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 (

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

Speed of Shallow Water Waves (Tsunamis)

Credits Cleve Moler, MathWorks Randy LeVeque and colleagues, University of Washington

Sound Waves

Gravity and Force

Gravitational Attraction

Newton’s Law of Gravitation

Newton’s Second Law

Acceleration and Velocity Velocity is change in distance over time. Acceleration is the change in velocity over time.

Planetary Motion

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, …

Complex Numbers Real Imaginary 1 + 2i

Sequence of Complex Numbers 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 Real Imaginary

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 = Area = b*h h b

Area of Parallelogram = b h

Area of Triangle = h b

Sweet Home 3D® (

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.