**Abstract:**

*The Shodor Education Foundation is dedicated to helping educators
and students at all levels understand and use technology appropriately
in math and science education. This non-profit organization focuses
on content, teacher, and student as the three elements essential in
computational education. There are many higher level concepts now open
to study at a younger age because of the computational power of computers.
Shodor's projects extend educational resources and opportunities as
far as possible. An emphasis is placed on science and mathematics explorations,
developing numerical models and simulations integrated with the curriculum,
professional development, and access to a network that supports their
use in a learner-centered environment.*

**Introduction **

The current mantra in education
is "technology, technology, technology." But teachers remain
frustrated with technology because they do not understand when it is
an appropriate tool to use. To teach a particular concept, sometimes
the best tool to use is pen and paper, sometimes manipulatives, and
sometimes a computer.

Many educational software
developers do not understand appropriate uses of technology either.
Much software is a drill and kill style: databases of practice problems
with graphics and sound to make the experience more interesting to students.
School administrators often do not understand how technology can be
used, so they purchase these types of software and become frustrated
because teachers are not using them.

In large part, teachers do
not use technology because they can teach the same concepts in their
classrooms without using a computer. There are many hassles in working
with computers: technical difficulties, technical support if something
goes wrong, security issues, etc. Large portions of class time are sometimes
spent just getting students logged onto the machines. These issues coupled
with software that only replicates what teachers already can accomplish
in the classroom keep teachers from using computer technology.

But computers do have excellent
applications in the classroom and can be time saving devices to teach
concepts. Computers are designed to perform repetitious computation
quickly. There are many concepts in science and math that involve a
great deal of tedious computation. Teachers now have the power to teach
those concepts without bogging down students in the details of those
computations and can focus the lessons on the concepts instead.

Computers should not replace
a student's understanding of arithmetic and algebra. Rather, when the
arithmetic or algebra hinder the teaching of a concept because of the
computation involved, the use of computers is appropriate and pedagogically
invaluable. The study of probability at the middle school level offers
an excellent example.

Students are taught how to
compute theoretical probability and also told the more times an experiment
is conducted, the closer the experimental probability will be to the
theoretical probability. If a coin is flipped one hundred times, theory
predicts the coin will land on heads fifty times. As a teacher with
lots of material to cover taking the class time to have students flip
a coin one-hundred times is not a feasible option and only a few flips
of the coin will not suffice. Even if a student flipped a coin one-hundred
times, they will not get exactly fifty-fifty because one-hundred is
a small number of independent, random events. It may take thousands
of such events to convince the doubting students a coin is fair or luck
has nothing to do with the results. A computer can simulate flipping
a coin thousands of times in a fraction of a second.

There are many higher level
concepts now open to study at a younger age because of the computational
power of computers. Modern science and mathematics are more concerned
with pattern recognition and characterization than with mere symbol
manipulation. The Shodor Education Foundation's mission is to help educators
understand how to incorporate technology in math and science classes
so students can study patterns difficult, if not impossible, to study
without computers.

There are three elements
essential to education and all three must be present and effective or
education process collapses: content, teacher, and student. Shodor uses
the framework of a tetrahedron as its symbol as a representation of
these interdependent elements. The tetrahedron is the simplest and most
stable of all regular three-dimensional solids. If any edge of the tetrahedron
is removed, the solid collapses. Shodor's various projects each address
all three essential elements and range from courseware development,
online course development, conducting workshops for K-16 educators nationwide,
and K-16 student development.

In support of Shodor's vision
to permeate math and science education with computational science methods,
Shodor always attempts to disseminate its resources as far as possible.
The name Shodor recalls the role of the hammer in the shodering process
of making and applying gold leaf. Gold leaf is gold hammered thin so
it can cover an object. Similarly, Shodor works to extend valuable educational
resources and opportunities as far as possible. A special emphasis is
placed on enabling authentic science and mathematics explorations at
all educational levels, developing numerical models and simulations
integrated with the curriculum, professional development, and network
access to support their use in learner-centered environments.

Below are brief descriptions
of Shodor's K-12 projects, computational modeling tools and resources
to support these projects, online course offerings, as well as undergraduate
projects. Projects that support middle school math and science curriculum
are noted in the descriptions. Links to the online materials and further
information on the projects are also provided.

**K-12 PROJECTS**

*Modeling and Visualization Workshops for K-12 teachers*

Email: workshops@shodor.org

One of Shodor's
expanding initiatives is offering workshops to introduce teachers at
all grade levels to modeling and visualization technologies, techniques,
and tools. The software used in the workshops concentrates on inexpensive
programs commonly used in most schools or specialized software freely
available on the web. Instruction stresses inquiry based learning. These
workshops, taught by national leaders in the use of computing tools
in science and mathematics, provide teachers with instruction and ideas
on how to integrate these technologies, techniques, and tools in their
own classrooms.

Workshop content
is not predefined. Shodor will work with institutions in advance to
develop an agenda appropriate to the needs of the participants. The
workshops therefore simultaneously meet Shodor's intent of putting modeling
and visualization tools in the hands of teachers while meeting the institution's
goals and teacher needs.

The workshops
may include the introduction of modeling software such as Project Interactivate,
STELLA, Mathematica, Excel, and Geometer's Sketchpad. Workshops also
involve teaching critical thinking skills when using numerical computation
to know if solutions are correct.

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