Introduction to ICTing and Mathing Across the History Curriculum. Part 1

I am currently writing a short book for preservice and inservice teachers of history at the precollege levels. The goal is to help their students learn to make more effective use of both Information and Communication Technology (ICT) and math in learning, understanding, and using the history they are studying. The book is also intended for the college and university faculty who teach such preservice and inservice teachers.

Nowadays I routinely make use of pithy quotations in the first part of articles and books that I am writing (Moursund, 2019). Each quote can be considered to be an insightful tidbit of history. The ones selected here are relevant to this short book. The first is from Neil Postman, an American author, educator, media theorist and cultural critic: “A new technology does not add something, it changes everything.”

It is clear that the discipline of Information and Communication Technology (ICT) developing during the past 75 years is, in fact, changing everything. As noted in the quotation below, while no longer in its infancy, ICT is far from being a mature, fully developed discipline:

Computer science began to be established as a distinct academic discipline in the 1950s and early 1960s. The world’s first computer science degree program, the Cambridge Diploma [Master’s Degree] in Computer Science, began at the University of Cambridge Computer Laboratory in 1953. The first computer science department in the United States was formed at Purdue University in 1962 (Wikipedia, 2020a).

It is important to understand that ICT and the changes it is bringing us are rapid and global. We must help our students learn to adapt to these rapid changes, and to be able to take full advantage of them.

My second short quotation is from a well-known American psychologist, Carl Rogers, who introduces another the key idea of this newsletter: “The only person who is educated is the one who has learned how to learn and change.”

My (first) wife and I got to know Carl Rogers while we were graduate students at the University of Wisconsin, Madison. Rogers’ statement suggests that two of the most important goals of schooling are students learning to learn and students learning to deal effectively with change. Ask yourself: How well are you, personally, and how well are our educational systems doing in these two endeavors?

My personal opinion is the importance of the changes that ICT is bringing and will continue to bring to education will prove to be second only to the importance of the development of reading and writing some 5,400 years ago. The development and eventual widespread acceptance of reading and writing certainly changed our world.

It has taken 5,400 years to achieve the world’s current level of literacy (World Population Review, 2019):

As a whole, the global literacy rate is quite high. The literacy rate for all males and females that are at least 15 years old is 86.3%. Males aged 15 and over have a literacy rate of 90%, while females lag behind at just 82.7%. Developed nations as a whole have a literacy rate of 99.2%.

The world’s first written language, Cuneiform, was developed about 5,400 years ago. Reading and writing proved to be very powerful aids to governments, businesses, historians, and many other people. Reading and writing are not easily learned in an apprenticeship-type of “learn by doing” type of educational system. So, about 5,200 years ago, schools were developed to teach these two subjects. If you teach history, you will likely be pleased to learn that the first schools also taught arithmetic (math) and history. For me, this suggests that scholars of that time recognized the value of reading and writing as an aid to representing, storing, and distributing historical knowledge.

The Cuneiform language contains symbols and words needed to deal with the math-related aspects of everyday life. Think of illiterate people being able to count small quantities and to do mental arithmetic on small numbers. Then think of the added capabilities of people as they learned to read and write numbers, store and retrieve numerical information, and do the equivalent of what we now call pencil and paper arithmetic. This was a huge step forward in developing the discipline of mathematics. Of course, neither paper nor pencils had yet been invented. Early students learned to write on wax-covered boards, the technology that was a predecessor to the slate and chalk technology.

The last two sentences make me wonder when slate and chalk were first used in writing. Hmm. Can I find this information on the Web? Of course:

The exact origins of the writing slate remain unclear. References to its use can be found in the fourteenth century and evidence suggests that it was used in the sixteenth and seventeenth centuries. The central time period for the writing slate, however, “appears to begin in the later eighteenth century, when developments in sea and land transport permitted the gradual expansion of slate quarrying in Wales and the growth of a substantial slate workshop industry.” By the nineteenth century, writing slates were used around the world in nearly every school and were a central part of the slate industry. At the dawn of the twentieth century, writing slates were the primary tool in the classroom for students. In the 1930s (or later) writing slates began to be replaced by more modern methods. However, writing slates did not become obsolete. They are still made in the twenty-first century, though in small quantities (Wikipedia 2019b).

