Wonder and Awe as a Habit of Mind

When students approach me with amazement in their new knowledge, I can hear the awe in their voices for all there is to learn about the world and I ask myself, “How can we inspire such excitement every day? How can we identify the best vehicles to facilitate student learning by fostering wonder and awe in our classrooms? Some of the true experts in fostering a habit of responding with wonderment and awe are early childhood and primary grade teachers. Teachers of our youngest learners fill ...

 1/9998 Produces Binary Output

The pattern will break down once you get past 8192, which is 2^13. That means that the pattern continues for an impressive 52 significant figures (well, it actually breaks down on the 52nd digit, which will be a 3 instead of a 2). The reason it works is that 9998 = 10^4 - 2. You can expand as   1 / (10^n - 2) = 1/10^n * 1/(1 - 2/10^n) = 1/10^n * (1 2/10^n 2^2 /10^2n 2^3 /10^3n ...) which gives the observed pattern. It breaks down when 2^k has more than n digi...

 Arthur Benjamin Explains the Fibbonacci Set

Now these numbers can be appreciated in many different ways. From the standpoint of calculation, they're as easy to understand as one plus one, which is two. Then one plus two is three, two plus three is five, three plus five is eight, and so on. Indeed, the person we call Fibonacci was actually named Leonardo of Pisa, and these numbers appear in his book "Liber Abaci," which taught the Western world the methods of arithmetic that we use today. In terms of applications, Fibonacci numbers appe...