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Visual Algebra with Technology

Visual Algebra with Technology. Don Allen. Using computers to …. Construct knowledge Validate knowledge Discover knowledge Simulate knowledge. OK, what’s the difference?. “What is visual knowledge?”. Contents. The issues of algebra Using data Building a model Types of assessment.

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Visual Algebra with Technology

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  1. Visual Algebrawith Technology Don Allen

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

  3. “What is visual knowledge?”

  4. Contents • The issues of algebra • Using data • Building a model • Types of assessment

  5. “What is your visual IQ?”

  6. Visualize the concept • Physical examples • Diagrams • Charts of data

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

  8. “Getting the buy-in.”

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

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

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

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

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

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

  15. What processes are good for visualization • Things you can see - static • Things that move - dynamic • Things you can feel? Hear? • Things you can touch?

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

  17. What about drill?

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

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

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

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

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