Download - Oi ed 2011 dr iot1 update
SubQuan:Math you can see
Ute FrenburgCooper MacbethAlexsis Kamala
Obama: STEMEducation a must-have
Science, technology, engineering, and math (STEM) education is of the utmost importance to all students and is critical to U.S. competitiveness, said President Obama at an April 20 town hall event held on Facebook’s Palo Alto, Calif. campus
Science Technology Engineering Mathematics
Biology Chemistry Physics Agricultural ScienceMathematics Statistics Computer Science Actuarial SciencePsychology Applied Mathematics Biochemistry Computer EngineeringElectrical Engineering Civil Engineering Aerospace engineering Food ScienceComputer Security Astrophysics Astronomy NanotechnologyNuclear Physics Mathematical Biology Operations Research BioinformaticsZoology Psychophysics Neurobiology BiomechanicsEpidemiology Acoustical Engineering Technology Education Mechanical EngineeringAtmospheric Sciences Chemical Engineering Geographic Information Systems
MathematicsIntroduction to Algebra Expressions and EquationsLinear Equations and Simultaneous Linear EquationsPolynomial Equations Partial Fractions TrigonometryBinomial Series Differentiation IntegrationFunctions Complex Numbers Hyperbolic FunctionsDeterminants Matrices VectorsDifferential Applications Partial Differentiation Curves and Curve FittingSeries Integral Applications Approximate IntegrationMultiple Integration First Order Differential EquationsSecond Order Differential Equations Laplace Transforms
MathematicsIntroduction to Algebra Expressions and EquationsLinear Equations and Simultaneous Linear EquationsPolynomial Equations Partial Fractions TrigonometryBinomial Series Differentiation IntegrationFunctions Complex Numbers Hyperbolic FunctionsDeterminants Matrices VectorsDifferential Applications Partial Differentiation Curves and Curve FittingSeries Integral Applications Approximate IntegrationMultiple Integration First Order Differential EquationsSecond Order Differential Equations Laplace Transforms
8th graders who scored at or above the Proficient level
2007 31% 2009 33%
Realize that the container shape doesn’t change the subQuan
but does change the quantity: base number
representation.
SubQuan different containers
SubQuan normalized containers
Hands-on SubQuanning
SubQuan with your hands to engage your kinesthetic memory.
“I see it!”
Cement your kinesthetic memory to your visual
instinct with an Aha moment.
Seeing Reality
If you did the exercises at
www.itonlytakes1.org subQuanning these
cubes should be quick.
(Answer on next page.)
Subquan Numbers Have Shape
We recognize squares and cubes but what are the others? Hmmm.
(Answer from previous page is two-six-five!)
others ?
square
cube
?
The Right Hand
Specialized 3-D binary base
number device used for naming
shapes and ‘really‘ learning how to count on your
fingers. (Answer: 84)
Virtual Cubes Are Beneficial
Snap-to Makes SubQuanning Quick
Not only can the little cubes snap in place but entire
groups can be easily moved.
(Can you figure out how many cubes are there now?)
Meta-patternsSame SubQuan,
Different quantities!
What is the meta-pattern? (see next slide)
The meta-pattern is five-six.
Where is the five in this data?
Where is the six?
PolynomialDerivation
Use spreadsheet for differences.
Lynn Arthur Steen warns, "an innumerate citizen today
is as vulnerable as the illiterate peasant of Gutenberg's time."
Master’s Thesis: Can children subQuan?
2nd PlaceVWBPE
2011
Number Shapes: Cube, Square, Seg
Seg Complements
COMBINING
Algebra I: Linear Equations
Algebra II: Quadratic Equations
Calculus: Derivatives
We produced two books, using SL, to present our ideas in the field.
An sQ Tale - The Future