NumbersAlive! hopes you all have a wonderful transition from 2017 to 2018.
As 2018 begins, consider how the change in the year utilizes numbers in an understood global manner How and why did this happen? Many cultures have their own calendars, but the world celebrates the new year with the same numbering system. Among the numbers 0-9, 8 is happy to replace 7, who hung on as long as possible as part of time’s name. Like the US presidency, the transition should be smooth. Numbers are part of every discipline/concept necessary for transforming young children into citizens
Geometry should be linked to numbers and our efforts to do so created Number Linx which was named the best invention of North America at the iCAN invited inventor conference in Toronto last August.
We are here to help all educators, parents and children understand what math is about and where it came from. We are focused on such questions and embrace historic and forward-thinking fundamentals to make math meaningful and real. Being everywhere you look we use actual photos, locations, quotes, etc. to demonstrate its usefulness. We encourage learners of all ages to observe, discuss, design, create, and make math! How and why were the systems we use today developed?
Everyone at NumbersAlive! wishes the world a peaceful, healthy, and meaningful 2018.
Celebrate As You Will
Winter’s often cold and snowy,
But winter holidays are always showy.
You might decorate a Christmas tree.
Or set a blaze of Chanukah lights.
Place clean boots for Santa on your porch,
Or pay respects at religious sites.
No holiday is better or best,
They are times for family, reflection, and rest.
No matter which holiday you call your own,
We hope it brings joy, more than you’ve ever known.
Although Christmas takes center stage in the United State, it’s not the only holiday Americans celebrate in December and January.
Christmas around the world
You all know that many Americans celebrate Christmas on December 25 by decorating a fine spruce, sharing a fine meal, and opening their first present either on Christmas Eve or Christmas morning.
But in Germany, Christmas revelers place clean boots by the front door on December 5 for Santa to fill with nuts, sweets, and small presents.
In Italy, kids eagerly await January 6, the day in ancient times when the three Wise Men arrived at Bethlehem and gave Jesus gold, incense, and myrrh. Today, Italian boys and girls believe a good old witch named “Befana,” leaves gifts for them.
Kwanzaa, created in the 1960s in response to racial strife in the U.S., celebrates the African American culture and community. The holiday’s seven days, which begin December 26 and end on January 1, centers around seven values – unity, self-determination, collective work and responsibility, cooperative economics, purpose, creativity, and faith. Each night, family and friends gather to light candles, feast, and talk about how each person can make the world a better place.
In early/mid December, Jews celebrate Chanukah by lighting a nine-candle the menorah, which symbolizes the miracle of faith. For eight nights, Jews light the menorah, exchange presents, and spin the dreidel, a gambling game for chocolate-covered coins called “gelt.”
Japanese New Year
It’s called ‘Omisoka,” and Japanese families celebrate it on December 31, the last day of the year. People clean their homes and remove clutter to welcome in the new year with a metaphorical clean slate. Family and friends feast together and often watch a nation-wide New Year’s talent competition until the countdown to midnight, when temples toll their bells.
If you have a copy of our The 12 Notes of Christmas, watch the entire film during the holidays that links each day 0 (Christmas Day) to 12 (Jan 6, Twelfth Night) as the numbers travel the world to create a musical band to celebrate Shakespeare’s 400+ legacy at the opening of Twelfth Night in the Globe Theatre. Learn instrument design linked to the day 0-12 as well as history and holiday food in each global location. Animated for kids and information for all ages. The mashup of the 12 Days of Christmas song and Twelfth Night by Shakespeare takes its goal from Duke Orsino’s line from the play, “If music be the food of love, play on!”
Check out the shop to order a film as it is great for the entire holiday season. The price is free but there is a $4.95 shipping charge for any total order.
Corresponding discussion questions are available at www.numbersalive.org/documents/12notes.pdf
Celebrate the holidays as you will!
Thanksgiving Day is finally here,
A time for family and food.
The holiday when you count your blessings.
And show your gratitude.
A roasted turkey takes center stage,
And glazed carrots round out the meal.
So take this chance to teach your kids,
The math behind each peel.
Thanksgiving can be a numbers game – literally. Here are some fun ways to use the holiday to teach and reinforce basic math concepts.
Sorting: Make a list of typical Thanksgiving foods and ask your family “learners” to sort and group the items. Ask how they would sort them to avoid the appearance of only one “correct” way to sort: size; color; “foods” we drink versus foods we eat; foods they love versus foods they’re forced to try; etc.
