for the general public.


File: Getty Center Central Gardens Wiki Commons



Companion Post: Trace Continuous Threads



Social Justice and Peace

There is a place in Washington DC called Busboys and Poets that believes social justice and peace are achievable goals.

What does this mean today? What data structures need to be built to further this goal? What geometry works best to distribute and streamline the information flow?

Peace Education Image by D@dalos
Today, there were 1000 monks and nuns in Myanmar seeking social justice in a quiet, peaceful manner. The Washington Post Express reported concern for the monks and nuns safety. The author noted the monks and nuns are the conscience of their country. Every country could use a group of people thinking, and acting, together like this for peace and social justice. This is what the monks look like.


AP Online via the Washington Post

Archiv-Burma, source reference

Here is where Myanmar, that was once Burma, is located:

East Asia Blog Spot

What are the optimal, most efficient paths for quiet, peaceful, social justice people to get the word out?


Social Network Diagrams and instructions available at Group10


Open Letter on Public Space

Architect Rem Koolhaas‘ Harvard Graduate School of Design Studio Project on the City proposes Lagos Nigeria be seen as a developed, extreme, pragmatic case study of a city at the forefront of globablizing modernity. Nigerian architect Uche Isichei observes “He seems to be drawn to the idea that these systems grow by themselves – organizations and structures that emerge primarily as a result of economic and social forces, free of any regulatory control or planning. See “For and From Lagos, Nigeria“.



Lagos, and all places all around the world need public space and sensible ways to organize the distribution of public information. It is nearly impossible to understand what it is like in Lagos with no libraries and parks. How the local community can see a bigger picture or conduct democracy without public information and public space as part of their daily life?
Accuracy&Aesthetics would like to create a public space/public information center in Lagos.  The vision is for a circular pedestrian space in a busy area surrounded with 100 maps mounted in 10 sets of 10 themes. The working title is Where is Lagos.


From AfricaMedia

“Maps” includes the geography of the city, country, continent, and world AND information visualizations showing the current state of public health versus impending spread of disease, Nigeria’s place in the world of science versus locations of local training centers, and other compare/contrast techniques to show the citizens of Lagos where they came from, where they stand today, and where they are heading.


HIV prevalence in adults in sub-Saharan Africa, 2005 (UNAIDS, 2006, p.14).

The place is intended to be permanent. The maps would be constructed of high resolution digital prints mounted to a metal substrate coated in vandal resistant acrylic polyurethane such as Armourseal. The maps will need to be made in the US or UK. Text will be provided in English, Hausa, and possibly a third language to be determined. We will work with the US consulate and other organizations to complete the translations. The goal is to construct simple block walls and install a patterned plaza hardscape of local materials to imply a complete circle around the space. Ideally, a mosiac style map would anchor the exhibit in the middle, hopefully designed by a local person. All construction and installation would employ local people. Maintenance procedures will be negotiated with local and global community-based organizations. There would be an opening event with music.



Do you have any ideas about which part of Lagos is most likely to benefit from a public place like this? Do you know of any organizations, including your own, who would be interested in contributing expertise or financial support towards this effort?

Thank you for taking the time to read this and please feel free to pass onto other who may be interested.


Deborah MacPherson



In many parts of the world, people have no voice or control over their future. Even in America, citizens have deep, serious questions about whether our voices actually have any impact on the national agenda, or any ability to change the direction we are heading. A classic protest refrain is “Show me what democracy looks like” “This is what democracy looks like!”


Mock elections in Bhutan or Druk Yul ? the Land of the Thunder Dragon – which has been ruled by an absolute monarchy for more than 100 years. From Land Where Democracy Would be King, Telegraph UK.


Musharraf Muzzles Media as Democracy Calls Grow, from the Sydney Morning Herald.


MasterDemocracy Copyright 2003-2006 by Alexeig Mathematician.

This is a reflection in Moskva river of the building which became famous due to confrontation between President Yeltsin and Parliament in October 1993. The confrontation ended with assault of the troops loyal to Yeltsin on this building where the Parliament was sitting. This resulted in casualties exact amount of which is still under debate.


Getty Images from The Greatest Innovation of All Time in Business Week.

9. Participative Democracy – Winston Churchill noted that democracy is the worst form of government?except for all the others. The morons running our country, state, or city may be thieves and scoundrels, but once this becomes clear we get to throw the bums out. So this Jeffersonian idea helps with riot control.


The Democracy Game by PopGamers. Download a free trial.


