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How do you perceive your topic? This assignment is divided into 2 parts. First, you’ll be asked to identify existing patterns in the content you’re teaching. After you’ve done that, you’ll have to think up new patterns that can be applied to that content. Let’s start with identifying/recognizing patterns. First of all, what’s the big deal with patterns, and how does identifying them in objects around us help in any way? Below are a couple of examples explaining the importance of such a skill. Example 1 Drawing the Pangaea by Alfred Wagner (Chapter 6, pp.104,105)

A lot of people are aware of the different continents, and probably a lot speculated on their formation. However, only Alfred Wegener took these observations seriously enough to make the connection between the shapes of the different continents. From this pattern, we were able to draw the conclusion that at one point in history, there used to be only one giant continent. This discovery yielded invaluable information that led to many other discoveries in turn. In this example, identifying an existing pattern helped solve a long-debated mystery about the origin of Earth.

Example 2 Mathematician Carl Friedrich Gauss (Chapter 6, pp.102,103) Try to add all the numbers from 1 to 100 and see how long it’ll take you. That’s what everyone would normally do to get the sum of these 100 numbers, but not Carl Gauss. Carl came up with a smart way of identifying a recurring pattern in these numbers: add 2 numbers from each extreme and you’ll get 100. 0+100, 1+99, 2+98 and so forth. As a result, Carl was able to answer the question in a much shorter time than anyone else having attempted the computation. In this example, identifying an existing pattern helped save time. It has also triggered the need to look for patterns in other cases as well. For more examples on how useful identifying patterns can be, check out the links below.    

Squaring numbers Surprising number patterns No need for multiplication Another surprising numerical pattern

Example 3 Musicologist Simha Arom (Chapter 7, pp.118,119) Simha Arom specialized in African music. He analyzed several hundreds of their polyrhythmic music to help understand how informally trained amateurs could produce such complex rhythmic patterns. The answer was the patterns these indigenous were using. He discovered that each group played a very simple beat, and when all these beats were superimposed, the resulting music by far too overwhelming for anyone to comprehend as is. This video is an example of the Aka Pygmy music. Notice how complex the rhythm is, yet it is performed by a combination of rudimentary music. In this example, identifying an existing pattern revealed the secret to forming much more complex patterns.

Example 4 Joseph Fourier (Chapter 7, p.125) In brief, Fourier helped design the modern synthesizer, which operates on Fourier’s principle that every complex pattern is actually a combination of a series of simple ones. The examples below show the origin of the big wave.

One way of combining 3 waves.

One way of combining 2 waves.

In this example, identifying an existing pattern helps understand more complex ones. By now, it should be clear that identifying existing patterns helps understand more complex patterns. So the first part of your assignment is to think of how identifying patterns in your content area topic helps solve problems or answer tricky questions. Remember that NOT all patterns are helpful. One last word on identifying patterns: “The complexity of the final product doesn’t reside in the complexity of the components but in the cleverness with which a handful of simple elements is used to generate diverse surprises.” (Chapter 6, p.135, par.1)

The other part of your assignment is to consider how new patterns can be formed to create new approaches to solving problems or answering tricky questions in your content area topic. Consider René Parola’s Optical Art: Theory and Practice, which provides examples and guidelines of how combining different simple patterns can result in more complex and interesting patterns. You can see some of these examples in the free publication of the first 22 pages of his book. Don’t bother reading every bit just yet (though you may want to do that later on). Simply look at the different examples and see how superimposing 2 or more different patterns can result in a completely unexpected one. I particularly like fig 1-7 on page 17. Both

patterns are 2 dimensional; however, the resulting pattern is 3 dimensional! A small shift in the bands created this effect. The benefits? Well, think about it as a way to create a 3D image on a flat surface. Not many can do that! Quick recap: Your assignment is divided into 2 parts: 1. Identifying some existing patterns in your content area topic and explain how this would help your students to better understand and handle your topic? 2. Form 1 or 2 new patterns in your content area topic and explain how this would help your students to better understand and handle your topic? (Think of the creative usefulness of the new patterns.) Doesn’t it look like a 3D bent pipeline? Well, it does to me any way. ď Š


This document highlights the importance of identifying patterns and forming patterns to trigger creativity in students.