1. Mathematics

2.  Organization is difficult.  Categories are hard to pick.  How is it done?

3.  Number  Quantity  Expressions  Equations  Functions  Modeling  Shape  Coordinates  Probability  Statistics

4.  Number properties and Operations  Measurement  Geometry  Data Analysis, Statistics, and Probability  Algebra

5.  4 th grade  Number  Geometric Shapes and Measures  Data Display  8 th grade  Number  Algebra  Geometry  Data and Chance

6.  Space and shape  Change and relationships  Quantity  Uncertainty

7.  But, it isn’t that important.  The structure of the standards doesn’t matter that much.

8.  Picking content is easy!  Involve mathematicians.  Oops! What’s your image of mathematicians?  Your image is wrong!  Think: Mathematicians are 13 th grade teachers.  Survey us.  Look at our placement tests.  Easy!

9.  PISA ◦ They don’t bother. Not about math.  NAEP ◦ Has content and kitchen sink.  Common Core ◦ Thinks (minimal) college readiness.  TIMSS ◦ Listens to mathematicians.

10.  Clarity is easy.  Use simple, precise, mathematical language.

11.  Compare and order whole numbers.  Solve problems involving proportions.  Compute with fractions and decimals.  Solve problems involving percents and proportions.  Very nice, straightforward, clear.

12.  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?”

13.  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.”

14.  Expressions  Equations  inequalities

15.  Linear  Quadratic  Exponential  trigonometric

16.  Symbols  Graphs  Tables  Diagrams  Written descriptions

17.  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!

18.  Elegant computations  Recognizing shapes and patterns  Representing changes in a comprehensible form  Understanding the fundamental types of change  This is not guidance with clarity!

19.  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.

20.  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.

21.  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.

22.  Probability and statistics are reasonable  But  They are 24% of the total standards.  That’s unreasonable.

23.  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.