Temperature: Using a thermometer is an important part of making sure a turkey is thoroughly cooked. Grab a thermometer and measure the temperature of food in and out of the refrigerator. If your young family member is in the kitchen when you’re roasting the bird, let her/him – carefully – take its temperature or read the thermometer when you stick it into different sections of the turkey. Depending on the age of the young person ask if they know whether the temperature is in degrees Fahrenheit or Centigrade and what the difference is. Give an older learner the opportunity to convert to the other scale from the one on the temperature tool poked into the turkey.
Division: How many pounds does your turkey weigh, and how many people must it feed? How much turkey can each person receive? If there’s a vegetarian in the group, how does that affect turkey portions?
Multiplication: Mashed potatoes, yams, and carrots provide a great opportunity to practice multiplication. If each guest eats a ½ cup of mashed potatoes, how many spuds will you need? Making pumpkin pie usually requires purchasing canned pumpkin. Estimate how many pumpkins are needed to create a small can/large can of pumpkin? If you have an old Halloween pumpkin have them cook the pumpkin and try to figure it out.
Budget: Learners in upper elementary, MS or HS could calculate the total spent on the Thanksgiving dinner and then determine the cost per person. Go over the receipts of the items purchased directly for the Thanksgiving dinner. Then have them search the internet for the “cost of Thanksgiving dinner in 2017” compared to prior years. A “market basket” comparison requires keeping the types of items the same to determine the change in the cost of living. They may have to recalculate the items purchased that are in the standard market basket in the articles located.
If you have other ideas, please send them to email@example.com. Have a wonderful and tasty Thanksgiving!
Exploring Universality: Does the World Really Use the Same Numbers?
Rebecca Klemm & Rachel Wallace
Pages 500-506 | Published online: 10 Nov 2017
In this article
• The Evolution to the Current Base 10 Place Value System
• Where Did “Arabic Numerals” Come From?
• How Do We Display and Explain the Universality of Numbers?
• Why Should We Discuss and Teach the Universality of Numbers?
• Questions for Further Discussion
Exploring Universality: Does the World Really Use the Same Numbers?
Arguably one of the most under-appreciated, yet ubiquitous and frequently utilized aspects of modern, globalized society, our number system exemplifies how we are inextricably interconnected. Indeed, without a universal number system, there would be no global collaboration and no global solutions.
Within a global citizenship education framework, we might consider what aspects of our lives and societies can be considered truly universal. It is interesting to consider whether numbers are universal and, if so, how that universality came to be. A short answer is that numbers are universal, or almost so, as are other structures of daily life, such as the annual calendar and units of measure. Another intriguing question is why language is not universal. While an in-depth investigation of this issue cannot be done in a short article, we can discuss what the universality of numbers says about our developing nature as global citizens.
Over time, humans have become more globalized as a result of trade, migration, travel, and, recently, the internet. More fundamentally, however, the current global world developed because humans are complex, curious, community-based creatures, capable of adaptation and invention. We adjust the environment to meet our needs. While such adaptation, of course, benefits us in our own lifetimes, as complex thinkers no longer concerned about daily survival, we can now also consider long-term global consequences.
The development of a universal number system is a wonderful example of how individual cultures evolved—and how their members became global citizens while still maintaining their own historic identities. Early humans communicated via drawings, movement, and story-telling. Language and number systems evolved from these communication strategies. A certain spoken word became associated with a certain picture, both being used to represent a specific thing, such as a horse. To distinguish characteristics, if important, the pictures needed to become more complex: two horses, large and small horses, male and female horses, etc. Picture communication was beautiful but time-consuming and so we humans developed writing systems to more efficiently communicate our messages. Numbering and counting systems also developed, but these systems, unlike languages, were eventually standardized to become almost universal.
The Evolution to the Current Base 10 Place Value System
Trade within the increasingly connected world necessitated a system that allowed measuring and counting across language barriers. The current base 10 place value system evolved to meet this need. It is used almost universally, or at least by every country that trades in the international markets. This system evolved as global cultures met and mingled, and their various number systems were necessarily adapted to allow for more precise communication.
Early number systems were visual and emphasized quantity by observation. These systems started by drawing a numeral glyph, or symbol, as one vertical segment, horizontal segment, knot, or symbol. Symbols for 2 and 3 were drawn as repeats of a mark for 1. The “one, two, many” theory suggests that some cultures developed words for “one” and “two” before anything else, and any amounts greater than two were simply referred to as “many.” For a family or small tribe, differentiation among only small quantities was sufficient (some aboriginal tribes in the Amazon may still use a numbering system like one-two-many). As human communities grew and lifestyles became more complex, a continual series of dots and dashes was hard to read quickly and consistently. The glyphs therefore evolved to accommodate human needs and physical limitations.
