Transcript Enhancing STEM Curriculum with MATLAB and Online Resources

Enhancing STEM Curriculum with
MATLAB and Online Resources
Dr. David Torres
Northern New Mexico College
2011 NSF Robert Noyce Conference
July 7, 2011
Northern New Mexico College
• Two-year and four-year college in Espanola, New
Mexico
• Enrollment is approximately 2300 students
• Hispanic Serving Institution
– 70% Hispanic
– 8% Native American
• Rural
• Bachelors Degrees
– Mechanical, Software Engineering
– Mathematics, Biology, Environmental Science
– Education
Friday Academy
• Students from Carlos Vigil Middle School in
Espanola explore fun activities in
mathematics, chemistry, biology and writing
at Northern New Mexico College on Fridays.
• This presentation is based on the challenge of
making the mathematics component of that
curriculum engaging to middle school
students.
Motivation for using Computer
Software
• Allow students to model complex physical
phenomena inexpensively
– Water and sound waves
– Planetary motion and gravity
• Allow students to explore mathematical
concepts in an exploratory way
– Sequences and fractals
– Area
MATLAB
• Software language distributed by MathWorks
– Programming and Visualization capabilities
• Interaction with MATLAB can be superficial or
extensive
– Easy to create 2D and 3D plots
– Solve equations governing fluid flow
• SciLab is a free version (http://www.scilab.org)
Relevance to Noyce Fellows
• Could use these codes or resources in their
own classrooms to engage and motivate their
own students.
• Resources require very little training.
– MATLAB
– Sweet Home 3D®
Waves
•Water
•Sound
Tsunamis
http://thewashingtonnote.com
Speed of Shallow Water Waves
(Tsunamis)
Speed  gravity* depth
Credits
• Cleve Moler, MathWorks
• Randy LeVeque and colleagues, University of
Washington
Sound Waves
Sound Waves
Gravity and
Force
Gravitational Attraction
F
m1
m2
Newton’s Law of Gravitation
m1m2
F G 2
d
Newton’s Second Law
F  ma
Acceleration and Velocity
• Velocity is change in distance over
time.
• Acceleration is the change in velocity
over time.
http://davidteacherzambia.blogspot.com
Planetary Motion
Sequences
Sequences
•
•
•
•
1,3,5,7,9,11,13, …
1,4,9,16,25,36, …
1/2 ,2/3, 3/4, 5/6, 6/7, 7/8, …
1,1,2,3,5,8,13,21,34,55, …
 1
1  
 1
1
1
 1
, 1  
 2
1
2
 1
, 1  
 3
1
3
1
4
 1
, 1   ,...
 4
Complex Numbers
Imaginary
i   1, i  1
2
1 + 2i
Real
Sequence of Complex Numbers
(a  bi)2  (a  bi)(a  bi) 
(a 2  abi  bai  b2i 2 ) 
~
2
2
~
(a

b  2
abi )  (a  b i )
~
a~
b
• Repeat
• Color points by distance from origin in the
complex plane
• Beautiful shapes called fractals can be formed
based on this simple procedure.
Sequence of Complex Numbers
Imaginary
2
1
3
4
Real
Mandelbrot Fractal
Magnify
Mandelbrot Fractal Magnified
Magnify
Mandelbrot Magnified Again
What’s Really Cool about Fractals
• When a portion of the fractal is magnified,
the magnified portion bears a resemblance to
the original fractal (self-similarity).
• YouTube videos magnify Mandelbrot fractals
billions of times and during the course of the
magnification, one sees variations of the
original fractal over and over again.
Area
Area of Rectangle =
h
Area = b*h
b
bh
Area of Parallelogram =
h
b
bh
Area of Triangle =
h
b
1
bh
2
Sweet Home 3D®
(http://www.sweethome3d/com)
Sweet Home 3D®
• Web site published by Emmanuel Puybaret
• eTeks® (company created in 1999)
Conclusions
• Software can be used to simulate physical
phenomena in an interactive way.
• Free online resources can be used to reinforce
and apply mathematics concepts.
• Such resources can be used to depthen the
extent of learning and show its application.