Issue Number 255 April 15, 2019

This free Information Age Education Newsletter is edited by Dave Moursund and produced by Ken Loge. The newsletter is one component of the Information Age Education (IAE) and Advancement of Globally Appropriate Technology and Education (AGATE) publications.

All back issues of the newsletter and subscription information are available online. In addition, seven free books based on the newsletters are available: Joy of Learning; Validity and Credibility of Information; Education for Students’ Futures; Understanding and Mastering Complexity; Consciousness and Morality: Recent Research Developments; Creating an Appropriate 21st Century Education; and Common Core State Standards for Education in America.

Dave Moursund’s newly revised and updated book, The Fourth R (Second Edition), is now available in both English and Spanish (Moursund, 2018c). The unifying theme of the book is that the 4th R of Reasoning/Computational Thinking is fundamental to empowering today’s students and their teachers throughout the K-12 curriculum. The first edition was published in December, 2016, the second edition in August, 2018, and the Spanish translation of the second edition in September, 2018. The three books have now had a combined total of more than 37,500 page-views and downloads.

Dave Moursund’s newly revised and updated book, The Fourth R (Second Edition), is now available in both English and Spanish (Moursund, 2018, link). The unifying theme of the book is that the 4th R of Reasoning/Computational Thinking is fundamental to empowering today’s students and their teachers throughout the K-12 curriculum. The first edition was published in December, 2016, the second edition in August, 2018, and the Spanish translation of the second edition in September, 2018. The three books have now had a combined total of more than 37,000 page-views and downloads.

Note to readers: The ongoing series on ICT Tools and the Future of Education will be continued in IAE Newsletter #255.

Some Roles of ICT and Math
in the History Curriculum (Chapter 2)

David Moursund
Professor Emeritus, College of Education
University of Oregon

Chapter 2: History Includes a Great Deal of Quantitative Data

“If it can’t be expressed in figures, it is not science, it is opinion.” (Robert A. Heinlein; American science fiction author; 1907-1988.)

Robert Heinlein’s quote reminds us that the sciences are based on data and therefore different from other disciplines of study. However, much of recorded history includes dates, time, distance, locations, amounts of money, and other quantitative data. We now use Information and Communication Technology (ICT) to compile, organize, and access this quantitative data. It is important that our history students become comfortable users of ICT and math in order to work with quantitative data, i.e., they are competently ICTing and mathing across the history curriculum.

Censuses are good examples of historical, quantitative data (Wikipedia, 2019b, link):

One of the world's earliest preserved censuses was held in China in AD 2 during the Han Dynasty, and is still considered by scholars to be quite accurate. The population was registered as having 57,671,400 individuals in 12,366,470 households.

Because I am a mathematician, I naturally used my math background as I thought about these census results. As part of my fact checking, I computed that the data indicated the average household size was 4.66 people. That seemed reasonable to me, since in those times people had large families, but many children died at childbirth or in their early childhood, and life expectancy was considerably less than it is today. I used the Web to determine that the average household size in the U.S. census of 1920 was 4.34. That reinforced my belief that the Chinese data were correct.

This Chinese census was a very impressive undertaking! I wonder about the mechanics of organizing and carrying out such a huge task. Could the census takers read and write? The percentage of the total population that could read and write at that time was quite small. I wonder how the census takers avoided duplications or missing people. I wonder about the accuracy of the reporting. How long did it take to do the census? Undoubtedly there were a number of births and deaths during that time period.

I wonder how information about this census has been preserved for more than 2,000 years. That’s an interesting question. Nowadays, humans store much of their collected data on computers. How long will this data last? This question underlies an entire modern discipline of study and research.

The Web article gave the Chinese census results in base 10 notation. I wondered what number system was being used in 2 AD. My Google search indicated that the Chinese developed a base 10 number system hundreds of years earlier, long before people in the “West” developed such a system. Indeed, the Hindu-Arabic base 10 number system was developed in India about 600 years after the Chinese census was taken. This example raises the question of what else did the Chinese invent first?

This is an aside: An amusing question—irrelevant to the data—occurred to me. Suppose that starting in 2 AD, this Chinese population doubled every century, up to the current time. What would that population be now? It would be more than a million times what it was in 2 AD. Since that did not occur, this raises a serious historical question about what prevented such population growth over the past 2,000 years. Here is a hint. What is the carrying capacity of the earth? That is, with current methods of food production, how many people can the earth feed by making use of all possible land that is not required for housing and other purposes? Clearly, disease, war, and starvation have had very major impacts on population.

