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The History of Counting
Drawing on years of research, a renowned archaeologist traces the evolution of counting. She shows how the concept of numbers came about, how various societies answered the question "How many?," and how our modern-day decimal system was developed. Engrossing and enlightening, this fascinating book introduces children to one of our most important inventions. 00-01 Utah Book Award (Informational Books) Notable Children's Trade Books in the Field of Social Studies 2000, National Council for SS & Child. Book Council
Hardcover
First published August 25, 1999
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Displaying 1 - 19 of 19 reviews
August 29, 2018
Great visual for young students to learn about the history of counting. This may even be new to most adults. Who ever questions where the numbers come from that we use every day or the importance of the placeholder 0, a digit that changed and advanced computation of numbers forever and propelled us to today!
This book illustrates the earliest known counting methods / systems. From counting without numbers, to concrete counting to abstract counting. Presenting the earliest counting devices from notches in bones of hunters and gatherers, Sumerian tokens, Numerals, Phoenician number base of 10, Greek numeral system, Roman numerals and the comparison of computing numbers to today's methods.
Really interesting and captures the attention of even the most uninterested students ;)
This book illustrates the earliest known counting methods / systems. From counting without numbers, to concrete counting to abstract counting. Presenting the earliest counting devices from notches in bones of hunters and gatherers, Sumerian tokens, Numerals, Phoenician number base of 10, Greek numeral system, Roman numerals and the comparison of computing numbers to today's methods.
Really interesting and captures the attention of even the most uninterested students ;)
December 8, 2019
Another unsuccessful attempt to stock our home library with some "beauty of math" content.
The first problem with this one is that I'm not sure who the target audience is.
(Italics shown are copied from the text)
^^ These are two paragraphs of five on a single page of a picture book, one which discusses concrete counting. This page introduces the Gilyak people and their counting system, then the quote above. The paragraphs are broken up by a smallish illustration of groups of two labeled with their Gilyak grouping names. This is okay, I guess. But then facing all this text is a full-page illustration of two men playing music (a saxophone and a guitar) in front of an audience.
I don't know. Who is this for?
Given the vocabulary and quantity of text, I'm assuming this is meant to be read aloud to kids 6-8yo, or maybe read-to-self 8yo-9yo range ... but at least half of the illustrations, like our musician friends, don't serve to add to or clarify the text.
I'm trying to imagine a third or fourth grader -- the age at which read-to-self seems maybe viable for this -- feeling engaged by this, and I can't. Trying to imagine that same fourth grader in a read aloud setting, and I don't see the illustrations being of help to hold her interest. Trying to imagine a younger crowd listening attentively to these sentences about taxation or how the Romans indicated thousands, and I don't see that happening, either.
My second problem is that this book, like so many others, fails to give due attention to India and does not even mention China.
After going out of their way to fit in half a page on the Gilyak of Russia, and on the Paiela of Papua New Guinea, the book gives only a brief nod to India with "The Arabs, however, called** these digits Hindu numerals because they had borrowed them from India. The earliest document bearing such numerals was written in the Indian Sanskrit language, about fifteen hundred years ago."
**past tense? I don't read or speak Arabic, but this feels wrong.
So. The people credited with the single most important leap in numeric script, and the discovery/invention of zero -- I mean to say, the culmination of this entire book -- gets only a passing mention. Le sigh.
And then, no China? Come on, now. The Chinese counting system predates the Roman one by about a millenium, and their abacus was brilliant. ALSO THERE ARE 1.7 BILLION PEOPLE STILL USING THIS NUMBER SYSTEM TODAY, right alongside the numerals we Westerners call Arabic.
While I applaud the concerted attempt to expand horizons by including Russia and Papua New Guinea in this conversation, it's simply inexcusable to limit mention of foreigners to those with "primitive" counting practices and to exclude the two most populous countries in the world from their rightful places in _The History of Counting_.
The first problem with this one is that I'm not sure who the target audience is.
Concrete counting shows how societies around the world faced the problem of handling plurality, or groups of many items, and found different solutions to express numbers.
The concrete numbers are similar to our terms twins, triplets, quadruplets, which refer to the number of children of the same birth, and duo, trio, quartet, which refer to groups of musicians. Both number words -- twins and duo -- indicate 2. But in neither case does the word separate the number from the thing that is being counted.
(Italics shown are copied from the text)
^^ These are two paragraphs of five on a single page of a picture book, one which discusses concrete counting. This page introduces the Gilyak people and their counting system, then the quote above. The paragraphs are broken up by a smallish illustration of groups of two labeled with their Gilyak grouping names. This is okay, I guess. But then facing all this text is a full-page illustration of two men playing music (a saxophone and a guitar) in front of an audience.
