place shape vs. place value
DESCRIPTION
CO11 Presentation looking at the shape of numbers in addition to the base-ten-centric place value. A visual foundation for math.TRANSCRIPT
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.