Introduction to ICTing and Mathing Across the History Curriculum. Part 5

The early history of weights and measures in the United States dates back to England:

The weights and measures in common use in this country at the time of the American Revolution were all of English origin and were in use in England at that period. The principal units were the yard, the avoirdupois pound, the gallon, and the bushel. More or less authentic copies of the English standards of the denominations mentioned had been brought over from time to time and adopted by the different colonies. Divergencies in these weights and measures were, however, quite common, due no doubt to the fact that the system of weights and measures of England was not itself well established, and hence the copies brought to this country were often adjusted to different standards.

That this condition was recognized very early is made evident by the Articles of Confederation which contained the following clause: “The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective States—fixing the standard of weights and measures throughout the United States.” This power was transferred to Congress by the Constitution of the United States in article 1, section 8, the language being as follows: “The Congress shall have Power … To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures” [Bold added for emphasis.] (Fischer, 1905, link).

George Washington, first president of the United States, recognized the importance of accuracy in recording weights and measurements when he said, “Uniformity in the currency, weights, and measures of the United States is an object of great importance, and will, I am persuaded, be duly attended to.”

The United States still uses its original system of weights and measures, called the United States Customary Units (USCU). Once a particular definition of a measure such as an inch or a yard is widely agreed on, it does not change over time. Thus, when I read a reliable article that tells me George Washington was six feet and two inches tall, I can compare this with my current height of about six feet, and have confidence that Washington was taller than I am.

The United States, Liberia, and Myanmar are the only countries that have not officially adopted the Metric System. (Ward, 4/1/2014, link). All three allow and support use of the Metric System.

The biggest reasons the U.S. hasn’t adopted the metric system are simply time and money. When the Industrial Revolution began in the country, expensive manufacturing plants became a main source of American jobs and consumer products. Because the Imperial System (IS) of measurements was in place at this time, the machinery used in these factories was developed to size in IS units; all of the workers were trained to deal with IS units; and many products were made to feature IS units. Whenever the discussion of switching unit systems arose in Congress, the passage of a bill favoring the metric system was thwarted by big businesses and American citizens who didn’t want to go through the time-consuming and expensive hassle of changing the country’s entire infrastructure. Many also believed that the United States should keep its particular system, setting it apart from other countries and symbolizing its status as a leader rather than a follower.

In modern times, most have accepted a joint unit system—teaching children in school both the traditionally used IS system and the metric system that most of the rest of the world uses. This is why U.S. measuring sticks, or rulers, often contain both inches and centimeters. Unfortunately for metrics fans, widespread acceptance of joint use also means that there likely will be no official phasing out of the IS system anytime soon (Encyclopaedia Britannica, 2020, link).

Today, the fact that the Metric System is accepted worldwide creates an ongoing problem for U.S. international banking, trade, travel, etc. Most students in our schools today learn both the USCU System and the Metric System, and how to convert measurements from one to the other. However, most do not learn the Metric System well enough to feel comfortable in using it.

Every field of science includes taking measurements, understanding them, and communicating them to others. Thus, it is not surprising that the world’s scientists developed and agreed on a common system of measurement. The SI system (International System of Units) consists of seven units of measure. It is called the Metric System and is the dominant system used in science as well as in international commerce and trade.

• the kilogram (kg), for mass
• the second (s), for time
• the kelvin (K), for temperature
• the ampere (A), for electric current
• the mole (mol), for the amount of a substance
• the candela (cd), for luminous intensity
• the meter (m), for distance

The development of the metric system was a huge step forward for humans.

Designed during the French Revolution of the 1790’s, the metric system brought order out of the conflicting and confusing traditional systems of weights and measures then being used in Europe. Prior to the introduction of the metric system, it was common for units of length, land area, and weight to vary, not just from one country to another but from one region to another within the same country. As the modern nations were gradually assembled from smaller kingdoms and principalities, confusion simply multiplied. Merchants, scientists, and educated people throughout Europe realized that a uniform system was needed, but it was only in the climate of a complete political upheaval that such a radical change could actually be considered (Rowlett, 4/27/2018, link).

