Introduction to ICTing and Mathing Across the History Curriculum. Part 4

Introduction to ICTing and Mathing
Across the History Curriculum. Part 4

“Time marches on.” (Multiple sources.)

“Time is the wisest counselor of all.” (Pericles; Greek statesman, orator, and general; 495-429 BCE).

Introduction

Historians study the who, what, where, when, why, and how of past happenings. We think of where in terms of three (spatial) dimensions, and when as a time dimension. It is common to use the term four-dimensional space in referring to these four dimensions (Wikipedia, 2020c, link):

[The mathematician and astronomer] Lagrange wrote in his Mécanique analytique (published 1788, based on work done around 1755) that mechanics can be viewed as operating in a four-dimensional space — three dimensions of space, and one of time.

A timeline is a graphic representation of the passage of time that often is used in the study of history. Quoting from study published in 2009 (Chen, 5/5/2009, link):

Adults spend a lot of time thinking about time — yesterday, today, tomorrow, hours and minutes are all part of an adult’s life. Young children, however, are concrete thinkers and don’t understand the concept of time and what it means. Children learn best when they can touch, feel or see something, so time can be confusing for them. A child’s readiness for learning about time is based on the stages of brain development.

As I thought about instructional uses of timelines, it occurred to me to wonder at what age children begin to understand time. It turns out that there has been considerable research on this topic (Droit-Volet, August, 2012, link). Here are three short quotations from the article:

What psychologists have discovered is that there is no simple, undifferentiated type of time knowledge. Instead, multiple forms of time emerge at different stages along the ontogenetic scale as a function of the development of underlying cognitive processes.

However, at the age of seven years, their time judgements improve because they acquire a symbolic representation of time. They represent time as something absolute that flows uniformly, and this enables them to measure the duration of events independently of their specific characteristics.

At the age of 10 years, children also begin to use verbal counting strategies, in the same way as adults, in order to ensure the accuracy of their time judgements. At eight years, although they are also capable of counting time, they do not spontaneously think of doing so unless instructed to by an adult. At five years of age, in contrast, they are unable to correctly count time, whatever the circumstances.

The Droit-Volet and Chen articles suggest to me that using timelines to help teach history is unlikely to be a good approach until about age 10 or so. Well before that age, however, children have developed some concrete knowledge about time and ordered events. For example, consider a pattern of getting up in the morning, having breakfast, having a long time in which various things occur until lunch time, similarly for the afternoon, then supper time, then events before bedtime. This type of events-based timeline does not contain any numbers.

Children gradually learn that this type of numberless timeline begins to contain specific other events. They may know that a TV program comes on at a particular time, or they may become accustomed to a message to put away your toys because supper is in 15 minutes, and so on.

Schools add to this structure. The day in a preschool, kindergarten, or elementary school is typically divided into time blocks, and in an order that is likely to be repeated day after day. That is, there is a reasonably well-structured timeline for the school day. In school, there is apt to be a large clock that students can view. With some instruction, students will begin to see time patterns in their daily activities. Thus, posting simple timelines depicting a time schedule for the day in an elementary school classroom can contribute to children developing time sense.

In conclusion, home, school, and growing mental maturity all contribute to children developing time sense. Teachers tend to believe that they are doing their share by teaching students to read analogue and digital clocks. However, there is far more to developing time sense than this.

Timelines

It was pointed out in the previous newsletter of this series that computer software can be quite helpful in the mechanical aspects of creating graphics. Good quality, free software is available to assist in creating timelines. Quoting from Top 10 Free Timeline Creation Tools For Teachers (Pappas, 2017, link):

The Internet is full of free tools that offer great and fancy features for timeline creation. Which ones are the best though? In this article, I’ll share the top 10 free timeline creation tools for teachers.

Figure 1 is a timeline for Benjamin Franklin, a very important person in the history of the United States (Juliaslidinghome, 3/24/2014, link).

  

Figure 1. The life of Benjamin Franklin

In this example, notice that the scale on the line is an equal interval scale timeline. Each interval is 10 years. It certainly is possible to create such a graphic representation without the use of a computer. However, a computer with timeline software is definitely a big help. Can you imagine completing a timeline by hand that is as complex as the one in Figure 1, and then finding a spelling error or date error, or an event you want to replace by a different event? It is easy to make such corrections and changes on a computer. In addition, the research needed to create such a timeline provides an excellent example of the usefulness of the Web.

Figure 2 is a timeline of a collection of popular Social Media platforms (McGuire, 4/11/2019, link). Notice how color is used to help distinguish between the various components of the timeline.

  

Figure 2. Colorful timeline of the creation of popular Social Media platforms.