I don't know. Who is this for?
Given the vocabulary and quantity of text, I'm assuming this is meant to be read aloud to kids 6-8yo, or maybe read-to-self 8yo-9yo range ... but at least half of the illustrations, like our musician friends, don't serve to add to or clarify the text.
I'm trying to imagine a third or fourth grader -- the age at which read-to-self seems maybe viable for this -- feeling engaged by this, and I can't. Trying to imagine that same fourth grader in a read aloud setting, and I don't see the illustrations being of help to hold her interest. Trying to imagine a younger crowd listening attentively to these sentences about taxation or how the Romans indicated thousands, and I don't see that happening, either.
My second problem is that this book, like so many others, fails to give due attention to India and does not even mention China.
After going out of their way to fit in half a page on the Gilyak of Russia, and on the Paiela of Papua New Guinea, the book gives only a brief nod to India with "The Arabs, however, called** these digits Hindu numerals because they had borrowed them from India. The earliest document bearing such numerals was written in the Indian Sanskrit language, about fifteen hundred years ago."
**past tense? I don't read or speak Arabic, but this feels wrong.
So. The people credited with the single most important leap in numeric script, and the discovery/invention of zero -- I mean to say, the culmination of this entire book -- gets only a passing mention. Le sigh.
And then, no China? Come on, now. The Chinese counting system predates the Roman one by about a millenium, and their abacus was brilliant. ALSO THERE ARE 1.7 BILLION PEOPLE STILL USING THIS NUMBER SYSTEM TODAY, right alongside the numerals we Westerners call Arabic.
While I applaud the concerted attempt to expand horizons by including Russia and Papua New Guinea in this conversation, it's simply inexcusable to limit mention of foreigners to those with "primitive" counting practices and to exclude the two most populous countries in the world from their rightful places in _The History of Counting_.
March 9, 2015
I give it epsilon (5) stars! There is a lot of information in this little book. It gives an overview of how numbers were developed, how different cultures counted before the use of Arabic numerals, how Arabic numerals were actually developed from Sanskrit (that I didn't know) among other things. A great read-aloud for early elementary, or a read-by-yourself for older elementary to middle school. There are a lot of things in this book not typically taught in schools, many things even adults (i.e., my mom) won't know!
October 23, 2012
There was a lot of information packed into this book and we found ourselves stopping and discussing every couple of pages. The illustrations were wonderful and integral to understanding the concepts presented. A very in depth summary of the History of Counting.
March 7, 2020
I honestly was not expecting this to be as good as it is. But it is very good and taught me a lot that I didn't know.
Some interesting facts in the book:
"In the recent past, the Veddas of Sri Lanka, who lived by eating the fruit and tubers of jungle plants, had only a few general words, such as a single, a couple, another one, and many, to deal with numbers."
It talks about body counting (pointing to a specific place on the body to represent each number). It does put a limit on the largest number. In Papua New Guinea the Paiela's highest number was 28 shown by two hands clenched together while in Paraguay, South America the highest number for those native people was 20.
"Still other peoples count concretely. This means that they use different sets, or groups, of numbers to count different categories of things. For example, the Gilyaks, who farm along the river Amur, in eastern Russia, have twenty-four sets of numbers. when a Gilyak counts trees, sticks, pencils, and some other long things, she uses the word mex for the number 2. When counting leaves, pieces of textile, and other flat items, she will use met for 2. And for berries balls and other round things 2 becomes mik. Note also that the Gilyaks' number sequences never reach much beyond 20. In other words, concrete numbers do not allow large quantities to be counted. concrete counting shows how societies around the world faced the problem of handling plurality, or groups of many items, and found different solutions to express numbers. The concrete numbers are similar to our terms twins, triplets, quadruplets, which refer to the number of children of the same birth, and duo, trio, quartet, which refer to groups of musicians. Both number words-twins and duo-indicate 2. But in neither case does the word separate the number from the thing that is being counted. The most universal way of counting, the one the majority of people use today, is known as abstract counting, using abstract numbers. We separate, or abstract, the idea of "one," "two," "three," and so on, from the thing we are counting. This system is very convenient because abstract numbers count anything and each abstract number is expressed by a word that remains the same no matter what is being counted."
"We owe the invention of abstract numbers to the Sumerians who lived in the first cities, in the region of present-day Iraq, about five thousand years ago. The Sumerian tablet in the man's hand shows an account of thirty-three jars of oil The sign on the right stands for "jar of oil." The other signs represent numbers. each circle is 10, and each long sign is 1."
