Empowering Young Mathematicians and Scientists
Through Technology
Published in the October 1998 issue of Curriculum
Administrator
© 1998 Gary S. Stager/Curriculum
Administrator Magazine
Increased access to microcomputers
and the availability of sophisticated software tools enable children
to learn math and science through the types experiences previously
reserved for adult experts.
It’s been said that if you
know the result of an experiment before you begin, it’s
not an experiment, but a demonstration. This notion also applies
to math. When you know the answer to the problem before you begin
or have solved the same problem countless times before, you’re
not thinking mathematically. You’re doing school math.
"For
the most part, school math and science becomes the acquisition
of facts that have
been found by people who call themselves scientists." (Goldenberg,
1993)
Computers offer
unprecedented opportunities for children to learn math and
science through the active process
of becoming a scientist or thinking mathematically. In the hands
of an imaginative teacher, the computer becomes a powerful object
to think with. The computer mediates a conversation with the
individual user  providing feedback in the form of errors, surprises
or new questions to ponder. With sufficient access, constructive
software and supportive adults, the computer gives students the
confidence that they can solve the problem athand, even if they
don’t yet know the path to that solution. In other words,
kids view themselves as scientists and mathematicians.
Computers can help learners concretize
previously abstract concepts, visualize complex relationships,
collect large quantities of data and check hypotheses quickly
and easily. Sophisticated habits of mind develop in children
who possess the fluency necessary to build computational models,
debug their thinking and express their new understanding.
New Content, New Tools, New
Ways of Knowing
Perhaps no subject of study bears
as little resemblance to the discipline it intends to teach as
mathematics education. Most mathematicians would be horrified
by how many pieces of educational software confuse the drill
of isolated techniques with mathematical understanding. The incongruity
between pedagogy, content and purposeful application occurs at
a time when mathematics is changing rapidly. Mathematicians and
scientists are alert to the blurring boundaries between different
branches of mathematics and other disciplines, new problem solving
approaches and the importance of mathematics in the social and
behavioral sciences. The increasing demands of the behavioral
and social sciences for reliable quantitative measurement and
analysis of new types of problems not only relies on mathematics,
but influences its development. Curriculum and pedagogy must
keep pace with this evolution.
...most educational software
powerfully reinforces the poorest sides of precomputer education
while losing the opportunity to powerfully strengthen the
best sides. (Papert, 1996)
Much has been written about the
societal demands for a mathematically literate population. We
live in a world awash in data. Good citizenship is dependent
on an ability to process often confusing and conflicting information.
Economic, political and social trends require students to have
a much deeper understanding and appreciation for mathematical
thinking now more than ever before. The pace of technological
innovation spurs the rapid evolution of mathematics.
The NCTM Standards state
that fifty percent of all mathematics has been invented since
World War II. (National Council of Teachers of Mathematics,
1989) Few if any of these branches of mathematical inquiry have
found a home in the K12 curriculum. Topics such as number theory,
chaos, topology, cellular automata and fractal geometry may appeal
to students unsuccessful in traditional math classes. These new
areas of mathematics tend to be more contextual, visual, playful,
experimental and fascinating than the traditional emphasis on
paper and pencilbased algebra and geometry. Technology provides
an opportunity for more children to view mathematics as a powerful
part of their own learning and to embrace the process of mathematical
inquiry. Even young children may learn powerful concepts of number,
space, probability and geometry through the use of MicroWorlds,
Turtle Math (http://www.microworlds.com) and other versions of
Logo.
A dignified mathematics for
children cannot be something we permit ourselves to inflict
on children, like unpleasant medicine, although we see no
reason to take it ourselves. (Papert, 1980)
Students and teachers can and should
explore these new mathematical domains. Prior to the availability
of personal computing it was tedious or impossible for children
to explore complex mathematical phenomena or make sense of large
collections of data. Paul Goldenberg, Senior Scientist at the
Education Development Center, suggests that it is difficult to
test out ideas unless one has a slave stupid enough not to help.
(Goldenberg, 1993) The computer is a splendid lab assistant,
yet the student still must do all of the thinking. Openended
software makes it possible to manage large bodies of data by
running tedious experimental trials millions of times if necessary,
collecting data and displaying it in numerical or graphical form.
Small changes may be made to an experiment without having to
start from scratch.
Software such
as The Geometer’s
Sketchpad (http://www.keypress.com/) and NuCalc (http://www.nucalc.com)
provide learners with openended tools for visualizing an enormous
range of mathematical problems. Teachers may use the same software
in dynamic presentations in which hypotheses may be tested and
variables changed without spending half the period writing and
erasing the chalkboard. SureMath (http://www2.hawaii.edu/suremath/)
even helps students solve multistep word problems. Business
applications like ClarisWorks and Microsoft Office may be used
to collect data, experiment with numerical conjectures and present
results on paper, the screen or World Wide Web.
