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K Werner Design Blog

Permutations



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Check out Khan Academy on Permutations!
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Permutations and Combinations

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" There are in fact 36 PERMUTATIONS (every possible arrangement, even the arrangements that appear similar). For example, 1,2 and 2,1 are the same COMBINATION, but there are two different PERMUTATIONS using these two numbers."

Mathematical Sketching

Mathematical sketching is an educational concept that uses  modern computer technological tools like digital pen, software, and touch screens to sketch mathematical problems  in a way that will show the real life application for such problems. A math pad is the result of this creative idea. 

"Mathematical sketching lets users create dynamic illustrations through the association of hand written mathematics and free-form drawings. These dynamic illustrations have the potential to provide useful insights into a variety of abstract concepts in Physics. Thus, mathematical sketching lends itself, with its pencil-and-paper-based interaction approach, to be a natural interface to intelligent tutoring applications."*

"
Dr. Joe LaViola, a professor in the College of Engineering and Computer Science,
...and several colleagues are working to commercialize the program and started a software company based in Boston, Massachusetts. He sees the application being commercially available in as little as one to two years.  Currently, testing of the application is being conducted with Calculus I students at UCF and he will extend the tests to Calculus II...Teachers have been overwhelmingly positive (of the program),” said LaViola. “Not only is it a tool for teachers to explain math concepts, students also benefit by being able to visualize them, which adds to their understanding. Although the program is currently only being tested at the high school and freshman college level, its reach could easily extend to middle and elementary school students as well,” added La Viola."**


*Towards Intelligent Tutoring with Mathematical Sketching
**Mathematical Sketching Comes to Life



Uso del Triangulo de Pascal

Pascal's Triangle