Mathcad in the Classroom: A Collaborative Environment for Learning Math and Science Concepts By Bon...
-
date post
19-Dec-2015 -
Category
Documents
-
view
217 -
download
0
Transcript of Mathcad in the Classroom: A Collaborative Environment for Learning Math and Science Concepts By Bon...
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
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 [email protected]
Beth Porter Mathsoft Engineering & Education, Inc. Cambridge, MA 02142 [email protected]