Generating a Sense of Wonder



Some of the LICIL related activities at SJC were described on the LICIL page on this site. The project closest to my heart, however, is my Generating a Sense of Wonder project. The goal I have set myself in this project is to develop a set of modules that can be presented to students for whom the beauty and profundity of mathematics have been obscured by the techniques employed in the discipline. It is my hope to convince students of the truth of the maxim that mathematics is ubiquitous, useful and (above all) beautiful. By selecting a variety of topics taken from every-day experience, I hope to inspire students with the beauty and utility of mathematics without overwhelming them with the machinery of the subject. In short, this is a project whose purpose coincides with its title: Generating a Sense of Wonder.

While the target audience is a general one, I hope specifically to focus upon future elementary school teachers. I see this group as particularly in need of having their senses of wonder awakened and nurtured. All too often, students in this group are highly math-phobic. Worse yet, they have the potential to contaminate the next generation with their unhealthy views. It is my hope, with this project, to break this vicious cycle of math phobia begetting more of same. I see no better way than by instilling in future elementary school teachers the very engine of inquiry: a healthy Sense of Wonder.
The modules are continuously being developed and revised. Here is a partial listing of the modules, to date:

1) Why do wheels sometimes look like they are spinning backwards? This module is dedicated to examining the stroboscopic effect in its various guises. A computer program was developed to help illustrate the ideas.

2) How far away is the horizon? This module explores the reasons for the horizon and shows how to calculate how far away it is as a function of one's height above sea-level. Related topics are discussed and three computer programs are used to help explore the topic further.

3) How did the Greeks determine the size of the Earth? This module describes the brilliant deductions of Eratosthenes and demonstrates (and celebrates) the power of pure reason.

4) A Mathematician Goes to Market. This module focuses on the various misconceptions that many people harbor regarding the elementary mathematics of commerce. From sales to sales tax to the abuse of logic used in advertisements, many common commercial topics are considered. A computer program is included which calculates discounts and surcharges and shows how they relate to one another.

5) A Mathematician Gets Behind the Wheel. This module explores cars, wagons and bicycles and the tracks they leave. Also, the way trains go around curves is discussed.

6) Size Does Matter! This module considers scaling and explores what changes as size varies. Not only volume and surface area, but even time is affected. A computer program is included to simulate a swinging pendulum with various arm lengths and various periods. The purpose is to illustrate natural frequency.

7) Subconscious Calculations. This module examines the tacit, subconscious mental calculations that we all make in every-day life. The realtive difficulties of these tacit calculations and the ones that we can do explicitly is discussed.
Long Island Consortium for Interconnected Learning


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