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Mathcad in the Classroom: A
Collaborative Environment for Learning
Math and Science Concepts
By Bon Sy and Beth Porter
Queens College/CUNY, Computer Science
Mathsoft Engineering & Education, Inc.
Bon Sy
 Queens College (CUNY) professor of Computer Science
 Mathcad User since 1988
 Hopes to attract students to science and keep them
interested through multi-modal approach to teaching using
technology
What is our goal?
Take a pattern approach for developing live data science
education materials using Mathcad, which means…
 Adopting patterns as a conceptual tool to encompass
different learning approaches and provide linkages
between them.
 Creating courseware that delivers effective learning,
even if individuals’ preferred learning styles vary.
Why are we interested in this problem?
 Large, ethnically and culturally diverse population to
serve:
 City U. of New York:
 17 colleges
 200,000 students
 Queens College
 1500 science students
 500 Computer Science undergraduate students
 200 Computer Science graduate students
 40 pre-engineering students
 Students exhibit myriad different learning styles, but
respond particularly to word-based reasoning,
skills-based practice, and visualization approach
Three key points
 There should be a general framework for science and
technology learning.
 Patterns provide a means of presenting information
from different perspectives and in different modalities.
 Learners can “tune” in to the ways that best suit their
learning style.
 There are ways of using Mathcad to develop
interactive, live courseware that facilitate learning and
provide a mechanism for successfully evaluating
student understanding.
What exactly is a pattern?
A pattern is a structure governed by rules…
Pattern theory [Grenander 1993 & 1996], Information theory
[Shannon 1948, Tufte ]
 Concept used in software design and information
display – explains complex phenomena through
pattern formation and deformation.
 Provides backdrop for science and technology
training — modeling process for engineering design
and scientific analysis
 Allows there to be links among various learning
approaches
An example of a pattern
 Exhibits regularity
 Consistent behavior of
data
 Elegant properties for
generalization and
prediction
 Examples:
 Fern fractal
 Tornados (weather
phenomenon with a
spiral rotating wind
circulation)
Three components of a pattern
Leaf Experiment, Part 1
 Mathematical structure
 Functional expression
 Visual model
 Concept abstraction

Graphical model
 Qualitative interrelationship
Extending pattern development
Leaf Experiment, Part 2
 Using randomization to “perturb” pattern
 Animating results
Four kinds of pattern manipulation
 Derivation
 Homogenous transformation  Structure discovery
 Synthesis
 Concept abstraction  Visualization
 Analysis (and Exploration)
 System identification  Mathematical function discovery

Summary
 Relationship declaration  Dependency/decision model
Interrelationships among pattern
manipulation
FROM \ TO
Mathematical
Visual
Graphical
Dependency
Mathematical
Derivation
Synthesis
Summary
Visual
Analysis
Derivation
Summary
Graphical
Dependency
Analysis
Synthesis
Derivation
Mathcad Examples
 Each file demonstrates:
 Deriving graphical representation from algebraic
representation
 Synthesizing relationship between abstract (mathematical
structure) and concrete (visual representation)
 Exploring underlying relationship or model by varying
parameters and analyzing graphical or numerical results
 Summarizing dependency relationship or building model
Lorenz
Attractor
 MCD
Visualizing a probability space
 MCD
Insertion Sort
 MCD
General framework for science &
technology learning
Pattern
Abstraction
General framework for science &
technology learning
Concept
Formulation
Built-in mechanism for learning
assessment
 Explore through visualization
 Discover dependency structure
 Analysis based on regression analysis
 Discover mathematical structure
 Pattern synthesis based on mathematical structure
 Discover visual structure