County-Level Cartogram by Sara Fabrikant

Due to popular demand, finally a cartogram on county level data. The counties are scaled by population (2000). The shading is the percentage of the popular vote for President Bush. The overall pattern (e.g., shape distortion of the U.S.) is similar as in the state-level cartogram. However, data at a finer spatial scale allows to see a more nuanced picture of the election results. Populous counties containing large cities (e.g., New York, Chicago, Los Angeles, San Francisco, etc.) are typically blue, even though they may lie deep in red state land (e.g.., St. Louis, Denver, Minneapolis, Miami, Palm Beach, etc.)


This Is What Democracy Looks Like a documentary film about the WTO protests in Seattle with narration by Susan Sarandon and Michael Franti. Music by Rage Against the Machine, Anne Feeney, Company of Prophets and others.

mass protest

Bloggers Freedom to Express


From Weazl’s Revenge, Not gonna stop ’til democracy returns.


From NotInHisName


CodePink Women for Peace. Encourages all actions from public education to free speech.


Rich Media Poor Democracy by Robert McChesney,


Perception and Crisis

In the book A Million Little Pieces, James Frey calls himself an Alcoholic, a Drug Addict and a Criminal. His limited perception of himself and the world around him is compellingly described. Forget the accuracy of this story, the aesthetics are more important.MillionLittlePieces
The author capitalizes unusual words for the chunks of information he perceives: Office, Woods, Bar, People, Daughter. It is extremely rare for him to see a bigger picture. He simply is not able or willing to process this kind of information. One time where it clicks into focus for him is copied without authorization below (pg 230). Background information is at the bottom of this post wherein readers are permitted direct access into the authors head for a full spectrum of human emotion from violent rage to a moment of clarity. After that happens, he states:
I sit and I stare at the World. I see it and hear it and I touch it and I feel it. It is what it is, dirt and rock and water and Sun and air and waves of light and waves of sound made up of definable elements. It can be created or reproduced by man at will. Science has given us that power.


Figure 14: Shown in light blue is the saddle-node periodic orbit that makes the spiking phase of bursting infinite. Andrey Shilnikov Professor of Mathematics at Georgia State University.

Now, what useful scientific and humanitarian goals can be accomplished with “light and waves of sound made up of definable elements” that “can be created or reproduced by man at will”? How can we manage all the information available to be presented in useful, empowering formats?

You Are Not Here: A World Poverty Map by the Chronic Poverty Center.
What benefit can regular people and people in need get from creating and seeing a bigger picture? What kind of information is it made from? Where does it originate? Can it be made from light and waves of sound we can experience? What prevents people in need from processing this kind of information? Reality? Fear? Lack of Control? Are people in Darfur ever able to have the luxury of spending time thinking deeply or is it a constant state of rush and confusion?


Map of Confirmed Damaged and Destroyed Villages by the Humanitarian Information Unit at the US Department of State.
The violent rage of society needs to go for a walk in the woods.


Photos courtesy of Chris and Tim Gerhardson in Lagos, Nigeria.
What if the problem of being unable to perceive a bigger picture was scaled up from an individual in need to a rapidly changing mega-city in need. For example Lagos, Nigeria? Or the whole continent of Africa?


Nobody is really sure how many people live in Lagos, let alone all of Africa. A recent house to house census in Lagos set the population at 9 million. The UN Population Fund disagrees and says 16 million. The Lagos state government insists the figure is 17 million. The UN has predicted by 2015, Lagos will be the third most populous city in the world with an estimated 23 million people.

t foo (growing)

saakee, d saakee (change, there is change)


How can a bigger picture be made for huge numbers of people in a buzzing metropolis like Lagos? What types of information need to be understood to help them the most?

waayar – d (progress, make with)

ma’aadinii (resources)

Do people in Lagos have time to be able to see where they stand and where they are heading? Not only in terms of geography, buildings, and number of people but in terms of their history, future, ideas, information and limited resources.

A current Accuracy&Aesthetics project is to gather and make a series of maps to help the people of Lagos understand where they are so they can participate in shaping their future, pursue happiness, and think big.

The digital age can help people in need by giving them new ways to see where they are and express their hopes and dreams. Hopefully, people everywhere in all living conditions can eventually show us who they are, and let us know what’s on their minds so we can help achieve their goals in both the short and long term. Maybe we will all learn something.

nak’ltaa (learn)

j nk’ai (having understanding)

gwaal (open one’s eyes widely)

k’oof, mashigii (opening)

dmkrd’iyy (democracy)

mur.y, saut (voice)

na’m (expression of agreement, interest)

dbaar, ra’yii (idea)

d’uur.iy, lbaar, r.hoot, saadrwaa, sanrwaa (information)

walaw (personal freedom)



You Are Here

Beautiful NASA photos below were sent by John Guinta . “…spectacular photos of our fragile planet. Please circulate them to as many people as possible.”

