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.
Stress and Education
Part 4:
Technology-based Stressors in Math Education
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.
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:
- 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.
- The capabilities and limitations of the machine. A four-function
handheld calculator cannot prepare a peanut butter and jelly sandwich
for you.
- An understanding of the problem being solved or the task being
accomplished.
- 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:
- 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.
- 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.
- 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.
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