Visual Algebra with Technology Don Allen Using computers

Visual Algebra with Technology Don Allen

Using computers to … l Construct knowledge l Validate knowledge l Discover knowledge l Simulate knowledge OK, what’s the difference?

“What is visual knowledge? ”

Contents l The issues of algebra l Using data l Building a model l Types of assessment

“What is your visual IQ? ”

Visualize the concept l Physical examples l Diagrams l Charts of data

“A first step to learning is too agree there is something worthwhile to learn. ”

“Getting the buy-in. ”

Public education … “We (the state schools) are the Mc. Donalds of education. We deliver a decent education at a reasonable price. ”

Using data l (1) Find data illustrating the points you want to make. l (2) Find an image illustrating the point you want to make.

Using data (1) l Insert the data into the spreadsheet l Manipulate the data to the desired form. l Create a chart l Further analysis

Using data (2) l Load the image into Digitizer l Set coordinates and scale factors l Digitize Using data (1) l Comparative analysis.

Building the model l Clarify dependencies/variables l Identify system parameters l Determine the unknowns l Define the relationships – use operations l Formulate an equation to be solved or evaluated

“What is visual knowledge? ” Visual knowledge is an intuitive understanding of variations and dependency according to visual representations of the information.

What processes are good for visualization l Things you can see static l Things that move dynamic l Things you can feel? Hear? l Things you can touch?

“What is your visual IQ? ” Visual IQ measures one’s level of analytic knowledge arising from visual information.

What about drill?

“The curriculum is a mile wide, but just an inch deep. ”

What about error? l Error is a part of everything real l But how much is error? l Overcoming error l Smoothing – but how? Averages l Least squares l Moving averages l

What do I want? l When a student looks at the Mc. Donalds arches, he/she sees a curve not a parabola and know why. l When a student looks at a common drinking fountain, he/she sees a parabola curve and knows why.

Formation of a coalition l Dedicated to finding visual interpretation of concepts from algebra and calculus l Willing to try new materials with assessment l Willing to develop new materials – using technology