One well-known ancient system still in use today is Roman numerals. Roman numerals are visual, “picture,” glyphs that describe quantities and dates. In this system, 1 is a vertical line (I) and 2 is two vertical lines (II). Rather than merely continuing with vertical lines ad infinitum, however, special glyphs were developed to represent 5 (V), 10 (X), 50 (L), 100 (C), 500 (D), etc. Subtraction was later introduced as another strategy to shorten the writing: 4 was written as IV (representing 5 minus 1), 9 was written as IX (10 minus 1), and 499 was written as ID (500 minus 1). The currently used Roman numeral glyphs are not necessarily the same as when the system began. It was adapted over time to simplify the way it was written and accommodate an ever-growing and more complex “global community.” Such adaptations, and the meeting and comingling of various systems, eventually led to our current universal number system.
* There are two possible variations for 1. The other is: (to be added)
Figure 1. Roman, Incan Quipu, Babylonian, Egyptian, and Chinese early number systems. Many have been lost to history but others, like the Chinese, remain, with evolutionary changes.
The Incan Quipu system was a primitive place value system; when 10 was reached, the knot counting started over with an empty space between the 1s, 10s, 100s, etc. The Chinese system was also a primitive place value system; these glyphs represent ivory or bamboo rods that were placed in a checker board-like “counting board.” The right-most column represented the ones, the next column to the left the tens, etc.
Different elements of the current base 10 place value system originated in different societies. While these global cultures developed independently and in isolation from each other, some important similarities can nonetheless be noted. All early numbering systems were based on counting, as numerical communication involved building temples, houses, and roads; measuring distances; and dividing crops for work payment. Most systems began with a 1 and continued along a “number line,” easily adapted to a measuring tool. Few cultures had an official zero, no matter what the “base” of the system. Eventually, it became clear that a simplistic picture-based counting system was inadequate for situations involving larger sums and numbers. Commerce and development required a way to easily distinguish 60 from 360 in a base 60 system, for example, or 10 from 100 in a base 10 system. The earliest solutions involved symbols, such as commas (Babylon) or blank counting rods (China), to represent a primitive form of place value. While Mayans were interested in elapsed time, and so their numbering system included a zero (0) as a starting point, assigning 0 the critical role in a place-value system did not come until much later.
Where Did “Arabic Numerals” Come From?
When did the world switch from these ancient systems to the contemporary numerals used today? The introduction of the printing press in the mid-1500s led to a “standard” set of numeral glyphs. Some countries or tribes do still write the numerals 0-9 slightly differently, as if writing with different dialects. Like an American speaking to a British citizen, these differences (such as a long-angled 1 or a cross on the “body” of a 7) rarely impede understanding.
Our current numerals are often called “Arabic” or “Hindu-Arabic” numerals, but their history is actually rather complicated and multi-cultural. Most historians believe the current numbers, and the origin of a place-value zero (0), come from India (most often attributed to the Brahmi system).1 Much of Europe was confused by the concept of nothing, and left it out of their formal counting systems. It was not necessary to define zero until trade required the ability to denote quantities “ordered but not yet delivered” or of poor quality. Statements of debt and IOUs could only be written in text until the introduction of zero and negative numbers provided a numerical notation. As prominent world traders, Arabs spread the concept of Hindu/Brahmi numerals around the world, often referred to as Hindu-Arabic numerals.
Why was the system from India adopted widely, rather than Roman numerals or another ancient number system? Accountants and other record-keepers desired a system that was less time-consuming to write and a place value system “fit the bill.” Earlier systems may have been nice for visual communication, but were time-consuming to learn and write and difficult to use for arithmetic.
As various countries, tribes, and other groups of humans joined the evolving global economy, they adopted the Hindu-Arabic numeral system. This now universal system simultaneously allows for global communication and retains a lot of evolving human history, evident in its various components. If a country, tribe, or group decides to remain independent, as many in the Amazon have, they do not need to adopt this system. However, participation in global trade demands adoption of the system to facilitate and provide consistency in trade. Although we do not have a universal language (yet) to describe all products traded, specific quantities and measurements are identified using the now-standard Hindu-Arabic numerals.
Figure 2. Evolution of Brahmi numeral system to modern glyphs
How Do We Display and Explain the Universality of Numbers?
As Dr. Rebecca Klemm travels the world speaking about the meaning of numbers, she is often asked if all countries really use the same numbers. When she realized that many educators and parents did not realize or understand the universality of numbers, she was inspired to create a learning tool to illustrate how one system of numbers is used worldwide and thus serves as a powerful example of an organically developed global agreement.
