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Getting to the Second Order: Moving Beyond Amplification uses of Information and Communications Technology in Education

Moursund, D.G. (2002). Getting to the second order: Moving beyond amplification uses of information and communications technology in education. Learning and Leading with Technology. v30 n1 pp6-. Available at

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I am pleased to have the opportunity to write for the first issue in Volume 30 of Learning & Leading with Technology. When I started this periodical nearly 30 years ago, I gave little thought as to what its future might be.

Like L&L, the field of Information and Communication Technology (ICT) in education has come a long way--but it has just scratched the surface of what is to come. During the past three decades, ICT has had some limited effect on curriculum content, instructional processes, assessment, and the professional lives of educators. But, for the most part our educational system has been "business as usual," with many small (incremental) changes. In total, our educational system has not changed much during this time.

Contrast this with the ICT-based changes outside of our educational system (Christensen, 2000; Moursund, 2001). There have been substantial gains in productivity attributed to ICT. Many new companies have been created and have prospered, and many other companies have proven unable to effectively deal with ICT-related changes.

My prediction is that the next three decades will see ICT being a disruptive force in education. Large changes will occur, and many of our schools and school systems that attempt to follow the "traditional" path of the past decades will not prosper. This article looks at where ICT in education is headed and what educators can do now to help significantly improve the quality of education our students are receiving.

Incremental Change

On May 6, 1954, Roger Bannister became the first person to break the 4-minute barrier in the mile foot race. Since then, through better training, changes in the track surface, better running shoes, and so on, the world record for the mile has been broken a number of times, and it is now about 3 minutes 43 seconds. This is an excellent example of incremental change, with small changes occurring from time to time. Note that the total improvement has been less than 8%.

Now, think about two possible goals in people movement:

  • The goal is to have a person run a mile as fast as possible, aided by "simple technology" such as good running shoes, a good running track, good coaching, and rigorous training.
  • The goal is for an ordinary person to quickly move a distance of a mile using appropriate, safe, modern technology.

Clearly, the more sophisticated technology that is allowed in achieving the second goal has made it easy for most people to break the 4-minute mile. Indeed, the technology need not be very sophisticated. Bicyclists and motorcyclists can move faster than the fastest runners. The first locomotives powered by steam engines were not an incremental change in transportation--they were a revolutionary change that contributed to significant changes in our society.

Amplification Versus Second-Order Change

To a considerable extent, new inventions are first used to "amplify" (do better, faster) what we are already doing (Moursund, 1997). Thus, a word processor can be used like an electric typewriter that has a memory. Using a word processor like an electric typewriter is an amplification (i.e., first-order) use of ICT. This type of use eventually led to desktop publication, a second-order use of the technology. Desktop publishing includes:

  • design for effective communication
  • appropriate use of styles and templates
  • appropriate use of typefaces and color
  • appropriate use of graphics; and
  • meeting contemporary publication standards

The word processor and desktop publishing facilitate the "revise, revise, revise" and the publishing phase of process writing. Desktop publishing was a disruptive technology, and it substantially changed the publishing industry.

Three conditions need to be satisfied to move from first-order to second-order applications of ICT:

  1. appropriate hardware and software
  2. a clearly recognizable benefit (i.e., intrinsic motivation) to people who potentially could make the move
  3. formal and informal training and education to help interested people make the move

For desktop publishing, the appropriate hardware and software became re available with the introduction of the Macintosh computer and desktop laser printer in 1984. Many people in publishing recognized the potential and were intrinsically motivated to move to desktop publishing. Through self-instruction, learning from their peers, and workshops and longer courses, a large number of people achieved levels of expertise that met their needs.

Some people would claim that our K-12 students have also made the move, because essentially all high school graduates know how to use a word processor. However, for most of them, use of a word processor is essentially at the amplification level and is far from meeting contemporary standards for desktop publishing.

Essentially the same analysis holds for developing and publishing documents in an interactive multimedia environment, and for a number of other uses of ICT. Many students and teachers find a variety of ICT applications to be intrinsically motivating. However, relatively few K-12 students have moved significantly beyond the amplification level in their uses.

Why is this? Let's go back to the three conditions necessary to move from first-order to second-order use.