"with the greater use of numbers also came the need for larger and larger numbers. In the country of Sumer, the most common large number that was used in everyday life was 60. It was called "the big one," which suggests that, at some time, it had been the highest number. But by 2500 B.C., the Sumerian largest number had grown to 36,000."
The Greeks (as the Phoenicians had done before them) used their letters as numbers. The first nine letters were the digits 1 through 9. The next nine letters stood for tens, and the last nine letters were the hundreds. The last letter stood for 900. They would then add small superscript signs to those numbers to indicate higher values.
"The Greek numeral system was troublesome, because it used as may as twenty-seven signs. By 200 B.C., the Romans improved on it by reducing the number of signs to seven letters." I for one, V for 5, X for 10, L for 50, C for 100, D for 500 and M for 1000. The fact that it didn't go beyond 1,000 indicates that most people had little need for numbers so high. However, by adding a line above a symbol they could multiply that number by 1,000.
"Where and when the Arabic numerals were invented is a mystery. So is the identity of their inventor. Why then are the digits of our counting system called Arabic numerals? Because it was the Arabs who brought them to Europe, around the year A.D. 1000, when they ruled Spain. The Arabs, however, called these digits Hindu numerals, because they had borrowed them from India. The earliest document bearing such numerals was written in the ancient Indian Sanskrit language, about fifteen hundred years ago. No one knows how long the system was used before that or what preceded it. The transition from Roman to Arabic numerals took centuries. The Europeans refused to change the old ways, saying for instance, that the signs for 2 and 3 could be easily confused. Finally, by around 1650, Arabic numerals were fully accepted in Europe."
Some interesting facts in the book:
"In the recent past, the Veddas of Sri Lanka, who lived by eating the fruit and tubers of jungle plants, had only a few general words, such as a single, a couple, another one, and many, to deal with numbers."
It talks about body counting (pointing to a specific place on the body to represent each number). It does put a limit on the largest number. In Papua New Guinea the Paiela's highest number was 28 shown by two hands clenched together while in Paraguay, South America the highest number for those native people was 20.
"Still other peoples count concretely. This means that they use different sets, or groups, of numbers to count different categories of things. For example, the Gilyaks, who farm along the river Amur, in eastern Russia, have twenty-four sets of numbers. when a Gilyak counts trees, sticks, pencils, and some other long things, she uses the word mex for the number 2. When counting leaves, pieces of textile, and other flat items, she will use met for 2. And for berries balls and other round things 2 becomes mik. Note also that the Gilyaks' number sequences never reach much beyond 20. In other words, concrete numbers do not allow large quantities to be counted. concrete counting shows how societies around the world faced the problem of handling plurality, or groups of many items, and found different solutions to express numbers. The concrete numbers are similar to our terms twins, triplets, quadruplets, which refer to the number of children of the same birth, and duo, trio, quartet, which refer to groups of musicians. Both number words-twins and duo-indicate 2. But in neither case does the word separate the number from the thing that is being counted. The most universal way of counting, the one the majority of people use today, is known as abstract counting, using abstract numbers. We separate, or abstract, the idea of "one," "two," "three," and so on, from the thing we are counting. This system is very convenient because abstract numbers count anything and each abstract number is expressed by a word that remains the same no matter what is being counted."
"We owe the invention of abstract numbers to the Sumerians who lived in the first cities, in the region of present-day Iraq, about five thousand years ago. The Sumerian tablet in the man's hand shows an account of thirty-three jars of oil The sign on the right stands for "jar of oil." The other signs represent numbers. each circle is 10, and each long sign is 1."
"with the greater use of numbers also came the need for larger and larger numbers. In the country of Sumer, the most common large number that was used in everyday life was 60. It was called "the big one," which suggests that, at some time, it had been the highest number. But by 2500 B.C., the Sumerian largest number had grown to 36,000."
The Greeks (as the Phoenicians had done before them) used their letters as numbers. The first nine letters were the digits 1 through 9. The next nine letters stood for tens, and the last nine letters were the hundreds. The last letter stood for 900. They would then add small superscript signs to those numbers to indicate higher values.
"The Greek numeral system was troublesome, because it used as may as twenty-seven signs. By 200 B.C., the Romans improved on it by reducing the number of signs to seven letters." I for one, V for 5, X for 10, L for 50, C for 100, D for 500 and M for 1000. The fact that it didn't go beyond 1,000 indicates that most people had little need for numbers so high. However, by adding a line above a symbol they could multiply that number by 1,000.
