Introduction to ICTing and Mathing Across the History Curriculum. Part 2

“School systems should base their curriculum not on the idea of separate subjects, but on the much more fertile idea of disciplines…which makes possible a fluid and dynamic curriculum that is interdisciplinary.” (Sir Ken Robinson; British author, speaker and international advisor on education in the arts to government, non-profits, education and arts bodies; 1950-.) [Bold added for emphasis.]

“We are not students of some subject matter, but students of problems. And problems may cut right across the boundaries of any discipline.” (Karl Raimund Popper; Austrian-born British philosopher and academic; 1902-1995). [Bold added for emphasis.]

Notice that the two quotations used to begin this newsletter focus on a combination of interdisciplinary studies and problem solving. They suggest that the curriculum we provide to our students should be much more interdisciplinary. History is certainly an interdisciplinary field of study, since every academic discipline of study has a history and builds on its collected knowledge and skills. Moreover, every academic discipline of study is interdisciplinary, in that it draws on knowledge, skills, and methodologies of other disciplines as it explores solving the problems and accomplishing the tasks that define the discipline.

Each of us lives an interdisciplinary life. Throughout your daily life you draw upon a huge range of knowledge, skills, and experiences that cut across many different disciplines.

However, our precollege and higher education schooling is mainly divided into courses or time blocks that each focus on a specific discipline. The two quotations present arguments that schooling should be more interdisciplinary. This can be accomplished by a combination of developing more interdisciplinary courses and by redesigning current courses so they are more interdisciplinary.

Elementary school teaching of reading and writing provide a good example. As students begin to gain rudimentary skills in reading and writing, they can and do learn to read and write across the curriculum. We not only want students to learn to read and write, we want them to learn to make effective use of these skills in each discipline area they study. Roughly speaking, in U.S. elementary schools we expect students to gain useful reading and writing skills by the end of the third grade, and we then emphasize the use of reading and writing as learning tools in each subsequent area they study.

Through a combination of informal (outside of school) and formal education, many of today’s children gain considerable Information and Communication Technology (ICT) and math skills before entering the first grade. This early introduction to ICT and math is interdisciplinary—it is woven into the children’s everyday lives. This can be used effectively and built on in every area that students study in school. That is the main theme in my free book, The Fourth R, which emphasizes ICTing across the curriculum (Moursund, 2018, link).

As noted in the previous IAE Newsletter, I am writing a short book about the roles of ICT and mathematics in the discipline of history, what I refer to as mathing and ICTing across the history curriculum. My goal is to encourage and help preservice and inservice precollege teachers of history make more effective use of ICT and math in working with their students.

This writing project was motivated by my work in trying to improve math education. Math educators routinely face the issue that calculators and computers can accomplish many of the tasks that students in math classes are learning to do by hand. Many math teachers (and many parents) consider it to be cheating when a student uses a calculator or computer to do work that traditionally (historically) students have learned to do using pencil and paper.

Teachers in non-math subject areas need not be bound by the decisions being made by the math education community about student use of calculators and computers to help solve math problems. In this and the next two newsletters, I will illustrate a number of effective uses of math in history education, ones where these uses of math are highly dependent on computer capabilities.

The issue of calculator and computer use in math education has been with us for many years. It was the focus of a UNESCO report, The Influence of Computers and Information on Mathematics and Its Teaching, published almost 30 years ago (Cornu & Ralston, 1992, link):

The three-way interaction between mathematics, computers and mathematics education is becoming stronger each year. How schools and universities should respond is still an open question. This document has been prepared to contribute to the debate. The following quotation from the Overview chapter states succinctly why this debate is so important: We are facing a situation in which children are taught to do mathematics in ways that are very largely outmoded, with at least 80% of curriculum time wasted on trying, more or less successfully, to develop [paper and pencil, and mental] fluency in skills of now limited value.