  1. Appropriate hardware and software. This is available in essentially all schools. Indeed, perhaps 2/3 of students have appropriate facilities at home. Thus, this is not the reason why so few students move beyond amplification of first-order ICT applications.
  2. Clearly recognizable benefits. For the most part, curriculum developers, teachers, students, and many other stakeholders do not recognize the potential benefits of moving beyond amplification. For example, I am not aware of any statewide assessment of students that tests for knowledge and skills in desktop publication, interactive multimedia publication, or full integration of ICT in math and science education. Such an assessment would need to be in a hands on mode, with the electronic copies being carefully analyzed and graded. Most K-12 students lack the maturity to recognize that something is missing in their ICT education, and they lack the knowledge of potential benefits of the second-order applications we are discussing.
  3. Training and education. Of course, self-instruction opportunities for K-12 students and their teachers are widely available. But, the formal instruction they are receiving--the students while they are in K-12 schools; the teachers while they are in their teacher education programs and inservice education--is totally inadequate to the task.

ICT in Math Education

The same type of analysis as was used with desktop publishing is relevant to math education, but additional issues will emerge. (Author's note: Read more about ICT in math education in Moursund, 2002a.) Moreover, the approach used here can be applied to other disciplines.

Begin with a set of goals for education in the discipline being analyzed. In math education, we want students to:

  1. Learn math and how to solve math problems that they encounters as they, work, study, and play in a wide variety of discipline areas.
  2. Learn to pose mathematical problems and represent problem situations as mathematical problems.
  3. Learn how to learn math.

Let's briefly analyze the potential for ICT to affect these goals.

  1. Learn math and how to solve math problems. Perhaps the largest potential ICT effect in math education is that calculators and computers can solve a very wide range of math problems. Thus, at the current time our math education system spends the majority of its teaching efforts and time helping students learn to do procedural tasks that machines can do faster and more accurately. The analogy with the mile foot race and traveling a mile aided by technology seem particularly powerful to me. A person plus machine can out perform a person alone in a wide variety of math problem-solving tasks. For example, consider graphing of functions and data.
  2. Learn to pose mathematical problems and represent problem situations as mathematical problems. This area is increasingly important as use of computational modeling steadily grows in each discipline. For example, one of the winners of the Nobel Prize in Chemistry in 1998 received the award for 15 years of work in computational modeling in chemistry. All of the sciences (including math) now include computational modeling as one of their major components. Computational modeling in economics has long been a productive approach to problems in this field. The spreadsheet is, of course, a powerful aid to computational modeling in business and many other fields. The digitizing and manipulation of film and video are examples of using computational modeling that makes use of quite sophisticated mathematics.
  3. Learn to learn math. Computer-assisted learning (CAL), intelligent computer-assisted learning (ICAL), and distance learning are all aids to learning math. Largely, CAL has been used at an amplification level in math education, as an automated flash card system with lots of bells and whistles. For the most part, distance learning is used to deliver the traditional curriculum. The Web is a global library, and learning to use the math global library is part of learning to learn math. For the most part, students are not learning to use the math global library.

Let's return to our three-item list of what is needed to move from first order to second order, and look at it from a math education point of view.

  1. Appropriate hardware and software. Math educators believe every student needs ready access to the ICT systems to be used in math education. This helps to explain the emphasis on handheld calculators. At the current time, the "ready access" requirement cannot be met by providing all students with handheld Internet-connected computers, or laptops and desktop machines. Progress in handheld computers and wireless technology is gradually eating away at this problem.
  2. Clearly recognizable benefits. The use of handheld calculators on state and national assessments is now generally accepted. Many students choose to carry a calculator and/or to have one readily available at home. But, little progress has occurred to allowing students to use more sophisticated ICT on math tests--thus, there is a severe restriction to potential benefits to students.
  3. Training and education. It takes very little time to learn to use a four-function calculator at an amplification level. However, ask yourself the following three questions:
    1. Do my students and I know how to make effective use of the memory (e.g., the M+) and the numerical constant features of a simple calculator?
    2. Do my students and I know how to detect and correct keying errors?
    3. Do my students and I use a simple calculator comfortably and easily in a manner that brings this computational power to all subject areas that we address?

Very few teachers answer "yes" to all of these questions. It is evident that it takes significant training and education to move beyond the amplification level in use of a simple calculator. The learning effort required for more powerful calculators and for computers is much larger.

Now, let's imagine what would constitute moving math education into broad-based second-order ICT applications. Again, I follow my list of three necessary conditions for this.

