Mathcad in the Classroom: A Collaborative Environment for Learning Math and Science Concepts

1. 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.

2. 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

3. 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.

4. 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

5. 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.

6. 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

7. 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)

8. Three components of a pattern Leaf Experiment, Part 1 • Mathematical structure • Functional expression • Visual model • Concept abstraction • Graphical model • Qualitative interrelationship

9. Extending pattern development Leaf Experiment, Part 2 • Using randomization to “perturb” pattern • Animating results

10. Four kinds of pattern manipulation • Derivation • Homogenous transformationÞStructure discovery • Synthesis • Concept abstractionÞVisualization • Analysis (and Exploration) • System identificationÞMathematical function discovery • Summary • Relationship declarationÞDependency/decision model

11. Interrelationships among pattern manipulation FROM \ TO Mathematical Visual Graphical Dependency Mathematical Derivation Synthesis Summary Visual Analysis Derivation Summary Graphical Dependency Analysis Synthesis Derivation

12. 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

13. LorenzAttractor • MCD

14. Visualizing a probability space • MCD

15. Insertion Sort • MCD

16. General framework for science & technology learning Pattern Abstraction

17. General framework for science & technology learning Concept Formulation

18. 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

19. 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/

20. 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.

21. 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

22. Mathcad is a universal tool for applied math • Broadly functional, appropriate for algebra and engineering applications, alike • Encourages good communication and collaboration skills • Affordable

23. 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

24. 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.

25. 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 browser • NEW! The Mathcad Application Server allows you to deploy live documents, but end users don’t need Mathcad, just a browser! • Launch Application Server Site • ALL members of the community can view your materials.

26. 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.

27. 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.

28. 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

29. 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

30. 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

31. 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.

32. Thank you! • Bon K. Sy • Queens College/CUNY, Dept. of Computer Science • Flushing, NY 11367 • bon@bunny.cs.qc.edu • Beth Porter • Mathsoft Engineering & Education, Inc. • Cambridge, MA 02142 • bporter@mathsoft.com