What an immeasurable benefit to people all over the world to have access to NASA’s big pictures. They are so beautiful. What else is available that everyone can look at and admire for free?

Semantic Mashup: A pragmatic approach for information integration at NASA will be presented by Andrew Schain, Chief Technology Officer, NASA Headquarters at a Semantic Technology Conference in San Jose, California at the end of this month.











T-shirts of even bigger pictures are also available:

you are here 1

Nate Brown at Penn State Math Department

you are here 2

Source unclear but graphics worth looking at on this site by Martha Fishfarm.

Best example found so far for You Are Here in semantic universe is a t-shirt by Moogle

How can large scale overviews of changes and dynamics in the semantic universe be as beautiful and dramatic as NASA images above?


Where is Lagos?

Zoob’ (bigger than, be) h too, m tum-m tumii, sif, suur, taswiir (picture)

Translations from the Hausa Database ? by Franz Stoiber, 2001.

Lagos Map from Oyibosonline, the Expat’s Guide to Nigeria.

Educate and inspire the people of Lagos with a series of bigger pictures. Show the locations of local schools, universities, and training centers. Place Lagos, Nigeria, and Africa within the context of whole worlds of geography, science, and resources. Establish a bigger picture for the people of Lagos to see where they are and provide hope in the future.

Install 100 maps of various types in a public place. If sufficient funds can be raised, also install with a computer to collect public opinion and provide Google Earth and similar exploration tools with a large database of maps.

30 maps will be historical: the same maps going through time – some Africa, some Nigeria, some Lagos, some the whole world, one a street map where the exhibit is. The maps are identified by year, author, and title.


West Africa, London Times, Andree, Richard 1895, from the David Rumsey Collection.

30 maps will be future maps: maps of science from Places & Spaces, information visualizations, and other modern maps.

La “Mappa” Par fxds, jeudi 23 novembre 2006 ? 12:04 FXDS
30 maps will be current maps such as Google Earth, famine watch and other geographic information pertinent to Africa, Nigeria, and Lagos.


This image of the northern portion of the Nile River was captured by the Multi-angle Imaging Spectroradiometer (MISR) on January 30, 2001. The Nile is the longest river in the world, extending for about 6700 kilometers (4163 miles) from its headwaters in the highlands of eastern Africa. (Credit: NASA/GSFC/JPL)
10 maps will be contest winners, a competition open to all, run as a program in partnership with a local educational organization to be identified in collaboration with US consulate press officer Tim Gerhardson. The workshop to discuss and select the 10 winning maps and install the 90 selected maps is slated for July 2008.

It is preferred for the exhibit to hang outside in a busy public area rather than inside a library or school. It should be a permanent installation. If you can help, tax deductible donations are through the Network for Good, contact us with suggestions or volunteer your expertise to help the people of Lagos to think big and see there is a big world full of opportunity out there.


Words May Hinder Math Skills

earspiral ~artist unknown

English Words May Hinder Math Skills Development

The words and symbols used to represent numbers may interfere with understanding of math concepts.

By Beth Azar at the Monitor by the American Psychological Association

Each time the government releases a new round of test scores, the United States laments the dismal performance of its children compared with children in other nations, particularly those from Asia.


And although differences in classroom instruction may be partly to blame, psychologists are finding that cultural differences in computational ability can begin before school and may have their roots in the words and symbols different cultures use to represent numbers.

For example, Asian children may get a head start in understanding that our number system is base 10 because their number words make that connection explicit whereas English does not. And fractions may pose a particular problem for all children in part because using the same numerals for fractions as for whole numbers may interfere with learning and in part because their brains are hard-wired to deal with whole numbers.

Classroom instruction may be able to address these inherent problems by explicitly teaching the concepts that children struggle with, says psychologist David Geary, PhD, of the Uni-versity of Missouri, Columbia.

Words get in the way

For English-speaking children, number words may hamper learning before they even enter school: Studies by researchers including Kevin Miller, PhD, of the University of Illinois Urbana- Champaign, consistently show that Asian children learn to count earlier and higher than their American counterparts and can do simple addition and subtraction sooner as well.

Researchers argue that differences in number words may be a major factor behind these differences. The culprit is the way English–as well as some other languages–treats numbers between 10 and 100. The teen numbers in these languages are irregular and difficult for children to learn and the rest of the count is separated into decades with words such as “twenty,” “thirty” and “forty.”