  1. Appropriate hardware and software. Students need a computer system with a large display, a full-size keyboard, and good connectivity. They need a full range of software that is designed to support the learning and using of math both in a math classroom environment and in the other environments (school, home, work, play) that they encounter.
  2. Clearly recognizable benefits. Students will recognize the benefits when the tool becomes an integral component of curriculum, instruction, assessment, and application in both the math classroom environment and in a wide range of environments outside of the math classroom. Students will be able to accomplish math-related tasks that they want to accomplish (intrinsic motivation) and cannot accomplish without the technology.
  3. Training and education. A substantial change in math education is needed to achieve second-order effects. Although calculators have given us some hints as to what is possible, calculators are too limited to transform math education. Imagine, for example, the effects of all K-12 students having routine access to "just in time" highly interactive intelligent computer-assisted learning and distance learning that covers all topics in the K-14 math curriculum. This instruction would include built-in, routine use of the capabilities of an ICT system. It would be provided on an ICT system with a large viewing screen, good keyboard as well as voice input, and good connectivity to the Internet.

Problem Solving

Each academic discipline addresses the issues of representing and solving the problems within the discipline. In this section, I use the term problem solving to encompass a variety of tasks such as:

  • posing and answering questions
  • posing and solving problems
  • posing and accomplishing tasks
  • posing and making wise decisions
  • using higher-order, critical, and wise thinking to do all of the above

Figure 1 illustrates six steps that might occur as one encounters and works to solve a math problem situation. The same type of diagram exists for each discipline area. At the current time, however, the point I am trying to make is perhaps best illustrated in math.

Figure 1. Diagram of math problem solving.

The six steps are:

  1. Understand the problem situation and translate into a clearly defined problem. What is the given initial situation and what is the goal? What are the resources and rules that apply to solving the problem? (Moursund, 2002b).
  2. Model the problem as a math problem. That is, translate the problem into a "pure" math problem. This is somewhat akin to what one does in translating a word problem into a set of equations to be solved.
  3. Solve the pure math problem.
  4. Translate the results back into a statement about the problem to be solved. This can be thought of as unmodeling, sort of the opposite of step 2.
  5. Check to see if the problem has actually been solved.
  6. Check to see if the original problem situation is resolved (solved). If it hasn't, reformulate the problem situation and/or problem and start over at step 1 or 2.

Estimates are that approximately 75% of K-12 math education time is spent helping students learn to do step 3 with reasonable speed and accuracy. Thus, the time spent learning the other steps is quite limited.

Step 3 is what calculators and computers do best. That is, the great majority of the K-12 math education curriculum consists in teaching students to compete with machines! This suggests that we might decrease the time spent in teaching by-hand methods of doing step 3, and spend the time that is saved in developing greater skill in doing all of the other steps. This would represent a substantial change in math education.

Remember, the analysis in this section focused on math. However, the diagram of Figure 1 is applicable in any academic discipline. Steady progress in each discipline is increasing the number of step 3 procedures that can be carried out by an ICT system and in which ICT is a major help to a person carrying out a procedure.

Science of Teaching and Learning

There is a large and rapidly growing body of knowledge called the Science of Teaching and Learning (Bransford et al., 2000). This research and practice-based knowledge provides a foundation for substantial improvements in our educational system. The problem, however, is how to achieve widespread implementation of this research and practice-based knowledge.

One way to think about this is to consider what can be mass produced and/or mass distributed, and what cannot. For example, it is very difficult to change the educational knowledge and skills of a few million teachers. It is relatively easy to mass-produce and mass distribute four-function handheld calculators. Although the writing of a book or a piece of software is typically done by a small number of people (not mass production), a book or software itself can be mass reproduced and mass distributed.

If ICT is going to help in substantially improving education, it will be through aspects of curriculum content, instructional processes, and assessment that can be mass-produced and/or mass-reproduced, and mass-distributed. The following list provides some examples. It provides some insights into the future of education.