Graphs and timelines are designed to communicate information to a particular audience. Thus, both the content and the design need to be appropriate to the communication task. The mechanics of creating a particular type of graphical communication requires knowledge and skills that students develop over time and in various courses. Thus, for example, you would not expect a typical first grade student to create timelines like those in Figures 1 and 2 because such students have not yet learned the needed reading writing, and research skills.

Both Figure 1 and Figure 2 contain considerable amounts of print. My eyesight isn’t as good as it used to be, and I find it difficult to read the small print in these two timelines. Think about this when you make use of a timeline in your writing and in presentations that make use of a projector.

Notice that the timeline in Figure 2 is not an equal interval scale. Many interesting timelines are not equal interval scales. Also, notice that both of these examples have time as the horizontal line. There is no particular reason why time is not the vertical line.

Handwriting can be thought of as a graphic representation of spoken language. For an alphabet-based language such as English, the number of different individual graphics (pictures) is quite limited. Other languages, such as the first written language Cuneiform, and the current language Mandarin Chinese, have a huge number of individual characters. From this point of view, a written list can be thought of as a graphic image. Such a list may contain numbered lines and the lines may be in a particular order, such as chronological.

Consider a list of some important times/events in our human past. As an example, here is a list that I recently created, mainly off the top of my head. You will want to create your own list that fits both your personal interests and your teaching interests.

1. Prehumans were hunter-gatherers and began to make tools appropriate to their needs more than three million years ago. These prehumans could learn a complex rock knapping skill from each other.
2. When conversational spoken language occurred is unknown, but likely occurred after the time homo sapiens began to appear in Africa approximately 200,000 years ago.
3. Homo sapiens migrated out of Africa and eventually spread across the globe starting about 100,000 years ago.
4. Homo sapiens developed imagination perhaps 70,000 years ago. Some evidence of this is provided by paintings and drawings on cave walls.
5. The Agricultural Revolution or the Agricultural Era began about 11,000 to 12,000 years ago. At that time, homo sapiens were still hunter-gatherers and the total human population was probably less than 10 million.
6. The Agricultural Revolution let to great increases in human population. We now have more than 30 cities with populations larger than 10 million (Young, 2/27/2019, link).
7. Increased population let to the development of towns, cities, states, and nations. These led to a variety of governance structures, police forces, military, wars, and taxes to support these types of structures that were not needed when people lived in small hunter-gatherer clans and tribes.
8. The development of reading and writing about 5,500 years ago led to the creation of schools and libraries.
9. The history of current widely practiced religions is mainly based on written records. However, evidence of ritual burial of human bodies dates back about 100,000 years (Wikipedia, 2020a, link).
10. The Scientific Revolution began in the mid 1500s and the medical sciences began to flourish beginning in the 1800s.
11. The Industrial Revolution began in the late 1700s.
12. Currently we are in the Computer Era that began in the 1950s.
13. Currently we are in a period of climate change due to global warming brought on by humans.

These 13 items are in sort of a timeline arrangement even though many of the items overlap in time. They could be represented in a horizontal bar graph with the horizontal axis being a time scale, but in this case the labels on the individual bars would be unwieldy.

Moreover, this collection of events does not lend itself to an equal interval scale timeline. Suppose that such an equal interval scale timeline used a length of one millimeter to represent a thousand years. Then the timeline would be more than three meters (nearly 10 feet) in length!

I believe every teacher is at least in some part a history teacher, and that every student is at least partly a student of history. Major historical events like those illustrated above are part of the history of humanity.

Here is a class-period-long or perhaps longer Timeline List activity that history teachers might want to try out with their students. Begin by creating a world historical events list like the one above, but one that is suited to your teaching situation. From it, select perhaps a half dozen items that you believe will be particularly interesting to your students. Then:

1. Have a whole class discussion in which students suggest events that they believe to be worthy of adding to your short list. Write the items on a whiteboard or chalkboard. Your students will likely produce a quite long list.
2. Next, explain that each student gets to have a small number of votes (such as five) for what they consider the (five) most important major events students in their class should learn about. Students collectively go to the board and put a mark beside each item they want to vote for.
3. Then divide the class into small groups of about three to four students, so they can discuss the whole class list of items and the preliminary voting done by the class. Each group is to come up with a small number of topics (such as five) that their group thinks are the most important to students in their age group.
4. Finally, the choices of the small groups are added to the main list on the board, using a different color of marker. That way the students can see the initial voting and then the new and different voting results. These results can be presented to the whole class for discussion.
5. A later section of this newsletter discusses Project-based learning (PBL). If you do steps 1-4 or some variation of them with your students, you are doing PBL

I created Figure 3 below to represent the advancing uses of computers over time in analyzing information. It has the appearance of an equal interval time scale, but the vertical hashmarks do not denote time. Rather, this is an understanding line scale. Schools stress learning for understanding. But, what does understanding mean in terms of this graphical representation, and how does it relate to what computers can do in helping to lead us from data to wisdom?

