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

 4 th grade  Number  Geometric Shapes and Measures  Data Display  8 th 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 13 th 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.