Compare and validate
 Summary and explanation
Web Courseware and Dissemination
 Content material depository & Mathcad forum
 (CS86) http://bonnet19.cs.qc.edu:7778/pls/forum/
 Media environment and application
 Windows 95, 98, 2000, XP, ME, or NT 4.0
 Mathcad, Microsoft Office
 Dissemination
 http://www.techsuite.net/bonnet3/nsf/ili01/
Conclusions
 Mathcad is an ideal tool for courseware development
because it offers many avenues to follow for
demonstration, exploration, discovery of patterns.
 Assessment involves capturing student understanding of
concepts through multiple representations.
 It is useful to implement a repository for scientific data
and a Mathcad-based courseware to broad dissemination.
 E-communities allow us to collaborate on developing the
tools for math and science learning across different
education levels and disciplines.
Beth Porter
 Education Product Manager at Mathsoft Engineering
& Education, Inc.
 Former math instructor
 Strong advocate for thoughtful use of technology in
teaching math, science, engineering, and social
sciences
Mathcad is a universal tool for
applied math
 Broadly functional,
appropriate for
algebra and
engineering
applications, alike
 Encourages good
communication and
collaboration skills
 Affordable
Interactive technology
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Live document interface is
easy to use and brings
interactivity to course
materials.
Interoperability with the Web
and other applications
allows communication and
collaboration across campus
and the world.
Great teaching and learning
resources are available in
Mathcad and online.

Mathcad Web Library
Creating Learning Opportunities
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Mathcad helps professors
create learning
opportunities through
inherent interactivity
Real math notation and
self-documenting nature of
worksheet reveals
techniques rather than
obscuring them.
Graphs, tables, built-in
functions and other tools
support full range of math
activities for math, science,
and engineering.
Mathcad on the Web
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When you create course materials in Mathcad and
save the to the Web, you can:
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View as static pages – no Mathcad required.
View as interactive pages – using Mathcad.
Edit right in the browser – using Mathcad.
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NEW! The Mathcad Application Server allows you to
deploy live documents, but end users don’t need
Mathcad, just a browser!
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Launch quadratic.htm in browser
Launch Application Server Site
ALL members of the community can view your
materials.
Instructor’s Companion
 Manage math-related coursework in one central
application
 Enhance static textbook materials
 Create interactive online courses
 Bring math alive for students in all disciplines – from
business to chemical engineering
 Bring course materials to the Web to reach a broader
audience of other teachers and learners
 Check solutions to tests and homework before
distribution.
Student-friendly Tool
 Easy to use, short learning curve and WSYWIG math
presentation
 Tons of built-in functions, 2D and 3D graphing, data
analysis tools, and other math features
 Excellent for managing homework
 Facilitates communication and collaboration among
students and between students and professors.
Mathcad prepares tomorrow’s engineers
 Mathcad is prevalent in the engineering workplace
 Learning Mathcad prepares students with marketable
skills for industry
 Students learn timely methodologies that can be
understood immediately in Mathcad
 Using Mathcad helps students develop good habits
for thinking about and articulating engineering
processes
Broad-based Solution for Math
 Standardize on one piece of software for all students
taking math, applied math, science, engineering and
social sciences
 Mathcad user groups and Web resources connect
students and faculty to the larger Mathcad community
and make its relevancy clear
 Even non-Mathcad users can make use of Mathcadproduced materials through a browser
Mathcad is Inexpensive
 Volume licensing provides full Mathcad – not a
deprecated “student” version
 Students use Mathcad for all their math-related work,
from homework assignments to papers to lab writeups
 Professors use Mathcad for course work,
dissemination, collaboration with colleagues, and
personal productivity
Mathcad is for ALL Students
 Software budgets are tight…
 Other prototyping software is expensive…
 So-called “learning” systems offer students little more
than rote skills practice…
 Mathcad is a rich environment suitable for all
students, at all levels, across all math-related
disciplines!
 Check out the Mathcad Web site at
http://www.mathcad.com for more information about
Mathcad products for higher education.
Thank you!
 Bon K. Sy
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Queens College/CUNY, Dept. of Computer Science
Flushing, NY 11367
[email protected]
 Beth Porter
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Mathsoft Engineering & Education, Inc.
Cambridge, MA 02142
[email protected]