  

Figure 3. A timeline-like graph that is not a timeline scale.

The first electronic digital computers were thought of as data processing machines. As computers became commercially available in the early 1950s, courses and programs of study about Data Processing sprang up wherever computers were available. In the sciences and technology, the stress was on processing data in science and technology. In business, the stress was on processing business data. Thus, computer courses emerged in college and university science and engineering departments, and also in business departments.

It soon became apparent to a number of researchers that data processing was too narrow a view. The term Artificial Intelligence (AI) was coined at a 1956 conference held at Dartmouth College (McCorduck, Minsky, Selfridge, & Simon,1977, link). Quoting the first paragraph of their 1977 panel discussion on the history of AI:

Though our discussion is entitled “The History of Artificial Intelligence”, in fact we are focusing here on one brief but highly significant moment in that history, the moment when art metamorphosed itself into science, from wish and dream to something like reality. As you will learn from each of the discussants, this metamorphosis took place at several locations during the early to mid-1950s, and its catalyst was the recognition that the computer was the most promising medium yet in which to realize what had been a human dream since earliest times, the creation of man-made, rather than begotten intelligence. [Bold added for emphasis.]

The popular press helped to publicize some of the ideas of AI. Here is a quotation from Arthur C. Clark, one of my favorite science fiction authors: “Before you become too entranced with gorgeous gadgets and mesmerizing video displays, let me remind you that information is not knowledge, knowledge is not wisdom, and wisdom is not foresight. Each grows out of the other, and we need them all.”

In Figure 4 below, I have expanded Figure 3 to include the concepts in the quote from Artur C. Clark.

  

Figure 4. Arthur C. Clarke’s Cognitive Understanding Scale.

Figure 4 has brief definitions of the scale’s five labels. I find that this combination of a graphic with descriptive words greatly improves its usefulness. However, this is a large amount of text to include in a graphic. The text size used in the scale is approximately the same as the text size used in the rest of this document. Thus, it should be as readable as the rest of this newsletter.

I have used this graphic in many presentations in my classes and with larger audiences. I display it for a long time so that the audience members have time to read and think about the entire contents and concepts of the scale.

The equal intervals in the scale used in Figures 3 and 4 are misleading. What can it possibly mean that the distance between Data and Information is the same as the distance between Knowledge and Wisdom? And, what is to the left of Data or to the right of Wisdom in Figure 3? Figures 3 and 4 are definitely not equal interval timeline scales!

This section is an important Computer Era history lesson for history teachers and their students, and for all readers of this newsletter. In your everyday communications, do you and your students distinguish between data and information? Figure 4 above is a graphic that may help.

As previously noted, the initial computers were thought of as data processing machines. They were designed to process numerical data (numbers). When a calculator or a computer adds a set of numbers, these machines do not know and do not need to know what the numbers are being used for or what they represent. The numbers might represent distances covered by different traveling sales people, sales data from different stores, populations of different countries, or calculations needed in designing and building atomic and nuclear weapons.

In communicating with you, a reader of this newsletter, what do I accomplish by using this graphical representation shown in Figure 4? I paint a picture of a very important idea in education. At one end of the scale we can have students memorize facts (data). In the center of the scale we can have students attribute meaning and understanding to this data that they have memorized. On the far end of the scale we want students to develop wisdom and foresight.

Computers are very good at memorizing data. In fact, they are much better than humans at this task. In many situations, they also are very good at processing data into information that can be used by people and machines to solve problems and accomplish tasks. For this reason, while early computers were considered to be data processing machines, they soon came to be called information processing machines.

Now, think about the right end of the scale in Figure 4. Here, human performance still far exceeds that of current computers. Researchers in artificial intelligence are working to decrease this difference between computer and human performance. They are making progress, but still have a very long way to go. Futurists are confident that further progress will occur.

In summary, the graphical representation used in Figure 4 is a powerful aid to communication. When I use it in a talk or in my writing, I can present important historical ideas and communicate very important information about the capabilities of people versus the capabilities of computers.

