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

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