Issue Number 249 January 15, 2019




ICT Tools and the Future of Education
Part 3: ICT and Math Education

David Moursund
Professor Emeritus, College of Education
University of Oregon

“Any sufficiently advanced technology is indistinguishable from magic.”

“Computers are incredibly fast, accurate, and stupid. Human beings are incredibly slow, inaccurate, and brilliant. Together they are powerful beyond imagination.” Note: This quote is often mistakenly attributed to Albert Einstein; most likely the correct attribution is to Leo Cherne at the Discover America Meeting, Brussels, June 27, 1968 (Shoemate, 11/30/2008, link).


Give a person paper, a quill pen, and ink, and the person may produce writings that have enriched the lives of millions of readers, much as Shakespeare did. Give a person oil paints, canvas, and brushes, and the person may produce paintings that have enriched the lives of millions of viewers, such as Michelangelo did. The paper or canvas, and the writing or painting implements, have no intelligence or self-contained creativity. But, humans using them produced miraculous products.

Until fairly recently, all of the intelligence, creativity, and drive required to be a good writer or artist came from the human being using the tools. This required many years of study, practice, and hard work on the part of the tool user. In recent years, Artificial Intelligence (AI) has made sufficient progress so that it has become a significant contributor to the intelligence and creativity of many people.

When a new tool is developed, the people of the world face the challenge of adjusting to the capability and limitations of the tool and learning to use it appropriately and effectively. If the new tool is a better bottle opener, our informal and self-instruction system is up to the task. When the new tool is as powerful and broadly applicable as reading and writing, the world is changed. We invented schools and schooling to help address this new challenge. It has taken us thousands of years for our schools to develop their current capabilities in teaching reading and writing, and using these capabilities throughout the curriculum—and we still are making progress.

Computers and related Information and Communication Technology (ICT) are much more like reading and writing than they are like a better bottle opener. Our informal and self-instruction system has proven capable of helping many millions of people learn to play computer games and to use a smartphone. However, our schools have so far made only modest progress with the challenges of effective integration of the use of computers and ICT into our formal educational systems.

Building on the Previous Work of Self and Others

I consider every person to be both a lifelong learner and a lifelong teacher. In every interaction you have with another person, you are actually playing both teaching and learning roles. Within the realm of teaching and learning, I believe the most important idea is learning to build on the previous work of self and others. Your own learning builds a repertoire of knowledge and skills that you can use in the future. Building on the work of others takes advantage of their knowledge and skills.

Think about oral communication. We learn oral communication from people who are already skilled speakers and listeners. Next, think about reading and writing. Humans developed reading and writing about 5,500 years ago. You learn to use these human-developed tools by using the help of teachers, family, friends, and others, combined with the knowledge about reading and writing that is available in print, online, and other resources developed by people.

It takes lots of work over an extended period of time to become skilled in oral communication, reading, and writing. Our informal educational systems and schools have gradually become better at helping children to gain these skills. So far, however, these is no magic pill. A person becomes better in these communication areas only through extended study and practice over many years.

Background Information about Math Education

As noted in the previous newsletter, math is a human-developed tool. Because this tool has proven to be useful across the many different disciplines in the school curriculum and in so many areas in the world outside of education, it has long been considered to be one of the basics of education.

Although considerable math vocabulary and ideas are built into our oral and written communication systems, the discipline of mathematics presents a quite different type of learning challenge. For example, consider writing. While errors in punctuation, spelling, and grammar may be distractive to a reader, they typically do not obscure the meaning of the message being communicated. In contrast, the smallest error in solving a math problem can produce a completely wrong result. A student learning math is faced by a challenge of achieving a level of perfection quite different than that a student faces in learning oral and written communication.

A significant fraction of PreK-12 school time is spent on helping students to learn math. Yet most students still do not find it easy to learn math and to effectively use math beyond solving relatively straightforward computational problems.

People have developed a plethora of aids to learning and doing math. The abacus, first developed about 2,500 years ago, proved to be a valuable aid and it is still in use. The bead frames used in primary schools can be thought of as abacus-type devices (Mastermind Abacus, n.d., link).

Progress in developing aids to learning and doing math was slow for many hundreds of years. Now we have very sophisticated electronic calculators and computers that have produced a much faster rate of change. However, the use of these aids has been slow to be widely adopted and integrated into schools.

For example, consider the extent to which students taking math tests are allowed to use today’s sophisticated handheld calculators and Web-connected computers. Both are routinely used as needed by people outside of school classrooms. Ask yourself, “Is there a major difference between what we are teaching and what will most benefits students as they become adults in our society?”

The Two Quotations Given at the Beginning of This Newsletter

I have long enjoyed the Arthur Clarke quotation that an advanced technology is indistinguishable from magic. What would people from two hundred years ago have thought about a Smartphone? Spend a minute thinking about the technologies and the technological progress that a Smartphone incorporates—surely our ancestors would have considered many of these capabilities to be magic! Now, if people in the more economically developed countries wanted to, they could provide every student with smartphones and computers—and thoroughly integrate their use throughout the curriculum (Moursund, 2018b, link).

The second quotation is particularly relevant to this and the next newsletter about math education. A hand-held calculator has no human-like intelligence, emotions, sense of itself, and so on. But, in the hands of an appropriately educated person, it can quickly and accurately accomplish a wide variety of math tasks that humans (unaided by such machines) are not very fast or accurate at doing.

