Information Age Education
   Issue Number 67
June, 2011   

This free Information Age Education Newsletter is written by David Moursund and Bob Sylwester, and produced by Ken Loge. The newsletter is one component of the Information Age Education project. See http://iae-pedia.org/ and the end of this newsletter.

Information Age Education is now publishing some of its materials in Kindle format. See http://iae-pedia.org/IAE_Kindle_Books for great prices on good materials.

Stress and Education Part 4:
Technology-based Stressors in Math Education


“To err is human; to really foul things up requires a computer.” See a 1969 possible source for this quote in article at http://quoteinvestigator.com/2010/12/07/foul-computer/#more-1699.

“A little learning is a dangerous thing. ” “Fools rush in where angels fear to tread.” (Alexander Pope, 1688–1744.)

The essence of this issue of the newsletter is captured by the quotes given above. For a great many people, computer technology is inherently stressful, and reasons for this are clear in the two quotes from Alexander Pope.

This is the final of four IAE Newsletters focusing on stress. We are particular interested in how chronic stress affects health and one’s cognitive capabilities. In brief, a little stress can be good, and chronic stress is bad.

In the third newsletter, we explored math education and noted that a combination of the challenge of the discipline and how it is taught can be quite stressful to many students. In this newsletter, we will look at Information and Communication Technology (ICT) both as a stressor of students and as a stressor to our math education system. A stressor for the system adds to the stress of students.


Historical Note

Historical records suggest that humans have long had an interest in counting objects and developing aids for record keeping and doing arithmetic. The Ishango bone pictured below is about 20,000 years old and appears to be engraved with tally marks. See http://en.wikipedia.org/wiki/Ishango_bone.

Ishango Bone

We are all familiar with the abacus. Predecessors were merely marks made in the dirt, and they were quite useful in doing addition and subtraction. The abacus is both a powerful computational aid and variations on it (such as bead frames) are still routinely used in math education. Over many centuries, humans developed math tables, calculators, slide rules, and computers as aids to doing computation.

We have also developed point of scale scanning equipment, odometers, speedometers, and global positioning systems. The trend seems clear. People find the need to measure and count things, collect and analyze data, develop and use mathematical models, and to do extensive manipulations and computations on data. Thus, ICT has steadily grown in importance.


Stress Related to ICT in Education

It’s likely that you aren’t very skilled at using an abacus or a slide rule, since it takes considerable learning and practice to develop a high level of expertise in them. It’s much easier to gain and maintain calculator skills.

Now, consider the sequence of tools: abacus, paper and pencil algorithms, and handheld electronic calculator. While each is a useful aid to doing arithmetic calculations, they vary considerably. One way to think about this is that an abacus is a physical representation of qualities, with addition being done by physically grouping beads that represent qualities. In some sense, it is “in tune” with a person who is at the Piagetian concrete operations level of cognitive development. However, it makes use of positional notation, which is a quite abstract idea.

Paper and pencil representations of quantity are more abstract. Many students thus have difficulty in developing mental models of quantity and manipulating quantity in paper and pencil arithmetic. Abstractions made possible by the language and notation of math have led us to (attempt to) teach math that is well above the cognitive development level of many students.

Calculators present a still greater challenge to developing an underlying conceptual understanding. It is easy to learn to push calculator buttons and read the results. However, think of the challenge of detecting keying errors and operational errors (such as multiplying when one should have divided) and having a conceptual understanding of processes and results.

The trio of abacus, paper and pencil, and calculator can be thought of in terms of their increasing level of abstraction. Increasing abstraction can be stressful to students who have not yet reached a sufficient level of cognitive development.

You are probably comfortable in using a 4-function calculator that can add, subtract, multiply, and divide. However, quite likely this calculator also contains M+, M-, and MC, and MR keys. These “memory” keys greatly increase the calculator’s capabilities. Many people find it stressful to deal with devices that have features or capabilities that they do not understand. (Do you feel a little intimidated by kids using their thumbs to rapidly sent text messages on a cell phone? How about learning to use other “powerful” capabilities of your cell phone?)

