Teachers-in-Service Program in Manitoba

Abstract

-This paper describes examples of a new range of activities intended to enhance the exposure of senior high-school students to engineering, technology, applied science and science. The activities are termed Teachers-in-Service Program (TISP), and have been proposed by the Institute of Electrical and Electronics Engineers (IEEE). Shortly after IEEE Canada brought TISP to this country, IEEE Winnipeg Section brought it to Manitoba. Our TISP activities to date have been very extensive and comprehensive [1].The mission of TISP is to foster interest in engineering, science and mathematics among students from grades 7 through 12 by providing teachers with tools and training (e.g., [2]) that can be used to give students interesting experience with science and engineering topics in the classroom. TISP provides a forum for IEEE volunteers to demonstrate the application of engineering, science and mathematics concepts by sharing their real-world experiences with local preuniversity educators. IEEE offers training workshops for its volunteers on how to provide the in-service program to local teachers. In Manitoba, we have expanded the TISP activities to include not only teachers, but also parents and students themselves. Our TISP activities are segmented into three classes: Tier1 that dedicated to students mostly (e.g., focused presentations, demonstrations and tours that reached over 1350 students in the previous year), Tier2 involving teachers mostly (e.g., workshops [3]), and Tier3 engaging students, teachers and parents (e.g., Space Camp [4], Near-Space Experiments, and communications with satellites through the University of Manitoba ground station [5]).

Implementation of a Chua Circuit to Demonstrate Bifurcations and Strange Attractors in a Class

“…In the case of dynamical systems (i.e., nonlinear dynamic systems that can exhibit chaos), the material taught requires considerable sophistication from the students, and explanations by traditional techniques may not be adequate [Kins12]. Consequently, using demonstrations of real examples of dynamical systems can ease the understanding of the underlying concepts, particularly when the demonstrations can behave in a fully-controlled fashion.…”

“…Around 1983, Leon Chua developed a nonlinear circuit (today known as the Chua circuit) that is capable of demonstrating a rich collection of dynamical phenomena, ranging from fixed points to cycle points, standard bifurcations (period doubling), other standard routes to chaos, and chaos itself (e.g., [Chua07], [Chua92], [ChPW95], [Chua06], [PaCh89], [Kapi02], [Ogor97], [Deva92], [Ott93], [AlSY96], [PeJS92], [Strog94], [BrHT10], [MaSi05], [OtSY94], [Kins12]). A few years later, Chua, Komuro, and Matsumoto proved rigorously that the Chua attractor is chaotic indeed [ChKM86].…”

“…The critical parameters are the ratios of the conductance of the nonlinear resistor in its middle G a to the coupling conductance G, and the outer conductance G b to G. The other parameters α and β relate the value of the capacitor C2 to C1 and to L, respectively. The circuit displays distinct classes of behaviour for different combinations of α, β, a, and b [Kins12]. For example, the full double-scroll chaos develops for α = 10.0, β = 14.87, a = -1.27, and b = -0.68.…”

“…Several alternative implementations for the Chua circuit have been considered for the demo in the fractal and chaos course [Kins12]. The selected circuit provides flexibility in order to demonstrate different states of the Chua circuit, and can provide detailed control over the behaviour of circuit.…”

“…The second main objective of this experiment is to demonstrate that the Chua circuit has a strange attractor (this name was coined by Ruelle and Takens in 1971 [RuTa71]). If the attractor exists, the process cannot be random [Kins12]. Since the Chua circuit has three degrees of freedom, its state space is threedimensional (3D).…”