The International Commission on Mathematical Instruction (ICMI) undertook a study, “The Influence of Computers and Informatics on Mathematics and Its Teaching”, which included a conference in Strasbourg, France in 1985, in which UNESCO cooperated. The outcome of the Study was a book published by Cambridge University Press, bearing the conference title. With the quick pace of change of computers, mathematics and its teaching, the book’s contents have become outdated. The development of this new document is explained in the Editors’ Foreword. [Bold added for emphasis.]

In brief summary, the bolded statement asserts that, in 1992, 80% of traditional math education time was spent teaching students to use by-hand methods to do tasks that calculators and computers can do. It is easy to argue about this 80% assertion. My personal informal research during my many years of teaching secondary school math teachers about the uses of computers in math education provided me with an estimate that at least 75% of curriculum time was used (wasted?) in manners discussed in the Cornu and Ralston report. So, I agree with their assertion.

I first started teachers about uses of computers and calculators in math education back in the summer of 1965. In those days, I was optimistic that these new ideas would rather quickly revolutionize math education. I was certainly naïve about how slowly curriculum content changes at the precollege level. The 1992 Cornu and Ralston report showed that we still had a very long way to go in realizing my dreams! Of course, some progress had occurred by then, and considerably more progress has occurred in the ensuing 27 years.

Graphing calculators first became commercially available in the mid 1980s (Wikipedia, 2020, link; Valentine, 3/11/2019, link). They quickly came into routine use by engineers, scientists, and others, and the use of slide rules virtually disappeared.

Gradually such calculators became commonly used in high school math classes. But, it took more than 30 years before their use was allowed in the Scholastic Aptitude Test (SAT).

In the past few years, students have been allowed to make use of a calculator on the SAT, a test that is widely used as part of the college admissions process (SAT, 2020, link).

The only Subjects Tests for which calculators are allowed are Mathematics Level 1 and Mathematics Level 2. You must put it away when not taking a mathematics test. A scientific or graphing calculator is necessary for these tests. We recommend using a graphing calculator rather than a scientific calculator.

A graphing calculator is an effective tool for graphing mathematical functions and carrying out a wide range of calculations. Notice that while the test itself is now sometimes delivered on a computer, students are not allowed to use the computer as an aid to solving the problems and answering the questions given in the math test or other parts of the SAT.

Reading and writing helped humans to accumulate knowledge and share it over distance and time. Eventually, the accumulated collection of written knowledge became large enough and valuable enough so that libraries were created. The accumulated documents were organized in a manner that helped researchers and other library users to find documents that were of particular interest to them. Thousands of years passed before the Dewey Decimal System and the Library of Congress Classification System were developed during the 19th century for organizing the shelving of books.

When you read the above paragraph, did it occur to you to wonder when the first large libraries were created? Nowadays, such information is at your fingertips (or at voice command). I just (verbally) asked Google on my smartphone, “When was the first library created?” The nearly immediate (print) response to my Google search was:

The word’s oldest known library was founded sometime in the 7th century B.C. for the “royal contemplation” of the Assyrian ruler of Ashurbanipal. Located in the Nineveh in modern day Iraq, the site included a trove of some 30,000 tablets organized according to subject matter.

This example illustrates five important aspects of my education.

1. First, I learned oral communication.
2. Second, I learned to ask questions about topics that interested me. (If you have raised children, you know that they learn to ask why questions at a very young age.)
3. Third, I learned to read and write. Both are valuable aids to learning on one’s own.
4. Fourth, I had a great many years of formal education, culminating in a Ph.D. in mathematics.
5. Fifth, ICT progressed rapidly during my lifetime. This has presented me, in my adult life, with a continual learning challenge. It also has presented me with tools (especially the Internet and Web) to meet this challenge. I have truly enjoyed this lifelong learning opportunity.

In terms of a modern education, the final point cited above is a game changer. Computers, the Internet and Web, and search engines have brought us a totally new approach for storing, accessing, and communicating collected information, as well as for learning and using one’s learning. Quoting from 100+ Internet Statistics and Facts for 2020 (Liedke, 1/4/2020, link):

As of January 5, 2020, there were 4,437,215,927 (4+ billion) internet users spanning the globe. [This is more than half of the world’s population.] This is compared to the 3.42 billion users recorded at the end of 2016.

