June 14, 2009
June 14, 2009
June 17, 2009
14.405.1 - 14.405.14
Demonstrations That Work in the Mathematics Classroom Abstract
Over the years we have developed several “hands on” demonstrations which help our students to visualize the mathematics they are learning. This paper will present several of these demonstrations including the cycloid curve and brachristochrone problem, Newton’s Law of Cooling, directional derivatives, Lagrange multipliers, centers of mass, spring mass systems, and others. By seeing actual demonstrations, students see the relevance of mathematics to the real world situations, and thus gain a sense that the mathematics they are learning is important in their lives as engineers.
In calculus courses, differential equations courses, and some upper division mathematics courses students are often presented with concepts that can be demonstrated with “hands on” demonstrations similar to those done in the chemistry, physics, or engineering class. Unfortunately, with the improvement of computer technology and the internet, some of these demonstrations have been relegated to a “show and tell” time for students to watch computer animation or downloaded videos. Still others believe such demonstrations are too time consuming or do not “add value” to the course. They may also believe that the apparatus used in these demonstrations is expensive. In this paper we will show several demonstrations that have been successfully used to help reinforce the mathematical concepts that the students are supposed to be learning.
While some of the equipment used does take some skill to build, none of the equipment used in these demonstrations is expensive. As the reader will see most of the equipment is made from “junk” that is lying around ones house, office, or can be borrowed from another department at your institution.
We will try to organize the demonstrations in an order that a student might encounter the topics in a standard mathematics curriculum at an institution where engineering is taught.
A. The cycloid curve
The first demonstration we will consider can be used in any calculus class where parametric equations are taught. This is a classical cycloid curve. To generate the curve we use a circular piece of wood in which a marker can be inserted on the circumference of the circle. (See the picture below.) Our apparatus also has a hole midway to the circumference which will demonstrate the path generated by a light or reflector which is placed beween the axis of a circle and its circumference.
Graves, E. (2009, June), Demonstrations That Work In The Mathematics Classroom Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. https://peer.asee.org/4797
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