Place Shape vs. Place Value

A visual foundation for math

A Dream Realizations

Presentation

with

Cognitive Engineering Research Laboratories

http://www.brothersoft.com/free-rainbow-screensaver-76363.html

Dialog modified from the movie Kate & Leopold (2001)

climate.met.psu.edu

CEO of Dream Realizations - Rebecca Reiniger

Alexsis (Anna-Marie), Cooper, and Ute (Rebecca) in Second Life.

Creative Director of CERLabs - Cooper Patterson

What is cognitive engineering?

www.osdata.com/system/physical/basics.htm Functional brain map from Science Daily by Daniel Oldjira Fufa.

The Dual Nature of Numbers: Cardinality & Ordinality

The Impact of Number

Language

Our Myopia with the Decimal System

Counting, an ordinal concept, dominates our early focus with numbers.

The patterns in our number words are

cognitively inconsistent with

our minds’ number sense.

Our myopia with base ten interferes with the discovery of place shapes and

subQuan meta patterns required for formula derivation and algebraic

manipulations.

The Three Blind Mice of Number Sense

Open Your Eyes and See!

Where is the world headed with numbers?

Single digit numbers of popular number systems binary 0 g number system 1 h 2 i 3 j

4 k 5 l

6 m 7 n decimal 8 o number system 9 p a q b r c s d t hexadecimal e u number system f v

duotridecimal* number system is the entire single digit set shown. * also called duotrigesimal

Place Value...

Very abstract relationship for youngsters.

119

128

146

205

10A

224

1013

10102

137

Ten

nine

eight

six

five

ten four

three

two

seven

One-Ro

One Hundred 2D 100A

1219

1448

2027

2446

4005

12104

100A

1219

1448

2027

2446

4005

12104

One Hundred 3D

The subQuan four three one two is composed of: 4 Cubes, 3 Squares, 1 Seg, and 2 Ones

Cognitive engineering perspective

H O W M A N Y ?

Each Place Value also shows Shape. The best part is that it works in ALL bases, not just base ten.

Place Shape!

If we verbalize the subQuan Algebraically: 4 ten Cubes, 3 ten Squares, 1 ten Seg, and 2 Ones

Compare the previous visual image to this excerpt from http://en.wikipedia.org/wiki/Positional_notation

Try describing this to an elementary student!

Excerpt from http://en.wikipedia.org/wiki/Positional_notation

The Dual Nature of Numbers: Cardinality & Ordinality

The Impact of Number

Language

Our Myopia with the Decimal System

Counting, an ordinal concept, dominates our early focus with numbers.

The patterns in our number words are

cognitively inconsistent with

our minds’ number sense.

Our myopia with base ten interferes with the discovery of place shapes and

subQuan meta patterns required for formula derivation and algebraic

manipulations.

The Three Blind Mice of Number Sense

Open Your Eyes and See!

Great. We have a foundation based on

Place Shapes.

What can one build on place shapes?

"We are here"

Visit us in Second Life to experience the full effect of 3D visualization.

You can help us discover all that changes when you start with Place Shapes.