Transcript National Education Standards

Mathematics


Organization is difficult.
Categories are hard to pick.
 How
is it done?










Number
Quantity
Expressions
Equations
Functions
Modeling
Shape
Coordinates
Probability
Statistics





Number properties and Operations
Measurement
Geometry
Data Analysis, Statistics, and Probability
Algebra

4th grade

Number
Geometric Shapes and Measures
Data Display

8th grade






Number
Algebra
Geometry
Data and Chance




Space and shape
Change and relationships
Quantity
Uncertainty
 But,
it isn’t that important.
 The structure of the
standards doesn’t matter
that much.








Picking content is easy!
Involve mathematicians.
Oops! What’s your image of mathematicians?
Your image is wrong!
Think: Mathematicians are 13th grade
teachers.
Survey us.
Look at our placement tests.
Easy!

PISA
◦ They don’t bother. Not about math.

NAEP
◦ Has content and kitchen sink.

Common Core
◦ Thinks (minimal) college readiness.

TIMSS
◦ Listens to mathematicians.


Clarity is easy.
Use simple, precise, mathematical language.





Compare and order whole numbers.
Solve problems involving proportions.
Compute with fractions and decimals.
Solve problems involving percents and
proportions.
Very nice, straightforward, clear.




Know when and how to use standard
algorithms, and perform them flexibly,
accurately, and efficiently.
Clean it up!
Know how to use standard algorithms
efficiently.
Do you really have to mention “accurately?”



Create and translate between different
representations of algebraic expressions,
equations, and inequalities (e.g., linear,
quadratic, exponential, or trigonometric)
using symbols, graphs, tables, diagrams, or
written descriptions.
Yikes! Analyze by counting.
Forget create. Use only “translate.”



Expressions
Equations
inequalities




Linear
Quadratic
Exponential
trigonometric





Symbols
Graphs
Tables
Diagrams
Written descriptions








20 different translations
4 different functions
3 different mathematical relationships
Total: 240 standards in one sentence!
Oops, forgot “create”
3x4x5=60
Total: 300 standards in one sentence!
Clarity, simplicity? No!





Elegant computations
Recognizing shapes and patterns
Representing changes in a comprehensible
form
Understanding the fundamental types of
change
This is not guidance with clarity!



Some parts of standards are not as important
as other parts of the same standard.
Some standards are not as important as other
standards.
Some content areas are not as important as
other content areas.


Create and translate between different
representations of algebraic expressions,
equations, and inequalities (e.g., linear,
quadratic, exponential, or trigonometric)
using symbols, graphs, tables, diagrams, or
written descriptions.
Tables to written descriptions, not as
important as symbols to graphs.




Compute with fractions and decimals.
Use data from experiments to predict the
chances of future outcomes.
One is essential math.
One is pretty important science.




Probability and statistics are reasonable
But
They are 24% of the total standards.
That’s unreasonable.





TIMSS does it.
They tell you what percentage of their test
will be on each area.
Others don’t succeed.
Even if you pick standards that are all
absolutely essential, some take more time.
It is a difficult problem.