I have just illustrated what I consider to be a very important lesson in student learning about history. Although I did not use a slate tablet while I was in school, I had heard about students using slate tablets. That is part of my general knowledge, perhaps learned in school, perhaps learned in my childhood reading. The tidbit of knowledge I had was sufficient to allow me to raise the slate question and to do a Web search. In summary:

1. I had a little bit of knowledge about (and the words for) this topic.
2. I was personally interested in learning more.
3. A search of the Web produced information that satisfied my need.

Initiating this Web search, looking briefly at the short descriptions of several of the results, and then browsing one of the articles that looked like it would satisfy my need took me less than two minutes!

The example also reminded me of a quotation about reading that I have used before. Over the years I have made a personal collection of quotations that I found interesting and might want to use in my writing. It took me less than a minute to search my collection in the IAE-pedia and locate this quotation from Frederick Douglass, a freed American slave who became an ardent abolitionist, orator, and writer: “Once you learn to read, you will be forever free.”

Frederick Douglass makes a very powerful and poignant statement. From a schooling point of view, I think this expresses his belief that learning to read would be the most important goal of schooling.

You probably have heard about the idea of students needing to learn to read across the curriculum. That is, we not only want students to learn to read, we want them to learn to read with understanding the content in each of the curriculum areas they study. With such reading skills, a student can make use of libraries to gain additional knowledge is areas that are of particular personal interest. But now, in addition to reading, we have many other aids to accessing and learning information. Voice input and output, along with interactive multimedia, are becoming better and better. So, one interesting question we might ask is whether these new aids will decrease the need for a student to develop a high level of reading skills.

Mathematics is both a very broad and deep discipline of study in its own right, and also an important component/tool in many other disciplines The same statement holds for ICT.

The following discussion provides you with a brief lesson in mathematics as it relates to some aspects of teaching and learning history. Here is a quote from the German mathematician Leopold Kronecker to get us started: “God created the natural numbers. All the rest is the work of man” (Moursund, 2019).

I think Kronecker makes a profound observation, and probably not one that you would have been likely to encounter during your K-12 education. Hmm. Who decides what aspects of math history should be taught in math classes and history classes at the precollege or higher education levels? A key aspect of education is learning make use of one’s knowledge, skills, and the resources that are available as an aid to new learning.

Think about the types of problems and tasks that you encounter in your everyday life. How many of these are quite specific to a particular discipline you studied in school, how many are interdisciplinary, and how many are ones that you learned outside of school?

PreK-12 schools are specifically designed to provide building blocks for further, lifelong education. For the most part, schools divide the instructional day into discipline-specific periods of study. Somehow or other students are expected to transfer the learning from each specific subject into the other subjects they are studying, and also to their life outside of school.

No wonder that transfer of learning is such an important idea in education. Hmm. Your own personal education has included a considerable emphasis on transfer of learning, right? (Or, wrong?) If you are a classroom teacher, do you place special emphasis on transfer of learning?

Continuing your math lesson… The natural numbers are the positive integers 1, 2 3, and so on. Humans have some innate ability to count. Starting with the innate ability to deal with small positive integers, humans developed zero as a number, negative numbers, fractions, decimal numbers, and lots more math. A number of other animals also have an innate ability to count small numbers of objects (Goldman, 11/27/2012).

My conclusion is that without reading and writing, we humans would not have many of the products and services that we consider to be important to having a good standard of living and quality of life. If you are a history teacher, this would be an interesting idea to explore with your students.

Let’s use measurement as an example. Long before the development of the first written language, people routinely dealt with problems that involved counting, weighing, and measuring. Think about measuring time. How old are you? Can you give your answer in years, months, weeks, and days? Each of these time units is a commonly used measure of time.
Hmm. How long is a day? In all of the countries of the world, is an hour the same length? How about the same type of question for a week or a month? Why do months vary in length, but weeks and days do not?

