Katherine Hoye, PhD candidate (current SD 114 instructor)
Systems Design
kahoye@engmail.uwaterloo.ca

Prof. Keith Hipel (previous SD 114 instructor)
Systems Design
kwhipel@engmail.uwaterloo.ca


Prof. Francis Tang, Linear Algebra in Engineering Coordinator (Math 115)
Pure Math
fcytang@math.uwaterloo.ca


Colin Campbell, Academic Computing
Information Systems and Technology
campbell@uwaterloo.ca

Design Mathcad-based Explorations of Linear Algebra Applications
                to accompany Studio-style Lecture/Tutorials for
                                  SD 114 (Linear Algebra)

The previous project produced Mathcad-based lecture and tutorial notes, together with a good yet sparse set of applications of Linear Algebra for students to emulate as homework problems.  There was not much knew learning in the homework as all the "punch-lines" had to be delivered in class to make sure everyone got them.

 
We propose to design applications for at least 10 of the weekly tutorials, and deliver them following a studio-style method where (1) background information is presented, and then(2) the students work through the exploration with teaching staff on-hand to ensure everyone discovers the "punch-lines".

The explorations will be made more engaging by gradually getting the students to decide what math to carry out for a given investigation, rather than always leading them through the steps and only challenging them by asking them to comment on what they observe.
 
 

Spring 2001:  Applications will be designed.  Wu (Kevin) Li, a PhD student in Systems Design who worked on the previous project, will again be hired, this time to create the new Mathcad applications under Kate Hoye's supervision, with support from Colin Campbell.  Work will begin in April so that we are one month ahead of the course as far as preparation goes.  The applications will be explored during the weekly tutorial times for the course using the new electronic classroom in Engineering, which we were invited to make application to use.

Fall 2001:  Applications will be tried on the approximately 1000 Math 114 students, under the direction of the course coordinator, Francis Tang.  As much as possible a studio-style approach will be taken.
 
 

Sy De 114 is the lead course in the Faculty of Engineering in using Mathcad in student-centered learning activities, and (together with Math 136) has lead to the introduction of Mathcad into Math 115 (Linear Algebra for Engineering), taken by freshman in other Engineering departments and in Science.  Extending the SD 114 adoption of Mathcad into extensive Engineering applications, is expected to lead to the adoption of Mathcad in several other math and engineering courses in Engineering.

Indeed the whole of Systems Design will be a cradle for the rest of Engineering as Mathcad is (hopefully!) extended to many of these courses which have analogs in other departments:
 
 

	Year 2	Year 3
Mathematical Courses:	211 - Differential Equations 213 - Probability 214 - Statistics	311 - Engineering Optimization 312 - Numerical Methods 331 - Engineering Economics
Engineering Courses:	281 - Mechanics of             Deformable Solids 282 - Fluid Mechanics 292 - Circuits, Instrumentation,             and Measurements	352 - Introduction to             Control Systems 381 - Thermodynamics 382 - Modelling and Simulation             of Mechanical Systems

In short, we feel these explorations will strengthen the students's math and engineering skills, and will lead to the adoption of Mathcad by additional courses, which will in turn strengthen students's math and engineering skills.

The actual explorations will be made as generic as possible, such that the other Linear Algebra courses at Waterloo can use them (in Math, Engineering and Science), and indeed similar courses at other universities can use them as we intend to submit the explorations to Merlot (www.merlot.org).

(We have laid the groundwork for one such exploration which culminates in the creation of an animation of a dynamic physical system (a double pendulum), one of the key application areas in Engineering.)
 
 

In placing a lot of weight on explorations of applications of Linear Algebra, we are in agreement with the views expressed in:
 
• Flewelling and Higginson, Realizing a Vision of Tomorrow's Mathematics Classroom - A Handbook on Rich Learning Tasks, Centre for Mathematics, Science and Technology Education, Faculty of Education, Queen's University, 2000.  Especially good quotations:

 
"Skills are to mathematics what scales are to music or spelling is to writing.  The objective is to write, play music, or solve problems - not just master skills".
National Research Council.

"Give a child a set of mathematical problems to be solved in ten minutes and graded for accuracy against the work of others, and the resulting performance may be dismal.  Put the same child in a situation in which the problems are made meaningful, the same mathematics is used, and the solutions matter, and the child's performance can soar."
Jeremy Kilpatrick & Edward Silver.


It is difficult to find many references to Mathcad in mathematics education specifically (the field is largely dominated by Maple and Mathematica), but a good general paper is:
 

• Lenox et al.  Computers in the Integrated Civil Engineering Curriculum: A Time of Transition.  Paper presented at 1997 American Society of Engineering Education Conference.  Located at: http://www.mathsoft.com/education/usma.html.  The authors predict that:
  

"Mathcad will be fully accepted as THE most useful computational tool by the math, science, and engineering community at USMA.  Mathcad will have a very positive influence as an integrator of topics within a course and of courses with[in] the overall civil engineering curriculum."

One of the authors, LTC Stephen J. Ressler, wrote us saying:
 
"All incoming USMA freshmen receive Mathcad pre-installed on their computers, and all of them learn to use it reasonably well in the four core math courses."

• Mick Bromilow, Course Team Chair of the Open University course on Mathematical Methods, Models and Modeling.  Quotation from a MathSoft press release:

 
"Our experience with Mathcad has shown us that it is an excellent tool for mathematics education ... It is very easy for the students to use and learn from Mathcad in an introductory setting. We are now turning to Mathcad 7 for our advanced students because it is even more important to provide them with a widely used professional tool that takes them beyond calculation exercises, helps foster an understanding of advanced concepts and prepares them for their technical careers."


It is also interesting to read descriptions of Mathcad in texts that have adopted it (complete list):
 

• Chapra and Canale, Numerical Methods for Engineers with Programming and Software

Applications 3rd Ed., McGraw Hill, New York, NY:
 
"Mathcad has a variety of functions and operators that allow convenient implementation of many of the numerical methods developed in this book. ...  Because of its ease of use, we believe Mathcad is particularly useful as a pedagogical tool."
• DesRues, Kevin, Explorations in Mathcad, Addison-Wesley, Reading, MA:

 
"With coverage of Mathcad ..., Explorations in Mathcad is designed to help students visually discover mathematics and understand it on an intuitive level."

Typed Name: _Kate Hoye_____________
 
 
 
 

Not available.

Typed name of head of department: __Ed Jernigan_______