A number of years ago, Google provided yearly reports on how many Web pages it routinely searched. It no longer provides this information. A 2013 article on Web statistics indicated that Google’s database contained 30 trillion documents at that time (Koetsier, 3/1/2013):

When you search, Google tries to figure out not just what you’re typing into the box, but what you mean. So algorithms for spelling, autocompletion, synonyms, and query understanding jump into action. When Google thinks it knows what you want, it pulls results from those 30 trillion pages and 100 million gigabytes, but it doesn’t just give you what it finds.

First, a ranking procedure uses over 200 closely guarded secret factors that look at the freshness of the results, quality of the website, age of the domain, safety and appropriateness of the content, and user context like location, prior searches, Google+ history and connections, and much more. [Bold added for emphasis.]

A 2016 article indicated that “Google’s Search Knows About Over 130 Trillion Pages” (Schwartz, 11/14/2016, link).

It boggles my mind to think of requesting my Google browser to search through many trillions of articles, select ones that it considers to be relevant to my request, order them using more than 200 proprietary criteria, and then report back to me in less than a second! This is now routinely done on a portable, multi-purpose tool we call a smartphone.

Information retrieval has always been an important aspect of schooling, and now the rapidly expanding field of ICT-based information retrieval is certainly a game changer. But, it is still up to the user to understand the information that is being presented and to make effective use of it.

Or, maybe it is not all up to the user. Computers can solve a wide range of problems and accomplish a wide range of tasks. Aha! This is another game changer. Computers, including robots and other automated machines, change what I personally need to learn to do using just my own mental and physical capabilities. My recommendation is that students should not spend their time learning to compete with ICT. Rather, they should spend their time learning to work with ICT in solving problems and accomplishing tasks across their interdisciplinary lives.

Teaching students the skills of effective online information retrieval has now become one of the most important aspects of ICTing across the curriculum. We now live at a time when humans and computers work together to solve problems and accomplish tasks. People and computers each have capabilities and limitations. An important part of a modern education is learning to live, work, and play in an environment in which today’s ICT capabilities are vast, and continue to grow with increasing rapidity.

The quote about the Google search engine given in the previous section includes the statement:

First, a ranking procedure uses over 200 closely guarded secret factors that look at the freshness of the results, quality of the website, age of the domain, safety and appropriateness of the content, and user context like location, prior searches, Google+ history and connections, and much more. [Bold added for emphasis.]

I added the bold for emphasis because the statement provides an important example of Big Brother is watching me. When I use the Google browser, it collects, maintains, and uses information about me (Curran, 3/30/2018, link). Out of curiosity, I just now did a Google search on “Big Brother is watching you.” George Orwell coined this phrase in the third paragraph of the first chapter of his novel 1984. Personally, I use the term more broadly to include not only governments, but also many corporations, social networking systems, and so on (Leetaru, 10/25/2018, link). The Big Brother image given below is from the Leetaru article.

Personal data has considerable commercial value. Did it ever occur to you to ask how Google can afford to make its search engine available free to users of the Web? (The company sells ads.)

As personal example, I make considerable use of my credit cards. In the past few years I find that I am receiving ads, both on my computer and via mail, that specifically target products I have purchased recently. Some ads come from the stores where I have made the purchases and some come from other stores that sell the same or similar products. The collecting, using, and selling of personal information has become a huge business!

The history of this business development is an interesting topic that cuts across many disciplines. I think this history is relevant to our children, history they should be learning about in their schooling across all subject areas. In what subject areas and at what grade levels do you think today’s students should learn about this Big Brother? Certainly Orwell’s book is an important part of literature. But, what about business or history courses? What about every course that makes use of online computer-assisted instruction? What about every course in which students are expected to routinely make use of resources available on the Web? What about the data that schools collect about their students? Who should have access to students’ report cards, attendance records, and so on?

