Monday, November 12, 2007

The Magic of Math

When I was in school learning my multiplication tables, we learned via the traditional algorithmic method to solve problems.

I discovered that there are more ways than this one to solve mathematic problems. YouTube.com contains streaming videos that demonstrate how these same kinds of problems can be solved differently. Each method covers a different kinds of learning strengths: spacial, visual, estimation, grouping, and so on.

In the first video, Do the Math, there is no sound. This is particularly powerful because it requires that you pay attention to what is happening. Dr. Richard Feynman, Quantum Physicist, developed this technique to graphically approximate and solve quantum field theory equations that could not be solved in any other fashion. He got Nobel Price in physics for these diagrams.

Feynman's Multiplication Diagram
Feynman's Multiplication Diagram asks
you to represent the place values of integers
with lines representing their numerical value.
The points where the lines cross assist
in finding the final value.


In the second video, Math Education: An Inconvenient Truth, M.J. McDermott explains and criticizes the current state of math education in 4th and 5th grades. She opposes the rigor with which alternative methods of solving math equations are being taught in the classroom. These alternative methods include:

The Cluster Method
The Cluster Method involves dividing
the problem into smaller parts iteratively
which then can be easily calculated.


The Lattice Method The Lattice Method asks learners to fill in a grid
which resembles a lattice (fence)
taking 3 steps:
multiply, carry and add.
(In this way, it is very
similar to our
Traditional Algorithmic Method.)

The Partial Products Method The Partial Placement Method emphasizes
place value and requires a fluency
of multiplying by powers of ten.



Because the traditional algorithmic method tends to produce more accurate results and is definitely more efficient than any one of the other methods shown, I agree that students should be learning this method as the foundation of their studies -- but not as the only way.

Not introducing alternative methods of understanding math -- or anything else for that matter -- impedes some learners from grasping concepts that would otherwise be easily accessible to them. Teaching only one way of doing things, in this sense, is stifling -- even discriminatory of other learning styles. It also keeps us from the creativity of solving new problems that our current methods have caused. Moreover, I don't believe one way of doing something is always the most practical, the most accessible, the most efficient, etc. etc. Drawing from a variety of tools gives people the ability to visualize, understand and solve problems in multiple ways.


Meaningful threads and articles about this video:





Sunday, November 04, 2007

Innovation: Room Dividers + Form + Use



When I think of a dressing screen, I think of the Venetian-style screen, the hidden figure behind showing only shadows between the thin slots before a dress and bloomers are thrown haphazardly over the top. They are are used as room dividers or to create privacy for dressing.

What about one that can be used for a white board?

Dressing screens come in different styles. I
discovered the Window Pane Shoji Dressing Screen and a variety of other interesting items derived from the design of wood frame squares, little windows covered with rice paper: end tables, lamps and lanterns.

Traditionally, the Shoji screen are standard door- or wall-sized and are used to section off entire rooms.


Where to Find

Shoji Lamp
Shoji Screen
Shoji White Board
Shoji Screens, Lamps & End Tables
Full-sized Shoji Screen Walls & Doors

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