These census examples led me to thinking about calendars. The date of the Chinese census is given as AD 2, and we recognize this as a Gregorian calendar date (Time and Date, 2019, link). Because we know that the Gregorian calendar was not developed until 1582, the original Chinese census data could not have been found with the year AD 2 already dated on it. Once again, the Web to my rescue. The beginnings of the Chinese calendar can be traced back to the 14th century B.C.E. The Chinese calendar is based on exact astronomical observations of the longitude of the sun and the phases of the moon.

This example emphasizes that the history of calendars can be an interesting and sometimes challenging discipline of study. We know that the date of the time at which an historical event occurred may be assigned to different years as different calendars are developed. Here’s an interesting question to pose to students, “If you were excavating a very old historical site and found a coin stamped with the date AD 2, would you immediately recognize it as a counterfeit?”

United States Census

The first census taken in the United States was in 1790 (Wikipedia, 2019a, link).

The United States Census of 1790 was the first census of the whole United States. It recorded the population of the United States as of Census Day, August 2, 1790, as mandated by Article I, Section 2 of the United States Constitution and applicable laws. In the first census, the population of the United States was enumerated to be 3,929,214.

Census data included the name of the head of the family and categorized inhabitants as follows: free white males at least 16 years of age (to assess the country's industrial and military potential), free white males under 16 years of age, free white females, all other free persons (reported by sex and color), and slaves.

Here are a few pieces of data from the 1790 U.S. census cited above:
I think what is most interesting about such data are the stories behind the data. For example, the U.S. Declaration of Independence states:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.

But, certainly slaves were not considered to be equal! Population data was needed to apportion the members of the House of Representatives among the states. Quoting from the original U.S. Constitution (U.S. House of Representatives, 2019, link).

Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons. The actual Enumeration shall be made within three Years after the first Meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such Manner as they shall by Law direct.

In this document, a slave counted as 3/5 of a person. What’s the story behind that?

Women were counted in apportioning the House of Representatives, but they could not vote. What’s the story behind that?

Notice the very small proportion of non-white free people in the U.S. in 1790. What’s the story behind that?


Access to Census Data

You have heard the statement, “Knowledge is power.” My quick search of the Web indicates this statement goes back more than 2,000 years. As more and more data are collected from all aspects of our daily lives, the question arises as to who should be able to access and use this important information.

For example, who should have access to the U.S. Census data, and when? This question was addressed by the U.S. Congress 40 years ago by Public Law 95-416 passed on October 5, 1978. The law protects census data for 72 years, and restricts access to decennial census records to all but the individual named on the record or their legal heir.

I find it interesting that the U.S has a law about the use of census data, but has relatively few restrictions about what individual companies can do in terms of collecting and using personal data. The laws in Europe are much more restrictive than are those in the United States.

Taxes

It was Benjamin Franklin, one of America’s founding fathers, who said, "In this world nothing can be said to be certain, except death and taxes." As students study taxes and taxation systems in America and throughout the world, they are yet again involved in ICTing and mathing across the history curriculum.

Long before the Agricultural Age began, a typical small clan of hunter-gathers roamed over an area that was probably less than a thousand square miles in size. (For example, think of a rectangular area that is 50 miles by 20 miles.) The clan had a leader, but did not have money and taxes. A primitive barter system sufficed for the exchange of goods with neighboring clans.

The Agricultural Age, beginning about 12,000 years ago, led to people living in fixed locations with relatively small populations. As populations grew, more complex systems of governance developed, and the cost of this government had to somehow be paid by those being governed. Over many centuries, large cites (city-states) developed, leading to the need for larger-sized governmental projects, including armies (Carlson, 9/1/2004, link):

The earliest known tax records, dating from approximately six thousand years B.C., are in the form of clay tablets found in the ancient city-state of Lagash in modern day Iraq.….
In Lagash taxes were very low, but in a time of crisis or war the tax rate was ten percent of all goods, which were primarily composed of food.

The last sentence indicates a tax rate of ten percent that was being used roughly 8,000 years ago. The tax rate of ten percent reminds me of tithing as mentioned in the Old Testament of the Bible. I also was curious about the use of the precise figure of ten percent. Has tithing always been ten percent across the world and throughout the centuries?

