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National Education Standards. Mathematics. Are standards hard to write?. Organization is difficult. Categories are hard to pick. How is it done?. Common Core has 10 content areas. Number Quantity Expressions Equations Functions Modeling Shape Coordinates Probability Statistics. - PowerPoint PPT Presentation
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National Education Standards
Mathematics
Organization is difficult. Categories are hard to pick.
How is it done?
Are standards hard to write?
Number Quantity Expressions Equations Functions Modeling Shape Coordinates Probability Statistics
Common Core has 10 content areas
Number properties and Operations Measurement Geometry Data Analysis, Statistics, and Probability Algebra
NAEP has 5
4th grade Number Geometric Shapes and Measures Data Display
8th grade Number Algebra Geometry Data and Chance
TIMSS has 3 for 4th grade 4 for 8th
Space and shape Change and relationships Quantity Uncertainty
PISA has 4 areas
But, it isn’t that important.The structure of the standards doesn’t matter that much.
So, organization is difficult.
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!
Anything easy about standards?
PISA◦ They don’t bother. Not about math.
NAEP◦ Has content and kitchen sink.
Common Core◦ Thinks (minimal) college readiness.
TIMSS◦ Listens to mathematicians.
Content Choice Styles
Clarity is easy. Use simple, precise, mathematical
language.
What else is easy?
Compare and order whole numbers. Solve problems involving proportions. Compute with fractions and decimals. Solve problems involving percents and
proportions.
Very nice, straightforward, clear.
TIMSS
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?”
Common Core, A step down.
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.”
NAEP, much further down
Expressions Equations inequalities
Three things
Linear Quadratic Exponential trigonometric
4 functions
Symbols Graphs Tables Diagrams Written descriptions
5 representations
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!
Translations among the 5
Elegant computations Recognizing shapes and patterns Representing changes in a comprehensible
form Understanding the fundamental types of
change
This is not guidance with clarity!
PISA, lowest of all
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.
Biggest Difficulty – Setting Priorities
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.
Recall NAEP
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.
TIMSS standards comparison
Probability and statistics are reasonable But They are 24% of the total standards. That’s unreasonable.
Common Core areas
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.
Setting priorities is difficult to fix