Figure 2 shows commonly used linear measures in the USCU and Metric systems, and Figure 3 shows some examples of USCU measures converted into metric measures.

Figure 2. Tables for USCU and Metric linear measuring
(Linear Measures, n.d., link1, link2).

In contrast to the Metric System, the United States Customary Units (USCU) System is not based on powers of ten. Thus, for example, there are not ten inches in a foot, ten feet in a yard, or a thousand yards in a mile. Figure 3 shows some common units of length in the USCU system. From this table you can see that the 100-yard dash, a common athletic event in the U.S., actually is a 91.44-meter dash. The International Olympics includes the 100-meter dash, but does not include the 100-yard dash.

Figure 3. Metric equivalent of some units of length in the USCU
system of measurement (Wikipedia, 2020c, link).

It is, of course, possible to use paper and pencil arithmetic algorithms to make conversions from USCU to metric, or vice versa. However, this type of arithmetic calculation is more suited to the capabilities of a calculator or computer.

A number of free websites contain conversions calculators that convert between the Metric System and the USCU System of measurements. One I found that might work with relatively young students is the Metric Conversions Calculator (Zeus, n.d., link). To use this site, one selects from the list: Distance/Length; Area; Volume; Weight; Temperature; Pressure; and Force. For example, I clicked on Distance/Length. The computer then gave me a list of boxes labeled in metric (millimeters, centimeters, meters, etc.) and a list of boxes labeled in USCU (inches, feet, yards, etc.). Just keyboard a number into one of the boxes and the computer quickly fills in all of the other boxes. (A few of my reader may have noticed the use of the word weight rather than mass. That technical detail is beyond the scope of this book.)

In this instance, I had to do quite a bit of trial and error before I became comfortable with the Metric Conversions Calculator website. This situation raises an issue that all technology-using people face. How difficult is it to become a comfortable, competent user of new technology? Can a typical person gain this knowledge and skill on their own —for example by some combination of reading the directions together with trial and error? Or, is formal training/education highly desirable? In the latter case, what roles should our schools play in this instruction?

As you ponder this question, consider the full range of capabilities of a Smartphone. What, if any, functions of the Smartphone should be taught in school? Questions of this type pose quite interesting challenges, as well as raising questions about what major changes we should perhaps think about making in our current educational systems.

For example, consider the metric/USCU conversion problem. Rather than learning about conversion tables and formulas, might it not be easier to just talk to your computer and ask it to do a conversion for you? In my case, as I am about six feet tall, I used voice input to Google to ask, “How much is six feet in metric?” Google had no problem handling this question.

But wait…there’s more. Actually, I am closer to 5 feet 11½ inches tall, so I next asked Google, “How much is five feet eleven and one-half inches in metric?” Google’s voice recognition system did a perfect job of converting my voiced question into printed text. However, Google could not provide an accurate answer to this new question. It attempted to answer the question through pattern matching with its humongous database rather than by understanding the actual math question that I asked.

This illustrates an important challenge in education. While computers are gaining in intelligence, they actually are still quite dumb. In each course students take, they need to be learning the capabilities and limitations of current computers as an aid to solving the problems and accomplishing the tasks that help to define the discipline being studied.

History Questions for Your Students

I continued my height exploration by asking Google these voiced questions:

1. How much is one half-inch in metric?
2. How much is 11 and one half-inches in metric?
3. I am six feet tall. Am I taller than the historical French leader Napoleon Bonaparte? Was he shorter than average for men of his time?

My computer gave useful answers to all of these questions. Moreover, I have opened up for you a fun way in which students can learn about history, voice recognition computer systems, and capabilities of computers in answering questions. Such activities can be carried out with a broad range of students and a broad range of questions. A challenge for students could be to pose measurement-related questions that they can answer, but ones their Smartphone cannot answer.