"Where and when the Arabic numerals were invented is a mystery. So is the identity of their inventor. Why then are the digits of our counting system called Arabic numerals? Because it was the Arabs who brought them to Europe, around the year A.D. 1000, when they ruled Spain. The Arabs, however, called these digits Hindu numerals, because they had borrowed them from India. The earliest document bearing such numerals was written in the ancient Indian Sanskrit language, about fifteen hundred years ago. No one knows how long the system was used before that or what preceded it. The transition from Roman to Arabic numerals took centuries. The Europeans refused to change the old ways, saying for instance, that the signs for 2 and 3 could be easily confused. Finally, by around 1650, Arabic numerals were fully accepted in Europe."
This entire review has been hidden because of spoilers.
August 31, 2017
This book was soo interesting! Math, history, geography, and culture all in one. The history of counting is a big story to tell, and the author does a good job here, making it succinct, clear, and full of fascinating details. I think it's key that she actually depicted pretty much all the systems she discussed - so kids can body-count or write in Sumarian symbols or Roman numerals.
Based on length, vocabulary and complexity of the concept, best for upper elementary or middle school (though I learned much and enjoyed doing so as a grown-up!).
Based on length, vocabulary and complexity of the concept, best for upper elementary or middle school (though I learned much and enjoyed doing so as a grown-up!).
August 11, 2020
This book is very well put together. Great illustrations to go along with the timeline of the development of counting and number systems. I think most people will learn something from this book, and it is very approachable for kids! The book includes a great glossary.
May 1, 2018
Probably way over the heads of most kids, but very interesting to me!!!
October 29, 2019
3-4 stars. Interesting but a bit long and boring.
June 28, 2020
This is a perfect book to read slowly, spreading over a 12 week term.
My kids were fascinated to learn about different ways of counting and how people through time and space have though about math.
My kids were fascinated to learn about different ways of counting and how people through time and space have though about math.
March 7, 2021
Very interesting!
September 16, 2022
Indispensible book for teachers and elementary classrooms. Beautiful and intriguing.
October 10, 2015
To say that this book traces the development of counting would by accurate, but certainly wouldn't give the author all the credit do her. An archaeologist who specializes in the Middle East, Schmandt-Besserat has focused her expertise on one of humankind's most essential activities. Written with scientific accuracy, the book makes this complex topic very accessible without losing track of important details.
The History of Counting moves from primitive counting methods through the expected ancient civilizations from Sumerian to Roman and finally to the Arabic system used today. The text is enriched with discussions of abstract counting, the use of ten digits and a look at people such as the Paiela of Papua New Guinea who utilize unique methods for counting or reckoning "how many."
Written at a fifth grade level, the book includes a glossary and is illustrated with glowing paintings that provide a beautiful counterpoint to the text.
The History of Counting moves from primitive counting methods through the expected ancient civilizations from Sumerian to Roman and finally to the Arabic system used today. The text is enriched with discussions of abstract counting, the use of ten digits and a look at people such as the Paiela of Papua New Guinea who utilize unique methods for counting or reckoning "how many."
Written at a fifth grade level, the book includes a glossary and is illustrated with glowing paintings that provide a beautiful counterpoint to the text.
February 13, 2017
Well, I learned a few things from this book. I had never heard of the 3 types of counting before: counting without numbers, concrete counting (eg., body counting), and abstract counting, which are the three stages in the development of counting into what we know it today. I also never knew about the marks that the Greeks and Romans used with their letter numerals to form larger numbers. This would be a great book to use in an introductory math class, to give a multicultural, historical aspect to the subject.
Most interesting!
Most interesting!
February 22, 2011
This is a book written by the same author who wrote the top-notch counting book my husband used in his anthropology class. It's simplified for kids with beautiful pictures added. It's excellent, though I need to stop trying to read it to 4 year olds. It goes a bit over their heads. I think I'll read it to the 7 year old again, I think he'll appreciate it more this time. :)
December 12, 2010
I loved the illustrations in this book. It was very interesting, and well done. It covers what an amazing invention the number 0 was, and how it has revolutionized the way that we work with numbers and can do calculations. This is one I definitely want to revisit when my children are older.
September 19, 2008
513.5 SCH
We used this for the lesson on counting. Comprehensive enough to overview counting's history, then the reader can do more research if wanted.
We used this for the lesson on counting. Comprehensive enough to overview counting's history, then the reader can do more research if wanted.
May 6, 2015
Inspired me to start counting the books I read.
Read
November 12, 2011Used to teach about the historical and cultural aspects of numbers and counting.
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