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National Education Standards

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.

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National Education Standards

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  1. National Education Standards Mathematics

  2. Are standards hard to write? • Organization is difficult. • Categories are hard to pick. • How is it done?

  3. Common Core has 10 content areas • Number • Quantity • Expressions • Equations • Functions • Modeling • Shape • Coordinates • Probability • Statistics

  4. NAEP has 5 • Number properties and Operations • Measurement • Geometry • Data Analysis, Statistics, and Probability • Algebra

  5. TIMSS has 3 for 4th grade 4 for 8th • 4th grade • Number • Geometric Shapes and Measures • Data Display • 8th grade • Number • Algebra • Geometry • Data and Chance

  6. PISA has 4 areas • Space and shape • Change and relationships • Quantity • Uncertainty

  7. So, organization is difficult. • But, it isn’t that important. • The structure of the standards doesn’t matter that much.

  8. Anything easy about standards? • 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!

  9. Content Choice Styles • 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. What else is easy? • Clarity is easy. • Use simple, precise, mathematical language.

  11. TIMSS • 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. Common Core, A step down. • 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. NAEP, much further 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.”

  14. Three things • Expressions • Equations • inequalities

  15. 4 functions • Linear • Quadratic • Exponential • trigonometric

  16. 5 representations • Symbols • Graphs • Tables • Diagrams • Written descriptions

  17. Translations among the 5 • 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. PISA, lowest of all • 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. Biggest Difficulty – Setting Priorities • 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. Recall NAEP • 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. TIMSS standards comparison • 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. Common Core areas • Probability and statistics are reasonable • But • They are 24% of the total standards. • That’s unreasonable.

  23. Setting priorities is difficult to fix • 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.

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