In writing this section, I considered making Figure 4 into concentric circles. The inner most (smallest) circle would be data. The outermost would be foresight. Education begins at the data level, with an ultimate goal of helping students develop wisdom and foresight. I believe that schooling and informal education at every level should span data, information, knowledge, wisdom, and foresight. As a child’s mind matures and becomes educated, it becomes more and more capable of spanning this entire range. A concentric circle graph shows growth based on all of the earning that has come earlier.

Gantt Charts

A Gantt chart combines both a timeline and a task analysis for a project. Here is a definition and an illustration (Figure 5 below) of a Gantt chart (Wikipedia, 2020b, link):

A Gantt chart, or harmonogram, is a type of bar chart that illustrates a project schedule. This chart lists the tasks to be performed on the vertical axis, and time intervals on the horizontal axis. The width of the horizontal bars in the graph shows the duration of each activity. Gantt charts illustrate the start and finish dates of the terminal elements and summary elements of a project.
…
The chart is named after Henry Gantt (1861–1919), who designed his chart around the years 1910–1915.

  

Figure 5. Example of a Gantt Chart with three milestones.

The first two columns name tasks to be accomplished by the project and estimated amount of time each will take. The remainder of this Gantt chart is like a horizontal bar graph, but with bars starting at differing times. The bars provide a graphic showing time lengths and over lapping tasks.

Project-based learning is an individual or group activity (project) that goes on over a period of time, resulting in one or more of: the following: a product; a presentation; a written report; a performance. It typically has a timeline and milestones for students to follow. This information can be presented as a Gantt Chart developed by the teacher, and then each student can develop their own Gantt Chart. The basic ideas of this valuable teaching tool are described in Principles of Project-based Learning (Laanpere & Pata, n.d., link.)

Project-based learning is based on a new paradigm of student-teacher relations. The task for the teacher is not so much to lead the learning process, communicate theoretical knowledge and apply suitable exercises or assessment methods, but rather to form a partnership with the students during learning – while the framework of what is to be learned is set by the curriculum, filling this framework with specific content and acquiring new knowledge is where the learners and the teacher should act in concert and to an equal extent. Projects are focused on the interests and needs of the students, thus upholding strong intrinsic motivation and dividing responsibility for the learning process between students and the teacher. [Bold added for emphasis.]

Have you ever considered the idea that your entire life consists of undertaking projects? From that point of view, school is a place and time where students receive formal instruction that helps to prepare them to plan and undertake increasingly complex projects.

This newsletter illustrates the concept that a combination of the powers of math and computers can empower students as they learn history and as they learn to communicate what they are learning. It has not attempted to be comprehensive. For example, consider a graphic generated by the use of a computer, but with a number of clickable pictures, words, and points in the graphic, where a click would take the student to additional information and instruction. These might well be interactive multimedia documents that were produced by a team of people.

If you are a history teacher, you might want to consider dividing your class into teams of perhaps three to four students, and each team undertaking a project of developing a multimedia document covering one of topics in the Timeline List your class developed while doing the activity presented earlier in this newsletter. Each team would work to develop educational materials that future students would find useful when they take your course.

The next two newsletters will complete our exploration of the roles of math and computers in history education, or ICTing and mathing across the history curriculum.

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Juliaslidinghome (3/24/2014). Examples of different kinds of timelines. Retrieved 2/13/2020 from https://www.slideshare.net/Juliaslidinghome/timeline-examples.

Laanpere, M. & Pata, K. (n.d.). Principles of project-based learning. Erasmus+. Retrieved 2/26/2020 from https://creativeclassroomproject.wordpress.com/creative-classroom-collection/project-based-learning/.

McCorduck, P., Minsky, M., Selfridge, O.G., & Simon, H.A. (1977). History of artificial intelligence. International Joint Conference on Artificial Intelligence. Retrieved 2/13/2020 from https://www.ijcai.org/Proceedings/77-2/Papers/083.pdf.

McGuire, S. (4/11/2019). Thirty-six timeline template examples and design tips. Venngage. Retrieved 2/13/2020 from https://venngage.com/blog/timeline-template/.

Pappas, C. (2017). Top 10 free timeline creation tools for teachers. Elearning Industry. Retrieved 2/3/2020 from https://elearningindustry.com/top-10-free-timeline-creation-tools-for-teachers.

Wikipedia (2020a). Burial. Retrieved 2/15/2020 from https://en.wikipedia.org/wiki/Burial.

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Wikipedia (2020c). Mécanique analytique. Retrieved 2/17/2020 from https://en.wikipedia.org/wiki/M%C3%A9canique_analytique.

Young, A. (2/27/2019). The world’s 33 megacities. Retrieved 2/15/2020 from https://www.msn.com/en-us/money/realestate/the-worlds-33-megacities/ar-BBUaR3v.