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

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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.

- 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

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.

- 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

- City U. of New York:
- Students exhibit myriad different learning styles, but respond particularly to word-based reasoning, skills-based practice, and visualization approach

- 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

- Exhibits regularity
- Consistent behavior of data
- Elegant properties for generalization and prediction
- Examples:
- Fern fractal
- Tornados (weather phenomenon with a spiral rotating wind circulation)

Leaf Experiment, Part 1

- Mathematical structure
- Functional expression

- Visual model
- Concept abstraction

- Graphical model
- Qualitative interrelationship

Leaf Experiment, Part 2

- Using randomization to “perturb” pattern
- Animating results

- Derivation
- Homogenous transformationÞStructure discovery

- Synthesis
- Concept abstractionÞVisualization

- Analysis (and Exploration)
- System identificationÞMathematical function discovery

- Summary
- Relationship declarationÞDependency/decision model

FROM \ TO

Mathematical

Visual

Graphical Dependency

Mathematical

Derivation

Synthesis

Summary

Visual

Analysis

Derivation

Summary

Graphical Dependency

Analysis

Synthesis

Derivation

- 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

- MCD

- MCD

- MCD

Pattern

Abstraction

Concept

Formulation

- 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

- 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/

- 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.

- 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

- Broadly functional, appropriate for algebra and engineering applications, alike
- Encourages good communication and collaboration skills
- Affordable

- 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

- 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.

- 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.

- 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.

- 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 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

- 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

- 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

- 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.

- Bon K. Sy
- Queens College/CUNY, Dept. of Computer Science
- Flushing, NY 11367
- [email protected]
- Beth Porter
- Mathsoft Engineering & Education, Inc.
- Cambridge, MA 02142
- [email protected]