Here is a history question for you and your students to explore. When did voice input (voice recognition) become good enough to be an easy, accurate, and cost-effective way to input data to a calculator or computer? And, what difference has this capability made in the school curriculum? (Saba, 9/28/2017, link).

It is easy to expand on this type of history question. Have your students name some important past technological developments that have now become commonplace and/or have now become so outdated that they no longer are widely used. The students can then explore issues such as

1. What problem did the technology help to solve?
2. What changes and problems did this technology make in our world?
3. What roles did our schools play in students learning to use the technology?

You have probably heard the statement, “Money is the root of all evil.” I was curious about this statement, so I looked it up on the Web. I learned that the Bible actually says that “the love of money is the root of all evil.”

On a more positive note, money facilitated a major important change from a barter system of exchanging goods and services to a currency means for such exchanges. One might claim, “Money is the lubricant for all modern societies.”

But, what about currency? What is a dollar?

The history of the United States Dollar refers to more than 240 years since the Continental Congress of the United States authorized the issuance of Continental Currency in 1775. On April 2, 1792, the United States Congress created the United States dollar as the country’s standard unit of money (Wikipedia, 2020a, link).

However, a dollar is not like the precise measurement of a length or a weight that does not change over time. One can use dollars to exchange for goods and services, but the amount per dollar of goods and services received is not a fixed, unchanging amount. This problem was certainly understood by people creating/defining coins or pieces of paper to be currency that can be exchanged for goods and services. One solution is to define a dollar in terms of a specific quantity of something that it is possible to measure accurately over time, such as a specified weight of gold or wheat. Thus, the United States eventually defined a dollar to be 1/35 of an ounce of gold, and issued paper dollars and coins based on that definition of money backed by gold stored in its vaults. This proved to be a useful approach to money, but one that was not without problems. The amount of goods and services that can be purchased for a dollar will vary over time according to supply and demand, and also with the quality of the goods and services. Moreover, the available supply of gold may not keep up with the needs of a growing, prospering society.

On June 5, 1933, the United States went off the gold standard, a monetary system in which currency is backed by gold, when Congress enacted a joint resolution nullifying the right of creditors to demand payment in gold. The United States had been on a gold standard since 1879, except for an embargo on gold exports during World War I, but bank failures during the Great Depression of the 1930s frightened the public into hoarding gold, making the policy untenable (History.com, 7/28/2019, link).

When compared to the history of prehumans and humans, the history of money is relatively short.

At the dawn of humanity, bartering was used in lieu of money to buy goods. As early man began to rear domestic livestock, one of the earliest forms of barter included cattle, sheep, as well as vegetables and grain.

The first known currency was created by King Alyattes in Lydia, now part of Turkey, in 600 BC. The first coin ever minted features a roaring lion.

Coins then evolved into bank notes around 1661 AD. The first credit card was introduced in 1946 (Burn-Callander, 01/20/2014, link).

I learned in high school that a group of Dutch traders purchased Manhattan Island (now New York City) in 1624 from the Native Americans for $24 worth of beads. Manhattan real estate has since become among the most expensive in the world. For some reason, the number $24 stuck in my head. Historical records indicate that such a transaction actually occurred, and that it involved more than 22 square miles of land (Soniak, 10/2/2012, link).

Suppose that the $24 had been invested in the stock market in 1624? What would it be worth now? Quoting from Soniak’s article:

One of the most persistent myths in American history is that European explorers really got one over on the Native Americans by purchasing the entire island of Manhattan—where property has averaged $1000+ per square foot over the last few years—for a measly $24 worth of beads and trinkets. It seems like the ultimate bargain, but the truth of the story is more complicated and murkier than that.

All students studying history face the challenge of determining whether they are being taught fake (or just incorrect) news. In my opinion, this is one of the most important topics that students should be exploring in their history curriculum. Can a student with access to the Web determine whether or not this “$24 story” is fake or incorrect news?

