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.

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 What exactly is a pattern?

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

FROM \ TOMathematicalVisualGraphical Dependency MathematicalDerivationSynthesisSummary VisualAnalysisDerivationSummary Graphical Dependency AnalysisSynthesisDerivation Interrelationships among pattern manipulation

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 MCD

Visualizing a probability space  MCD MCD

Insertion Sort  MCD 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)  Media environment and application  Windows 95, 98, 2000, XP, ME, or NT 4.0  Mathcad, Microsoft Office  Dissemination 

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  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  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  When you create course materials in Mathcad and save the to the Web, you can:  View as static pages – no Mathcad required.  View as interactive pages – using Mathcad.  Edit right in the browser – using Mathcad.  Launch quadratic.htm in browserquadratic.htm  NEW! The Mathcad Application Server allows you to deploy live documents, but end users don’t need Mathcad, just a browser!  Launch Application Server SiteApplication 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 Mathcad- produced 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 write- ups  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 for more information about Mathcad products for higher education.

Thank you!  Bon K. Sy  Queens College/CUNY, Dept. of Computer Science  Flushing, NY   Beth Porter  Mathsoft Engineering & Education, Inc.  Cambridge, MA 