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

By Bon Sy and Beth PorterQueens 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 developmentLeaf 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 \ TO Mathematical Visual Graphical Dependency

Mathematical Derivation Synthesis Summary

Visual Analysis Derivation Summary

Graphical Dependency

Analysis Synthesis Derivation

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

LorenzAttractor

MCD

Visualizing a probability space

MCD

Insertion Sort

MCD

General framework for science & technology learning

PatternAbstraction

General framework for science & technology learning

ConceptFormulation

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

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 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.

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 http://www.mathcad.com for more information about Mathcad products for higher education.

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