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## National Education Standards

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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**NAEP has 5**• Number properties and Operations • Measurement • Geometry • Data Analysis, Statistics, and Probability • Algebra**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**PISA has 4 areas**• Space and shape • Change and relationships • Quantity • Uncertainty**So, organization is difficult.**• But, it isn’t that important. • The structure of the standards doesn’t matter that much.**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!**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.**What else is easy?**• Clarity is easy. • Use simple, precise, mathematical language.**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.**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?”**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.”**Three things**• Expressions • Equations • inequalities**4 functions**• Linear • Quadratic • Exponential • trigonometric**5 representations**• Symbols • Graphs • Tables • Diagrams • Written descriptions**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!**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!**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.**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.**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.**Common Core areas**• Probability and statistics are reasonable • But • They are 24% of the total standards. • That’s unreasonable.**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.