Think about the increasing level of cognitive challenge of scientific calculators, of programmable and graphing calculators, and of computers. If one can accurately tell such machines what you want them to do for you, and if what you want done is within the capabilities of the machine, then you can use calculators and computers to accomplish a very wide range of math and non-math types of tasks. The users of such machines face:
  1. The challenge of learning specific human-machine interfaces—how to give instructions to a particular machine. This requires a level of precision well beyond what people are used to in ordinary human-to-human communication.

  2. The capabilities and limitations of the machine. A four-function handheld calculator cannot prepare a peanut butter and jelly sandwich for you.

  3. An understanding of the problem being solved or the task being accomplished.

  4. Haunting memories of,  “To err is human; to really foul things up requires a computer.”
Here is another way to describe the situation. Computer technology empowers users. However, the full capabilities of such machines are so great that they are overwhelming, frightening, and quite stressful to many people. Computerized instruments and devices designed to make life easier often add to one’s level of stress.


Stress on Our Math Education System

Our math education system is under attack. Students are not performing as well on national and international assessments as many people would like. While government and business call for still more emphasis on math education, there is a growing gap between what is being taught and how math is used outside of school.

In the “authentic” world of ordinary people making use of math, it is routine to make use of calculators, computers, and other ICT. Within school, a great many teachers still believe that it is “cheating” to use a calculator, and that first students must master paper and pencil arithmetic. Similarly, many educators feel it is “cheating” to make use of the computer algebra software systems that can solve equations, do algebraic manipulations, and carry out many other tasks that students learn to do using paper and pencil techniques.

Educational researchers emphasize that authentic assessment needs to be based in authentic content and authentic instruction. Computer technology is stressful to our math education system because:
  1. Calculators and computers can solve or greatly help in most of the types of problems that students are studying in the curriculum. Marshall McLuhan’s statement that “The medium is the message” is especially poignant in math. Our math education system is being especially stressed by how it should deal with computer capabilities as aids to problem solving versus paper and pencil aids to problem solving.

  2. Computer-assisted Learning and the more recent Highly Interactive Intelligent Computer-assisted Learning (HIICAL) are steadily increasing in capability. What are appropriate roles for human teachers as an increasing amount of what they do can be done by computers? Keep in mind that the computer systems doing the instruction can also solve the problems that they are teaching students about, but that a great many teachers have little knowledge and skill in using scientific calculators, graphing calculators, and sophisticated math software on computers. The availability of such math-related hardware and software that they do not know how to use can be stressful.

  3. The types of authentic problem analysis, problem understanding, and problem solving needed nowadays are captured in the term “computational thinking.” Computational thinking encompasses learning to use one's human and computer brains in combination. See http://iae-pedia.org/Computational_Thinking. Computational thinking is now well entrenched in many disciplines that make use of math, but it has a very long way to go in math education.

Final Remarks

ICT is a change agent. Moreover, it is a change agent that, itself, has a fast rate of change. For many people and for many systems, change—and especially, a high rate of change—is stressful. This is certainly true in math education. The technology (and often, the lack of the technology) can be stressful to students. It can also be stressful to teachers and to the overall content, instruction, and assessment of our math education system. Stress to the math education system and teachers can carry over to students.

Outside of school, students function in an “open” ICT environment. In school, curriculum content, instructional processes, and assessment lag far behind this open ICT, hands on environment that students take for granted.


References

Caine, Geoffrey and Caine, Renate N. (n.d.) Community First! How Process Learning Circles can increase joy, reduce stress, and optimize professional development. Caine Learning Center. Retrieved 6/10/2011 from http://www.cainelearning.com/Community.html.


About Information Age Education, Inc. 

Information Age Education is a non-profit organization dedicated to improving education for learners of all ages throughout the world. Current IAE activities include a Wiki with address http://IAE-pedia.org, a Website containing free books and articles at http://I-A-E.org, a Blog at http://i-a-e.org/iae-blog.html, and the free newsletter you are now reading.

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