She developed a poster for educators that showed the universality of the numeral glyphs 0-9, and how they are written in the major languages of the world. This resource illustrates visually that we all use the same numerals/number system, and also highlights that we write them slightly differently in each individual language, or language family.
The poster includes languages from each continent (other than Antarctica), those that contributed most to world trade and those that were spoken and/or written by the greatest portions of the global population. Identifying which languages to include was difficult, as there are literally thousands of languages spoken and/or written around the world, with about one-third of them spoken by 1,000 people or fewer.
In the center section of the poster, 28 currently spoken languages are listed, providing a visual demonstration of the variability of written languages in describing one concept. The languages are grouped into:
• The six official languages of the United Nations (English, French, Spanish, Mandarin Chinese, Russian, and Arabic)
• Other languages spoken/written across all continents
• Visual and kinesthetic languages (American Sign Language, maritime signal flags, and die-cut braille all “viewers” can engage with)
• Computer language (i.e., binary or base two)
• Two “constructed” languages: Esperanto and Klingon.2
When multiple languages use the same glyphs for the numbers, one language is included as a representation of the language family (e.g., Mandarin, Cantonese, and Japanese are represented by Chinese). Along the border of the poster, the word “numbers” is translated into 36 other languages.3
Figure 3. World Numbers Poster © Rebecca Klemm and NumbersAlive! Press 2013
Why Should We Discuss and Teach the Universality of Numbers?
The universal nature of the world’s “standardized” number system is an important aspect of modern, globalized society for many reasons. It is a valuable and prominent example of an important system that was created through international cooperation, whether intentional or not. The system we use today was developed over time, as societies developed and began to interact with each other. The story of humankind’s journey from isolated communities into a global society is important to learn and teach in order to encourage future generations to understand the importance of and continue to pursue international trade and other relationships. The history of our modern number system also demonstrates that no non-protected societies exist in isolation. Given the ease and popularity of travel and communication today, in addition to the continued importance of international trade, it makes even more sense to tap into the different experiences and insights of various cultures and peoples as we continue to improve global society.
In addition, understanding the history of our universal number system can contribute to discussions about how ideas are shared and transmitted. This article examined trade as a catalyst for globalization of the “Arabic” numeral system, but trade was not the only way ideas were spread. Historically, conquest and colonization also played a role, as have religious missionaries. Even today, as we develop new and easier ways to communicate and travel, we are really developing new and easier ways to spread ideas, practices, and perspectives that are already leading to new projects that would have been inconceivable without such collaboration.
In conclusion, the universality of our number system offers proof that we are all inextricably connected. It is important to recognize this so that we and future generations can take advantage of the possibilities that international collaboration opens up.
Questions for Further Discussion:
1. What else can you think of that was influenced by multiple cultures/societies? Alternately, what hasn’t been influenced by multiple cultures/societies?
2. How would the world be different if we didn’t have one universal number system? How would it be different if we all adopted Esperanto?
3. Why did the attempt to create a universal language fail while a universal number system appeared to develop organically?
4. What projects require collaboration to be usable/best form, either at a personal or global level?
1 Read about some new findings regarding the history of the zero symbol https://www.theguardian.com/science/2017/sep/14/much-ado-about-nothing-ancient-indian-text-contains-earliest-zero-symbol
2 Esperanto was developed by Polish-Jewish ophthalmologist L. L. Zamenhof and first published in Unua Libro, on 26 July 1887. It is the most widely spoken constructed language in the world. Klingon was fully developed for the science fiction franchise Star Trek, as an alien-sounding language and was fully described in the 1985 book, The Klingon Dictionary, by Marc Okrand.
3 Slovenian, Albanian, Belarussian, Tajik, Latvian, Czech, Danish, Dutch & Flemish, Zulu, Macedonian, Filipino, Yiddish, Latin, Lithuanian, Hmong, Telugu, Serbian, Norwegian, Hungarian, Haitian Creole, Romanian, Kurdish, Estonian, Hawaiian, Gujarati, Ukrainian, Afrikaans, Galician, Persian/Farsi/Dari, Uzbek, Turkmen, Georgian, Armenian, Kikuyu, Samoan, Kazakh.
Exploring Universality: Does the World Really Use the Same Numbers?, Childhood Education, Volume 93, 2017 – Issue 6: Global Citizenship Education on Nov 10, 2017, Taylor & Francis online at http://www.tandfonline.com/doi/full/10.1080/00094056.2017.1398563