Long before the development of reading and writing, people preserved and passed information from generation to generation via oral history, songs, dances, the tools they made and used, their routine customs and social structures, and so on. Now, an education that includes learning to read and write is considered to be a birthright of children throughout the world.

Students in the “good old days” had relatively limited access to print materials. Especially in schools and libraries, this access was limited to materials that had been screened carefully by the teachers or librarians.

The Internet and Web have greatly changed this situation. Unfortunately, in many cases available online material is tainted by being highly biased or even deliberately faked. Thus, an important part of a modern education is helping students learn to separate the wheat from the chaff. This is especially true in the humanities, such as history, ancient and modern languages, literature, philosophy, law, politics, religion, and art.

Good progress toward achieving this goal is occurring in the wealthier nations throughout the world. But, it is not just the connectivity that is important. It is the effective use of this connectivity in schools, homes, and informal education.

Have you considered that all information stored on the Web is historical information? (It was written and stored in the past.)

We are now collecting and storing historical information at a prodigious rate. Of course, much of the information being produced and stored is not available on the Web. For example, just think of the many billions of digital photographs that people are taking and storing on their home computers and/or on their smartphones. Think of the millions of stories and reports being written and stored on home computers as well.

The ability to make changes to digital photographs and videos has added to our problems. It used to be that one could trust photographs and videos. Now, the use of fake videos and still photographs is commonplace. This is still another challenge to educating our children (and adults) to learn to verify as well as to understand the information they receive from all resources.

In brief summary, helping students learn effective ways of organizing, evaluating, interpreting, reporting and using this vast amount of available data is a very important component of the study of history today. Both math and ICT con provide important and quite useful aids to those endeavors. ICT is both a wonderful gift and, in terms of fake news, it also can be a major threat.

The next two newsletters in this series will explore additional aspects of mathing and ICTing across the history curriculum. Some topics to be covered include graphical representations of historical information, and an introduction to data bases, statistics, and future studies.

Cornu, B., & Ralston, A. (1992). The influence of computers and informatics on mathematics and its teaching. UNESCO. Retrieved 1/1/2020 from https://unesdoc.unesco.org/ark:/48223/pf0000093772.

Curran, D. (3/30/18). Are you ready? Here is all the data Facebook and Google have on you. The Guardian. Retrieved 1/25/2020 from https://www.theguardian.com/commentisfree/2018/mar/28/all-the-data-facebook-google-has-on-you-privacy.

Koetsier, J. (3/1/2013). How Google searches 30 trillion web pages, 100 billion times a month. Venture Beat. Retrieved 1/12/2020 from https://venturebeat.com/2013/03/01/how-google-searches-30-trillion-web-pages-100-billion-times-a-month/.

Leetaru, K. (10/25/2018). Social media companies collect so much data even they can’t remember all the ways they surveil us. Forbes. Retrieved 1/24/2020 from https://www.forbes.com/sites/kalevleetaru/2018/10/25/social-media-companies-collect-so-much-data-even-they-cant-remember-all-the-ways-they-surveil-us/#204d0d577d0b.

Liedke, L. (1/4/2020). 100+ Internet statistics and facts for 2020. Retrieved 1/12/2020 from https://www.websitehostingrating.com/internet-statistics-facts/.

SAT (2020). Calculator policy. Scholastic Assessment Test. Retrieved 1/20/2020 from https://collegereadiness.collegeboard.org/sat-subject-tests/taking-the-test/calculator-policy.

Schwartz, B. (11/14/2016). Google’s search knows about over 130 trillion pages. Search Engine Land. Retrieved 1/25/2020 from https://www.internetlivestats.com/google-search-statistics/.

Valentine, N. (3/11/2019). The history of the calculator. The Calculator Site. Retrieved 1/23/2020 from https://www.thecalculatorsite.com/articles/units/history-of-the-calculator.php.

Wikipedia (2020). Graphing calculator. Retrieved 1/24/2020 from https://en.wikipedia.org/wiki/Graphing_calculator.