Oh, by the way. How long is an hour? Well, you might say that an hour is 60 minutes, and a minute is 60 seconds. Did you ever wonder about how people decided that a week is seven days, a day is 24 hours, an hour is 60 minutes, and a minute is 60 seconds? Are these science questions, or history questions?

My quick search of the Web produced the following historical information (Molyneux, n.d.):

Why are there 60 seconds in a minute, 60 minutes in an hour and 24 hours in a day? Who decided on these time divisions?

THE DIVISION of the hour into 60 minutes and of the minute into 60 seconds comes from the Babylonians who used a sexagesimal (counting in 60s) system for mathematics and astronomy. They derived their number system from the Sumerians who were using it as early as 3500 BC. The use of 12 subdivisions for day and night, with 60 for hours and minutes, turns out to be much more useful than (say) 10 and 100 if you want to avoid having to use complicated notations for parts of a day. Twelve is divisible by two, three, four, six and 12 itself – whereas 10 has only three divisors – whole numbers that divide it a whole number of times. Sixty has 12 divisors and because 60 = 5 x 12 it combines the advantages of both 10 and 12. In fact both 12 and 60 share the property that they have more divisors than any number smaller than themselves. This doesn’t, of course, explain how this system spread throughout the world.

The article Day in the Wikipedia provides additional information on this topic (Wikipedia, 2019a).

The statement by Phil Molyneux provided the information I was looking for. It took me about two minutes to locate, read, and copy it. During this time, I was doing a published-literature-type of historical research. That is, I posed a history-type of question and did the research to find an answer.

What do you think about the observations on the number of divisors of 60? I found this part of the answer particularly pleasing, probably because of my mathematical background. Here are four observations:

1. In terms of the type of historical research that novices are apt to need to do, the Web is a game changer. Nowadays, I believe all students who are capable of learning to read and write can and should become facile at doing this type of research on the Web. Indeed, I think that such use of the Web should be a routine activity in history courses. A textbook or two is far too limiting for such courses being taught today.
2. How do I know if the information I retrieved is correct information, as opposed to fake news? Molyneux’s article, “Red Tape, White Lies,” was published in The Guardian, a reputable publication that I have found to be dependable. The information is consistent with knowledge that I carry in my head. If I have doubts, I can explore other resources that my Web search engine located for me.
3. Perhaps you have heard the following advice to news reporters: “Tell the reader who, what, where, when, why, and how.” In the short paragraph I quoted above, Molyneux certainly provides an impressive example of meeting these guidelines in his short explanations!
4. Molyneux’s last sentence about these systems of time division now being used throughout the world provides a good example of a worldwide solution to a worldwide problem. This made me think about the many problems facing our world today, and how difficult it is to get worldwide cooperation in addressing these problems. History provides us with a variety of examples of how the world has indeed cooperated in the past in dealing with some worldwide problems. Here is a challenge to you. Can you name some other examples of past successes in world cooperation to deal with a worldwide problem? So far, we are not doing very well on the global warming problem.

The advice to reporters in Item 3 above includes where. How does one specify the location of a particular place in a town, city, state, or country? How does the captain of an ocean-going boat determine the location of that boat in an ocean? Quoting from “Brief History of Maps and Cartography” (Abner, 2008):

Cartography is the art and science of making maps. The oldest known maps are preserved on Babylonian clay tablets from about 2300 B.C. Cartography was considerably advanced in ancient Greece. The concept of a spherical Earth was well known among Greek philosophers by the time of Aristotle (ca. 350 B.C.) and has been accepted by all geographers since.

Greek and Roman cartography reached a culmination with Claudius Ptolemaeus (Ptolemy, about A.D. 85-165). His “world map” depicted the Old World from about 60°N to 30°S latitudes. He wrote a monumental work, Guide to Geography (Geographike hyphygesis), which remained an authoritative reference on world geography until the Renaissance.

