Visual AlgebraVisual Algebrawith with

TechnologyTechnology

Don Allen

Using computers to …Using computers to …Construct knowledgeValidate knowledgeDiscover knowledgeSimulate knowledge

OK, what’s the difference?

“What is visual knowledge?”

ContentsContents

The issues of algebraUsing dataBuilding a modelTypes of assessment

“What is your visual IQ?”

Visualize the conceptVisualize the concept

Physical examplesDiagramsCharts of data

“A first step to learning is too agree there is something

worthwhile to learn.”

“Getting the buy-in.”

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

Public education …Public education …

Using dataUsing data

(1) Find data illustrating the points you want to make.

(2) Find an image illustrating the point you want to make.

Using data (1)Using data (1)

Insert the data into the spreadsheetManipulate the data to the desired form.Create a chart Further analysis

Using data (2)Using data (2)

Load the image into DigitizerSet coordinates and scale factorsDigitize Using data (1)Comparative analysis.

Building the modelBuilding the model

Clarify dependencies/variablesIdentify system parametersDetermine the unknownsDefine the relationships – use operationsFormulate 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 What processes are good for visualizationvisualization

Things you can see - staticThings that move - dynamicThings you can feel? Hear?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?What about drill?

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

What about error?What about error?

Error is a part of everything realBut how much is error?Overcoming errorSmoothing – but how?

Averages Least squares Moving averages

What do I want?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.

Formation of a coalitionFormation 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