Mathematical thinking and the scientific
method become commonplace when children have adequate access
to computers and software like the programs mentioned above.
This type of learning is interdisciplinary in nature. When a
student builds their own virtual pet, collects acid rain data,
creates a program to solve linear equations after a Mozart sonata
is played, constructs a LEGO robot to solve a problem in SubSaharan
Africa or analyzes the impact of gerrymandering on representative
democracy they have blurred the artificial boundaries between
subject areas and made important intellectual connections. The
work of students is of real consequence and often of a higher
standard than required by the curriculum. More importantly, the
student is free to acquire and exhibit this new knowledge in
their own voice. Problem solving is embedded in a personally
meaningful context.
Science Inside and Out
Simulations,
commercially prepared or studentdesigned, allow the learner
to perform experiments
that would be either too expensive, dangerous, costly or time
consuming if performed in other ways. Interactive Physics by
Knowledge Revolution (http://www.krev.com) is a sophisticated
simulation and modeling environment. Widget Workshop (http://www.maxis.com)
lets kids construct imaginative inventions complete with logic
gates, input/output devices, switches and whimsy. Ever wonder
about the cause of traffic jams or why birds flock? StarLogo
(http://starlogo.www.media.mit.edu/people/starlogo/) is an incredibly
powerful environment for exploring artificial life, emergence
and decentralized thinking. Best of all, it’s free.
Part of the
lure, mystery and fun of science is that it is messy. Science
lives in beakers, wires,
petri dishes and machines. Education is just beginning to embrace
ways in which computers can enhance scientific inquiry outside
of the computer. Thousands of children have "done real science" by
participating in the National Geographic Kid’s Network.
Kids all over the world collect data and conduct local experiments
and then share their information with fellow scientists and adult
experts who may be engaged in important research. The Concord
Consortium’s Hazenet (http://www.concord.org/haze/) project
asks children to build a specialized instrument and collect data
about particulates in the atmosphere. The Internet provides children
with a vehicle for collaboration, data dissemination, and interaction
with experts and publishing. Learners of all ages can share their
experimental results, simulations and conclusions with others
online and make significant contributions to the world of ideas.
Engineering
is an extremely tactile branch of science, yet overlooked traditionally
by school. LEGO’s
Control Lab (http://www.lego.com/dacta/) invites kids to build
machines and conduct physical experiments with a construction
kit comprised of LEGO, a computer interface, motors, lights and
sensors. The Personal Science Laboratory (http://www.teamlabs.com)
is a collection of robust microcomputerbased lab probes designed
to collect experimental data in chemistry, biology, physics,
life and earth science. The probes measure temperature, light,
pH, and motion. Data collected by the sensors is communicated
to Excel for analysis and interpretation.
At a recent conference, Dr. Robert
Tinker, Director of the Concord Consortium and one of the pioneers
in microbased lab science discussed the need for smart probes.
Such probes would eliminate the need for a computer and interface
box because advances in computer technology makes it possible
to have the computing power in the probe itself. Students can
take the probe out in the field to conduct experiments beyond
the walls of the laboratory. Such probes are happy to sit outside
in the rain for several weeks. Tinker went on to demonstrate
a prototype of a motion sensor and computer housed in a lantern
flashlight. The flashlight/probe can be carried wherever it is
needed and data later uploaded to a Palm Pilot or other lowcost
computer for analysis.
Where Do I Begin?
There are numerous web sites full
of collaborative science and math projects. Such sites offer
project ideas, opportunities for teacher collaboration, software
tools, reference materials or online experts. The Concord Consortium
(http://www.concord.org) and TERC (http://www.terc.edu) offer
web sites full of collaborative projects, teacher development
opportunities and research reports for progressive educators
interested in math/science education. The Math Forum (http://forum.swarthmore.edu)
offers an amazing assortment of services, projects and materials
for students and teachers. A list of books recommended for teachers
interested in constructionist approaches to learning math and
science is available at http://www.stager.org/books.html.
References
Stager, G. & Cannings,
T. (1998) Online Communities as a Vehicle for Developing Secondary
Mathematics
Teachers. In Proceedings of the 1998 National Educational
Computing Conference. Eugene, OR:NECA.
Goldenberg, E.P. (1993). Linguistics,
Science, and Mathematics for Precollege Students: A Computational
Modeling Approach. Revised from Proceedings, NECC ‘89
National Educational Computing Conference, Boston, MA. June 2022,
pp. 87 93. Newton, MA: Educational Development Center.
Papert, S. (1996). The Connected
Family  Bridging the Generation Gap. (1996) Atlanta: Longstreet
Press.
Papert, S. (1980). Mindstorms:
Children, Computers, and Powerful Ideas. (Second Edition,
1993) New York: Basic Books.
Stager, G. (1997). Logo and Learning
Mathematics  No Room for Squares. In Logo a Retrospective,
pp 153170. Edited by C. Maddux and D.L. Johnson. Binghamton,
NY: The Haworth Press.