It is easy to expand on this type of history question. Have your students name some important past technological developments that have now become commonplace and/or have now become so outdated that they no longer are widely used. The students can then explore issues such as:

1. Did the U.S. dollar exist in 1624?
2. Did the Native Americans living in or near Manhattan Island own that land?
3. Did the Native Americans living in or near Manhattan Island have sufficient legal knowledge and understanding so they could enter into such a business transaction?
4. Was $24 a fair price for the land?

I did a rather superficial Web search on each of these questions. While the U.S. dollar did not exist in 1624, one can look at how much the beads cost in Dutch guilders, and from that make an estimate that the 60 Dutch guilders in 1624 corresponded to $24 U.S. So, the $24 may well be a good estimate.

Manhattan traces its origins to a trading post founded by colonists from the Dutch Republic in 1624 on Lower Manhattan; the post was named New Amsterdam in 1626. Manhattan is historically documented to have been purchased by Dutch colonists from Native Americans in 1626 for 60 guilders, which equals roughly $1059 in current terms (Wikipedia, 2020b, link).

Native Americans understood ownership of horses and other types of personal goods. One can make good arguments that, at least in some parts of America, the Native Americans had established long-lasting communities and understood land ownership. My hastily-done research did not determine whether Native Americans living in the area of Manhattan Island practiced land ownership.

Hmm. I thought more about the horses part of the previous paragraph. When did horses first become available to Native Americans? I always thought that they were brought to America by the very early settlers from Europe. But, my recent Web browsing on this question provided me with convincing evidence that there were horses in America before Christopher Columbus “discovered” America in 1492. If you are a history teacher, you might want to have some of your students research this topic.

My final question is to ask whether the $24 worth of beads was a “fair” price. It certainly does not sound like a fair price. But wait. We may be looking at this in an incorrect manner. Money can be invested so that it earns interest or grows in value over time.

Suppose that $24 was invested at seven-percent a year, compounded yearly, from 1624 to 2020. Over very long periods of time, the U.S. Stock Exchange has seen an average gain of about seven-percent per year (Hamm, 10/29/2019, link).

Over the past 395 years, the $24 would have grown to about 9.7 trillion U.S. dollars. The math is simple enough. Calculate 1.07 raised to the 395th power, and multiply the result by $24 (there are a number of free websites that can do this compound interest calculation). This is a very large number. Indeed, it is probably enough to buy at current prices all of the land included in the original purchase agreement (Wikipedia, 2020b, link).

The above discussion mentions converting Dutch guilders into American dollars. While our world has made great progress in developing a uniform system of measurements (the metric system) it has not succeeded in developing a uniform measure of currency. Thus, there is daily fluctuation in value among the large number of different currencies used in our world. Occasionally, there are huge changes as a country experiences extreme inflation.

My purpose in doing the mental and Web exercises described above was to illustrate that many students at the middle school and secondary school level are capable of posing history-related questions and exploring possible answers through use of the Web and other resources. I strongly believe that such thinking and research can (and should) become a significant component of their precollege history education.

Many people are concerned about the quality of life of people living in their own country or in other countries. They want to help improve quality of life. But, how does one measure quality of life? Think about the difficulties of developing a definition that endures as the world changes. A definition developed a few hundred years ago would not contain routine access to technologies such as radio, television, antibiotics, cars, airplanes, the Internet and Web, and Smartphones.

In summary, humans have developed precise definitions of weights and measures that can remain unchanged over time. But many other things we want to measure do not lend themselves to precise measurement. This is a challenge to historians.

Historians gather and analyze data and information about events and situations that occurred in the past. Some of the gathered data and information may be quite precise and verifiable using a variety of old and new techniques. Today, for example, you can learn some of your own personal history by having your DNA analyzed. In current times, more and more raw data is being gathered and stored in computer systems that facilitate easy computerized analysis and retrieval.