In most Asian languages the number words are far more consistent. In China, for example, the teen words are presented as 10 plus some ones: Eleven is simply “ten one,” 12 is “ten two” and 13 is “ten three.” This pattern continues into the decade numbers where 20 is “two ten,” 30 is “three ten” and 45 is “four ten five.” The language makes it obvious that the number, system is base 10.

This difference in language may partly explain why most Asian children learn by the mid-dle of first grade to subtract and add by thinking of numbers in as a 10 and some ones–an extremely helpful and efficient method of doing addition and subtraction, says Geary. In contrast, children in the United States, where much of the cross-cultural work has been conducted, rarely use such a method, even as they get older, Geary and other researcher find.

In fact, Chinese children who are good at counting at age 5 are already beginning to understand that teen words can be thought of as 10 plus some ones, find psychologists Karen Fuson, PhD and Connie Suk-Han Ho, PhD, of the Chinese University of Hong Kong. No children in the United States or England, regardless of their counting proficiency, understood this concept by age 5, they found in a series of studies published in the Journal of Educational Psychology

(Vol. 90, No. 3, p. 536 544).

Children in the United States eventually learn that the number system is base 10 and that teens are tens plus ones, but only the most mathematically adept children ever learn to add by adding up to 10 and then adding the remaining ones (as with adding 7+8 by breaking 7 into 5 and 2, adding 2 to 8 to get 10 and then adding 5 for 15), says Fuson.

She has emphasized teaching about base 10 in a curriculum she’s developed and is finding in preliminary evaluations that when taught this way children from poor inner-city schools districts quickly begin to outperform children from wealthier school districts. Countries that have similar language problems, but better math scores than the United States, may already use this kind of instruction.

Friction with fractions

Teachers may also need to work on the way they instruct children in fractions, which are notoriously difficult even for adults, say researchers.

Children may have trouble with fractions for several reasons, says Rochel Gelman, PhD, of the University of California, Los Angeles, whose research is geared toward understanding how children’s notion of fractions develops. For one, because they learn to use numerals as whole numbers, it might confuse them to use the same symbols in a different way. It may also be that children have hard-wired mental structures that are designed to handle whole numbers and have trouble dealing with fractions.

A new study by University of Chicago psychologist Janellen Huttenlocher, PhD, and her colleagues supports the latter theory. They find that when numerals are removed from the equation and children are asked to calculate with fractions using nonverbal tasks, they do quite well.

In the study of 3- to 7-year-olds, instead of asking children to add numerical fractions, the researchers asked children to recreate fractional sums using wedge-shaped pieces of sponges that, when put together, formed a circle. As the children aged, they grew better at solving the nonverbal fraction problems. In fact, their skills improved in parallel, though at a slower rate, with their skills for manipulating whole numbers.

This finding indicates that children are able to manipulate fractions when they can form a mental model of the problem using real-world objects. They stumble only when they’re asked to work with fractions represented as numerals, says Huttenlocher.

“With fractions the villain is putting 3’s over 4’s,” says Huttenlocher, whose study is published in Developmental Psychology

(Vol. 35, No. 5, p. 164 174). “Children can mentally handle fractions, but the numbers get in their way–so with 4/5 and 4/8, children think 4/8 must be more because there’s an 8 there.”

Gelman agrees that interference is likely part of the problem. But she also believes–based on research in animals and humans–that there is an innate and hard-wired part of the brain that was designed through the course of evolution to handle whole numbers. This predisposition makes it easier for children to learn about whole numbers and hinders their learning of fractions, she argues.

“It’s hard to think that we have trouble learning fractions just because we have no experience with numbers used this way,” says Gelman. “That can’t explain why the fraction problem extends well into college for some people.”

Regardless of why children, and adults, have trouble with fractions, most researchers agree that teachers should introduce fractions in the context of real-world examples, including slices of a pie, pieces of an apple and portions of candy

Further reading

* Geary, D. Reflections of evolution and culture in children’s cognition: implications for mathematical development and instruction. American Psychologist, Vol. 50, No. 1, p. 24 37.


Inviting the General Public to your Database


What are the requirements for the general public to be able to move through shared databases?

How can huge numbers of people be provided with basic services they need in?an information?place?

What can we learn from architects and urban planners about the design of physical space?to reapply the best practices and design principles?to semantic space?

What about the reality that regardless of designs and intended functions, people tend to walk outside?the lines?