Consider the capabilities of a very inexpensive hand-held 6-function calculators. Workings with decimal numbers, such calculators can add, subtract, multiply, divide, and calculate square roots. Hmm. When was the last time you encountered the need to divide a six-digit integer by a four-digit integer and calculate the (positive) square root of the result—using only paper, pencil, and your brain? My 8-digit solar-powered calculator that I bought for $3.33 in 1989 can quickly tell me that the square root of (695,344 / 3,921) is 13.316847. (Occasionally I see such calculators on sale for a dollar.) Of course, I have trouble imaging why I would ever want to do such a calculation except to impress my readers!

My Kindle Fire Tablet that I bought on sale for $29.99 about a year ago can handle such calculations using voice input and voice output. But, neither my calculator nor my Kindle Fire Table has any understanding of what it is doing, or why. That is, computers display a type of machine-like intelligence, but are totally lacking the type of intelligence that we call human understanding.

Computers and Spoken Language

I believe a very important aspect of a modern education is to gain increased understanding of current capabilities and limitations of computers, and what lies ahead in the relatively near future. I also strongly believe that every teacher, in every discipline of study, has the responsibility of helping their students to gain an increased insight into the current and emerging capabilities of computers within the discipline they are teaching.

I want you to imagine what math education will or could be like when a student can speak to a computer, orally posing a math problem. The student and the computer will interact orally as they work together to clarify details of the problem. The computer will then solve the problem. I believe today’s K-12 students will live many years of their adult lives in a world where this computer capability has become commonplace!

This will, of course, require having computer systems that are quite capable in dealing with spoken language. Consider the task of translating from one human language to another. We now have computer systems that can accept natural language speech as input, translate the speech into text in the speaker’s language, then translate that text into any of a large number of other languages, and finally output the translation in a voice that is a good imitation of the original speaker’s voice (Moursund, 2018a, link). I find that truly amazing. (It reminds me of the Tricorder in the original Star Trek television series from more than 50 years ago.)

A modern education includes a significant focus on education-related technological progress. In the science fiction of Star Trek, when Captain Kirk and other officers are facing a major problem, they meet to discuss the problem. The ship’s computer is present and listening to the conversation, and responds to questions directed to it. The computer seems to be able to answer any question that is based on the accumulated knowledge of the human race. This is not unlike IBM’s computer named Watson that defeated two past Jeopardy champions in a question-answering Jeopardy TV program in 2011 (Wikipedia, 2018b, link).

Disciplines of Study

Each individual discipline of study can be defined by the types of problems it addresses, the problem-solving tools and methodologies it has developed, and the accumulated results it has achieved. That is, problem solving is an integral part of each discipline of study.

Problem posing is the process of identifying and communicating a problem to be considered and possibly solved. Within each discipline of study, researchers and practitioners pose and study both new problems and past problems that are still of current interest and importance.

All students can learn to pose problems within a discipline they are studying. Nowadays, a student can also learn to search the Web and other resources in a quest to find out what is known about a particular problem. If the problem has been solved, it may well be that a solution process or answer is available on the Web.

This situation creates a potentially very valuable addition to teaching and learning in any discipline. Think about this in the discipline of mathematics. Students who learn to read and write in a natural language can also learn the rudiments of reading and writing math. With this knowledge they can look up math-related information about problems posed by others and themselves.

I like the analogy of reading across the curriculum and mathing across the curriculum. Schools have long promoted reading across the curriculum, and using reading as a routine learning vehicle. One of the weaknesses in our current math education system is that many students do not learn to read math well enough to learn math by reading a math book. In many ways, our math education system is still surprisingly similar to the “oral tradition” type of teaching used before books became readily available.

Problem Solving Using Mathematics

Why do our schools pay so much attention to math and math problem solving? Perhaps the simplest answer is that so many of the problems faced by people living in today’s world are math related. We want to prepare students to adequately deal with these math-related aspects of everyday life.

Because math is such a rigorous discipline, based on carefully considered definitions and proofs, a huge number of different types of math problems have been studied and solved over the years. Unlike many problems in other disciplines, once a math problem has been solved, others can confidently use and build on the results. Today’s students can access, learn to use, and build on many hundreds of years of accumulated math knowledge. Moreover, we now have available a large collection of computer programs able to solve the types of problems that we currently teach students to solve by hand.

To Be Continued in the Next Newsletter

This newsletter has provided some insights into why math is such an important part of education, why problem solving is central to doing and using math, and some roles of computers in solving various types of math problems.

The next newsletter will explore a six-step problem-solving process based on the work of George Pólya that can be used in attempting to solve a variety of math problems, and the roles of humans and computers in carrying out these steps (Pólya, 1957).

References and Resources

Mastermind Abacus (n.d.) What is an abacus? Retrieved 12/23/2018 from http://www.mastermindabacus.com/history.html.

Moursund, D. (2018a). Information Age Education in translation. IAE-pedia. Retrieved 12/30/2018 from http://iae-pedia.org/Information_Age_Education_(IAE)_in_Translation.

Moursund, D. (2018b). Technology and problem solving. IAE-pedia. Retrieved 12/20/2018 from http://iae-pedia.org/Technology_and_Problem_Solving.



Shoemate, B. (11/30/2008). Einstein never said that… Ben Shoemate Blog. Retrieved 12/23/2018 from http://www.benshoemate.com/2008/11/30/einstein-never-said-that/.

Wikipedia (2018a). Computer simulation. Retrieved 12/28/2018 from https://en.wikipedia.org/wiki/Computer_simulation.

Wikipedia (2018b). Watson (computer). Retrieved 12/31/2018 from https://en.wikipedia.org/wiki/Watson_(computer).




Email: moursund@uoregon.edu.

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