The sciences prosper because they are built on a solid foundation of experimental data, underlying calculations, and theory. Many aspects of our progress in the sciences have been very useful to historians. Both the work of archeologists as well as ongoing progress in understanding human and other genomes have contributed greatly to our understanding of history.

Tools and capabilities made available through the combination of computers and mathematics have proven to be very valuable aids to learning history as well as to supporting historical explorations. These aids to being an amateur historian are sufficient so that students of all ages can “do” some of the types of things that historians do. They can learn to pose questions and to explore possible answers about important aspects of history.

The next newsletter in this series of ICTing and mathing across the history curriculum will explore causality and Future Studies. Historians often analyze historical data and information in an attempt to determine causality. For example, what actually caused World War I? What actually caused the Great Depression? The types of research done in exploring such questions can be applied to current times in an attempt to predict the future. Future Studies is now accepted as a legitimate branch of history.

Burn-Callander, R. (10/20/2014). The history of money: from barter to bitcoin. The Telegraph. Retrieved 3/7/2020 from https://www.telegraph.co.uk/finance/businessclub/money/11174013/The-history-of-money-from-barter-to-bitcoin.html.

Encyclopaedia Britannica (2020). Why doesn’t the U.S. use the metric system? Retrieved 3/8/2020 from https://www.britannica.com/story/why-doesnt-the-u.s.-use-the-metric-system.

Fischer, L.A. (1905). History of the standard weights and measures of the United States. Retrieved 3/2/2020 from https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=2ahUKEwiv57yGjf3nAhUlJTQIHX
jYCSsQFjADegQIAhAB&url=http%3A%2F%2Fnvlpubs.nist.gov%2Fnistpubs
%2FLegacy%2FMP%2Fnbsmiscellaneouspub247.pdf&usg=AOvVaw0txpxsM
MoEUcTVbqISsPzs.

Hamm, T. (10/29/2019). Average stock market return: Where does 7% come from? Retrieved 12/29/2019 from https://www.thesimpledollar.com/investing/stocks/where-does-7-come-from-when-it-comes-to-long-term-stock-returns/.

History.com (7/28/2019). FDR takes United States off gold standard. Retrieved 3/5/2020 from https://www.history.com/this-day-in-history/fdr-takes-united-states-off-gold-standard.

Linear Measure (n.d.). Tables for metric and U.S. measuring. Infoplease. Retrieved 3/5/2020 from https://www.infoplease.com/math-science/weights-measures/tables-for-metric-measuring and https://www.infoplease.com/math-science/weights-measures/us-weights-and-measures.

Rowlett, R. (4/27/2018). The Metric System. Retrieved 2/27/2020 from www.ibiblio.org/units/metric.html.

Saba, M. (9/28/2017). A brief history of voice recognition technology. CallRail. Retrieved 3/4/2020 from https://www.callrail.com/blog/history-voice-recognition/.

SJM Corporation (n.d.). A brief history of geometry. Retrieved 3/5/2020 from http://www.thegeodes.com/templates/geometryhistory.asp. 

Soniak, M. (10/2/2012). Was Manhattan really bought for $24? Mental Floss. Retrieved 12/26 2019 from https://www.mentalfloss.com/article/12657/was-manhattan-really-bought-24.

Ward, A. (4/1/2014). Countries that haven’t adopted the metric system. MentalFloss. Retrieved https://www.mentalfloss.com/article/55895/countries-havent-adopted-metric-system.

Wikipedia (2020a). History of the United States dollar. Retrieved 3/9/2020 from https://en.wikipedia.org/wiki/History_of_the_United_States_dollar.

Wikipedia (2020b). Manhattan. Retrieved 3/7/2020 from https://en.wikipedia.org/wiki/Manhattan.

Wikipedia (2020c). United States Customary Units. Retrieved 3/9/2020 from https://simple.wikipedia.org/wiki/United_States_customary_units.

Zeus (n.d.). Metric conversions calculator. Zeusinc. Retrieved 3/4/2020 from https://www.zeusinc.com/resources/calculators/metric-conversions-calculator/.