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