The Application of Engineering and Technology to the Teaching of Mathematical Skills

Monday, June 26, 2006 - Thursday, June 29, 2006

Schedule (Workshop Summaries below)

MONDAY, June 26, 2006

9:00 – 9:15 -- Welcome and introductory remarks
Associate Dean David Reibstein
Professor John Tavantzis
Fenster Hall – Room 425

9:15 – 12:00 -- Mathematics and Applications of Triangulation
Professor Bruce Bukiet
Fenster Hall – Room 425

12:00 – 1:00 -- LUNCH

1:00-4:00 -- Mathematical  Applications in Heat Transfer
Professor Manny Perez
Faculty Memorial Hall

TUESDAY, June 27, 2006

9:00 – 12:00 -- Mathematics in Fluid Dynamics
Professor John Tavantzis
FENSTER HALL – Room 42

12:00 – 1:00 -- LUNCH

1:00 – 4:00 -- Introduction to Boolean Logic and Digital Circuits
Professor John Carpinelli
Fenster Hall – Room 425 (Faculty Hall - Laboratory 318)

WEDNESDAY, June 28, 2006

9:00 -12:00 -- Engineering Concepts in High School Mathematics
Mr. Harry Sugar
Fenster Hall – Room 425

12:00 – 1:00 -- LUNCH

1:00 – 4:00 -- Engineering Design Process – Puzzle Cube
Ms. Levelle Burr-Alexander
Fenster Hall – Room 425

THURSDAY, June 29, 2006

9:00 -11:30 -- Careers in Engineering
Professor & Associate Dean Ronald Rockland
Fenster Hall – Room 425

Tools in Engineering – Group Discussion
Professor John Tavantzis
Fenster Hall – ROOM 425

Closing Remarks
Associate Dean David Reibstein
Fenster hall – room 425

11:30 -- LUNCH and CHECK-OUT

Workshop Summaries

MONDAY, June 26, 2006

9:00 – 12:00 -- Mathematics and Applications of Triangulation
Professor Bruce Bukiet
Fenster Hall – Room 425

Triangulation, a process by which locations are computed using limited data, has applications in finding the epicenter of an earthquake, tracking submarines in the ocean or elucidating where a large explosion occurred. To solve simple problems in triangulation requires only some problem solving skills and high school algebra and pre-calculus. In this presentation, we will discuss the mathematics behind triangulation and use it to solve problems in the areas noted above.

1:00-4:00 -- Mathematical Applications in Heat Transfer
Professor Manny Perez
Fenster Hall – Room 425 Faculty Hall – Room 110)

In the midst of rising energy prices and shortages, the efficient utilization and conservation of energy is a timely and important topic. An understanding of Heat Transfer is a key factor in this endeavor.   We will discuss the basic principles of Conduction, Convection and Radiation Heat Transfer and how mathematics plays an important part in utilizing the principles of heat transfer in engineering design.  Examples of typical heat transfer problems and mathematical solution techniques will be covered.

TUESDAY, June 27, 2006

9:00 – 12:00 -- Mathematics in Fluid Dynamics
Professor Michael Siegel
Fenster Hall – Room 425

Fluid dynamics is an ideal area to study the application of mathematics in engineering, since experiments are easily performed and many of the basic principles can be understood with elementary mathematics.  In this talk we discuss some concepts of fluid statistics and dynamics, which has many applications to engineering problems. We also consider the basic connection between flow and pressure, and apply it to problems such as pipe flow, rotating fluids in a container, and lift on airplane wings. In addition, we will consider some statistical measurements in order to derive certain

1:00 – 4:00 -- Introduction to Boolean Logic and Digital Circuits
Professor John Carpinelli
Fenster Hall – Room 425 (Faculty Hall - Laboratory 318)

Digital logic forms the basis of many electronic devices we use in everyday life, ranging from simple digital thermometers to CD players to computers.  This session will explore the fundamentals of Boolean logic and digital circuits in electrical and computer engineering.  Participants will learn the basics of Boolean logic and how to implement logical functions in circuits.  A laboratory activity provides hands-on experience with digital logic components.  Participants will perform an experiment to verify the functions of several digital logic chips and determine the functions of an unknown chip.