The oldest maps mentioned above were created more than a thousand years after the invention of reading and writing. The existence of such early maps, however, does not tell the map users where various cities and other places were actually located in the world. For that, we needed the invention and use of longitude and latitude (Wikipedia, 2020c):

Eratosthenes in the 3rd century BC first proposed a system of latitude and longitude for a map of the world. By the 2nd century BC, Hipparchus was the first to use such a system to uniquely specify places on Earth. He also proposed a system of determining longitude by comparing the local time of a place with an absolute time. This is the first recognition that longitude can be determined by accurate knowledge of time. [Bold added for emphasis.]

The science and mathematics involved in determining location is extensive and complex. In addition, notice the last sentence quoted above. Accurately determining one’s location when sailing in an ocean required having an accurate way to measure time. The invention of accurate clocks was a major breakthrough in science and technology. I enjoy reading the history of such achievements.

For years, I have made extensive use of a Global Positioning System (GPS) as I drive from one location to another. The current system makes use of 24 satellites, and determines location with an accuracy of about one foot. The GPS in my Smartphone can provide me with both driving and walking directions.

Google Maps is a web mapping service developed by Google (Wikipedia, 2020b):

It offers satellite imagery, aerial photography, street maps, 360° panoramic views of streets (Street View), real-time traffic conditions, and route planning for traveling by foot, car, bicycle and air (in beta), or public transportation.

Just for fun, let me share a story. A number of years ago, I was visiting a public school third grade class. While talking with two boys in the class, I asked them to tell me what time it was. They looked at the analog clock on the wall and both were able to correctly “say” the time. Then I asked them questions about how many minutes until the next recess (which was at a fixed time each day) and how long before the end of the school day, and neither could answer. So, even though they had learned to read an analog clock, they had yet to understand the meaning of the numbers they were obtaining by reading the clock.

This personal experience in a third grade classroom illustrates a key concept in math education. We want students to understand what they are doing in math, and this involves the need for them to develop number sense. Rote memory and the mechanical use of algorithms do not suffice. Digital watches and clocks obviate the need to translate analog to digital, but these still do not solve the need for an understanding of the numbers being produced.

One can think of a digital watch as a type of artificially intelligent tool. Today’s smart watches have considerably more intelligence that the first digital watches, and their level of intelligence is continuing to improve.

Over thousands of years, mathematics has developed into a special purpose language of its own, a language that is embedded into natural languages. This special language of mathematics has some resemblance to our natural languages of English, Spanish, Mandarin Chinese, etc. (Moursund, 7/20/2019). The science and engineering disciplines all make extensive use of the language and capabilities of mathematics, and all have special vocabularies that are important to their disciplines.

A student learning history must be able to deal with the familiar natural languages used for speaking and reading as well as with the languages of math and of the various disciplines that are important to the part of history being studied.

The next IAE Newsletter will continue this discussion of the roles of math and ICT in learning and using history.

Aber, J.S. ( 2008). Brief history of maps and cartography. emporia.edu. Retrieved 1/5/2020 from http://academic.emporia.edu/aberjame/map/h_map/h_map.htm.

Goldman, J. (11/27/2012). Animals that can count. BBC Futures. Retrieved 12/22/2019 from https://www.bbc.com/future/article/20121128-animals-that-can-count.

Molyneux, P. (n.d.). Red tape, white lies. The Guardian. Retrieved 12/21/2019 from https://www.theguardian.com/notesandqueries/query/0,5753,-1487,00.html.

Wikipedia (2020a). Computer science.. Retrieved 1/5/2020 from https://en.wikipedia.org/wiki/Computer_science.

Wikipedia (2020b). Google maps. Retrieved 1/6/2020 from https://en.wikipedia.org/wiki/Google_Maps.

Wikipedia (2020c). History of longitude. Retrieved 1/5/2020 from https://en.wikipedia.org/wiki/History_of_longitude./

Wikipedia (2019a). Day. Retrieved 12/22/2019 from https://en.m.wikipedia.org/wiki/Day.

Wikipedia (2019b). Slate (writing). Retrieved 12/23/2019 from https://en.m.wikipedia.org/wiki/Slate_(writing).

World Population Review (2019). Literacy rate by country 2019. Retrieved 1/4/2020 from http://worldpopulationreview.com/countries/literacy-rate-by-country/.