  1. Highly interactive intelligent computer-assisted learning (HIICAL) can be mass-reproduced and mass-distributed. Eventually we will have HIICAL that covers the full range of curriculum that a K-12 student person might want to study. This will be a slow, gradual process. HIICAL will incorporate what is known about the science and practice of effective teaching and learning. Eventually we will have a substantial amount of HIICAL that can teach better than an average classroom teacher who is attempting to teach a whole classroom full of students. At the current time there are a modest but growing number of examples of such HIICAL. An excellent example is provided by the Fast ForWord software used to help severe speech delayed students (Fast ForWord, 2002). Some of the "Help" features being built into modern pieces of software can be categorized as HIICAL.
  2. Software that can solve or help solve a specified category of problems can be mass-reproduced and mass-distributed. Examples include the spelling checker, thesaurus, and grammar checker in word-processing software; math problem-solving software such as Mathematica or Maple; and statistics and graphing software. It is disruptive to curriculum content when curriculum is changed from teaching students to do tasks by hand to teaching students to do such tasks in a computer-assisted environment. Many teachers are skilled in teaching the lower-order skills needed in problem solving and are not comfortable moving to an emphasis on higher-order skills.
  3. Interactive assessment (computer-assisted testing) making possible both self-assessment and assessment at a time that is convenient to the student. Though such tests are expensive to develop, they are gradually coming into widespread use. Eventually it will be possible for students to easily assess themselves on whatever they are striving to learn. Often this is a feature of HIICAL.
  4. Individualized instruction. Constructivism and individualization are highly touted in education, but are not well implemented. This is partly because an individual teacher cannot readily know in detail what each of their students knows and adjust the instruction so that it builds on the knowledge each individual student already has. At the current time, developing and implementing an individual education plan is costly relative to the current per-pupil costs of general education. An interesting aspect of ICT is that it can support a great deal of individualization in a mass-production mode.
  5. All students will have routine access to the Web. Neither the teacher nor the books available in one's classroom or school library hold a candle to the size of the emerging global library available on the Web. It is somewhat disruptive to a teacher for students to find information the teacher does not already know.

Concluding Remarks

The totality of human knowledge continues to grow quite rapidly. Thus, our educational system is faced by content-related problems:

  1. What should we help students store in their heads? Remember, a student can learn only a tiny (and steadily decreasing) fraction of the totality of human knowledge. Thus, our educational system needs to continually reexamine this issue.
  2. What should we help students learn to do making use of aids such as ICT, books, and other mind tools? Remember, a steadily growing amount of this knowledge is stored in computers in "the ICT system can do it for you" mode (as in step 3 of Figure 1).

ICT can help students to learn more, better, and faster. Still, such improvements are incremental. They are not second-order changes. They cannot hope to begin to make a dent into the rapidly growing totality of human knowledge.

ICT can solve many of the problems and accomplish many of the tasks that students are currently learning to do by hand. Moreover, ICT can help students become substantially more productive in solving problems and accomplishing tasks. If appropriately educated, a student working with an ICT system can far out perform a student who lacks such an aid in a wide range of problem-solving tasks. Our educational system will be significantly change education in the next three decades as it incorporates the idea of educating students and ICT to work together.

For ICT-using teachers, the message is clear. Work to move yourself and your students--your curriculum, instruction and assessment--from amplification (first-order) uses of ICT to second-order uses of ICT.


Fast ForWord:




Bransford, J. D., Brown, A. L., & Cocking R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

Christensen, C. (2000). The innovator's dilemma: When new technologies cause great firms to fail. New York: Harper Business.

Moursund, D. G. (1997). Beyond amplification. Learning & Leading with Technology, 24(8), 4-5.

Moursund, D. G. (2001). The innovative educator's dilemma. Learning & Leading with Technology, 28(8), 4-5, 16.

Moursund, D. G. (2002a). Improving mathematics education [Online]. Available:

Moursund, D. G. (2002b). Increasing your expertise as a problem solver: Some roles of computers [Online]. Available:


Computer-Assisted Learning (CAL): Includes drill and practice, tutorials, simulations, and virtual realities designed to help students learn. CAL includes the "Help" features built into software applications and can be a component of a Web-based distance learning course.

Constructivism: The learning theory that students construct knowledge by building on their current knowledge. This theory helps make the distinction between teachers teaching and students learning, and it supports the need for individualization of instruction.

Disruptive Technology: A new technology that is disruptive to a current business or way of doing things. For example, the automobile was disruptive to the horse and buggy industry; the microcomputer and word processing software were disruptive to the typewriter industry.

Highly Interactive Intelligent Computer-Assisted Instruction (HIICAL): Begin with CAL. Design it so there is a great deal of interaction between the computer and the learner. Enhance this with artificial intelligence to improve the quality of the instruction and the interaction. The result is HIICAL. For more, see L&L 28(7).

Information and Communications Technology (ICT): ICT is an expansion on the term information technology (IT) designed to stress that communications technology such as the Internet is an important component of the field.

Intelligent Computer-Assisted Learning (ICAL): Use of artificial intelligence to improve CAL. For example, an ICAL system may contain models of the learner, the curriculum content, the teaching process, assessment, reward structures, and so on. These are combined and used in an intelligent fashion to increase the quality, quantity, and speed of student learning.

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