WEDNESDAY June 28, 2006

9:00 -12:00 -- Engineering Concepts in High School Mathematics
Mr. Harry Sugar
Fenster Hall – Room 425

1. Introductions and Icebreaker
2. Investigating Functions with the Graphing Calculator:  Participants will construct a face using basic functions and translations.  This is a great project for students learning about functions and the use of the graphing calculator as an investigative tool.  (Application in Algebra 2)
3. Designing a Cone of Maximum Volume:  Using a round coffee filter and cutting out sectors with different central angles, participants will construct cones and calculate their volumes, graph the volume as a function of the central angle, and determine the central angle that achieves maximum volume.  (Application in Pre-calculus)
4. Free Graphing Program and Free Geometry Sketching Program for use in delivering lessons and for student.  WinPlot and WinGeom are two programs all teachers should be using.  These programs can be run from a disk, CD, or USB drive; they don’t require installation on the computer.  Participants will graph functions with parameters that can be changed by dragging a slider to see how the graph changes.  Participants will construct a triangle and show no matter how the shape of a triangle changes, the sum of the angles is 180 degrees.  These are great tools to use in the classroom and for students to use at home, the library, or on any PC.  (Applications in Algebra, Geometry, Pre-calculus, and Calculus)
5. Designing and Delivering Challenging Practice, Projects and Tests with Scientific Notebook.  Participants will learn about this powerful mathematical tool that does word processing, graphing, and computer algebra, and enables the teacher to deliver customized mathematics for each class.  Designing projects where students can take the time to work on them can be difficult in high school math because each student would need a different problem and the teacher would have to generate solutions for every student.  Participants will learn how a one-time effort can be used to create different projects and different take-home tests with solutions for each student that can be used over and over again for future classes.
6. Summary and Wrap Up:  Developing critical thinking skills through investigative learning is good preparation for future engineers and scientists.

Note: The purpose of this presentation is to provide participants with classroom activities they can use directly and introduce them to powerful tools they can use and customize for their individual classrooms.

1:00 – 4:00 -- Engineering Design Process – Puzzle Cube
Ms. Levelle Burr-Alexander
Fenster Hall – Room 425

Engineering is the application of mathematics and science to solve real world problems in society.  The Engineering Design Process is a methodical approach to defining the problem, understanding the design criteria and constraints, developing solutions and implementing the optimal solution based on factors identified through the criteria, constraints and the nature of the problem.  All fields of engineering employ a wide variety of mathematics disciplines from algebra, geometry, trigonometry and calculus.  At the post-secondary level, engineering students typically take mathematics courses in calculus, differential and partial differential equations, probability and statistics, complex variables and, in some disciplines, up to discrete and vector analysis.  According to Schoenfeld (1992), there are five key elements for understanding mathematical cognition:  (a) a knowledge base, (b) problem solving strategies or heuristics, (c) effective use of resources, (d) mathematical beliefs (affects), and (e) and engagement of mathematical practices.  Highly competent engineers use all five elements in their every day practice in the fields of engineering.  Participants will learn about the importance of each step in this design process and apply the principles of mathematics to designing a puzzle cube.

Schoenfeld, A.H. (1992).  Learning to Think Mathematically:  Problem-solving, Meta-cognition and Sense-Making in Mathematics.  In Handbook for Research on Mathematics Teaching and Learning.  Grouws, D. (Ed.).  New York:  MacMillian.

THURSDAY, June 29, 2006

9:00 -11:30 -- Careers in Engineering
Professor/Associate Dean Ronald Rockland
Fenster Hall – Room 425

The field of engineering provides a breadth of career paths from the traditional fields of chemical, civil, electrical, industrial and mechanical engineering to the specialty areas such as bio-medical engineering, computer engineering and nanotechnology.  It is a field that has evolved throughout the centuries based on sound mathematical and scientific principles of the time period.  According to the Accreditation Board for Engineering and Technology (ABET),

Engineering is the profession in which a knowledge of the mathematical and natural sciences, gained by study, experience, and practice, is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the benefit of mankind.
[Landis, 1995]

Participants will learn about the traditional and emerging fields of engineering and the academic requirements necessary for a successful career in engineering beginning from secondary to post-secondary levels.

Landis, R. (1995) Studying Engineering, A Road Map to a Rewarding Career.  Burbank, California:  Discovery Press.

Tools in Engineering– Group Discussion
Professor John Tavantzis
Fenster Hall – Room 425

Engineers utilize a broad range of tools to assist in the Engineering Design Process and the many facets of engineering.  With the advancement of technology, there are a variety of software packages that are among the “tools of the trade”.  Participants will discuss some of the software packages used by engineers; also the role education and mathematics play in the life of an engineer will be a forum for dialog.