This led me to wonder when were the written mathematical ideas of fractions and percentages developed? My Web search indicated that fractions were used in ancient Rome, perhaps as long as 2,800 years ago. Roman mathematical computations were sometimes expressed in fractions of 100, and this concept later evolved into percentages.

Final Remarks

Earlier in this series, I quoted British historian Arnold J. Toynbee, "History not used is nothing, for all intellectual life is action, like practical life, and if you don't use the stuff well, it might as well be dead."

Think about substituting the word math for the word history in Toynbee’s quote. Our schools require students to take many years of math. This instruction emphasizes both math content and uses of math to help solve problems. When I write and talk about mathing across the curriculum, I mean learning to use math as an aid to understanding and solving problems across the curriculum. I also write and talk about today’s many uses of Information and Communication Technology (ICT) in all discipline areas. Thus, my unifying theme is ICTing and Mathing across all of the curriculum.

One of my most favorite math quotes is from Leopold Kronecker, a Prussian mathematician and logician who argued that arithmetic and analysis must be founded on whole numbers, “God made the integers; all the rest is the work of man.”

In essence, Kronecker was saying that, except for the integers, all of math was created by people. From that point of view, most of the math content that students learn in school today is relatively ancient history, and this history is rooted in human needs to solve problems that were important individually and/or in their societies.

I believe the teaching of history at the precollege level can be made more interesting to students if more emphasis is placed on the types of problems that people have been trying to solve over the centuries. We can gain increased insight into some of these problems through the analysis of quantitative data that has been gathered. Today’s students can relate to the historical census and tax data discussed here as examples of such data in the daily lives of the people they are studying.

References and Resources

Carlson, R.H. (9/1/2004). A brief history of property tax. Retrieved 3/22/2019 from http://webcache.googleusercontent.com/search?q=cache:NiIG_galrq4J:www.websitebox.com/file/7329/Property_Tax_History_1_-_Shortened.pdf+&cd=3&hl=en&ct=clnk&gl=us&client=firefox-b-1-d.

Moursund, D. (2018). The Fourth R (Second Edition). Eugene, OR: Information Age Education. Retrieved 3/21/2019 from http://iae-pedia.org/The_Fourth_R_(Second_Edition). Download the Microsoft Word file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/307-the-fourth-r-second-edition.html. Download the PDF file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/308-the-fourth-r-second-edition-1.html. Download the Spanish edition from http://iae-pedia.org/La_Cuarta_R_(Segunda_Edici%C3%B3n).

Time and Date (2019). The Gregorian calendar. Retrieved 3/25/2019 from https://www.timeanddate.com/calendar/gregorian-calendar.html.

U.S. House of Representatives (2019). Proportional representation. Retrieved 3/25/2019 from https://history.house.gov/Institution/Origins-Development/Proportional-Representation/.

Wikipedia (2019a). 1790 United States census. Retrieved 3/21/2019 from https: //en.wikipedia.org/wiki/1790_United_States_Census.

Wikipedia (2019b). Census. Retrieved 3/24/2019 from https://en.wikipedia.org/wiki/Census.

Author

David Moursund is an Emeritus Professor of Education at the University of Oregon, and editor of the IAE Newsletter. His professional career includes founding the International Society for Technology in Education (ISTE) in 1979, serving as ISTE’s executive officer for 19 years, and establishing ISTE’s flagship publication, Learning and Leading with Technology (now published by ISTE as Empowered Learner).He was the major professor or co-major professor for 82 doctoral students. He has presented hundreds of professional talks and workshops. He has authored or coauthored more than 60 academic books and hundreds of articles. Many of these books are available free online. See http://iaepedia.org/David_Moursund_Books .

In 2007, Moursund founded Information Age Education (IAE). IAE provides free online educational materials via its IAE-pedia, IAE Newsletter, IAE Blog, and IAE books. See http://iaepedia.org/Main_Page#IAE_in_a_Nutshell . Information Age Education is now fully integrated into the 501(c)(3) non-profit corporation, Advancement of Globally Appropriate Technology and Education (AGATE) that was established in 2016. David Moursund is the Chief Executive Officer of AGATE.

Email: moursund@uoregon.edu.

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