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### Transitioning to the Common Core: Focus and Purpose

Patrick Callahan

Co-Director, California Mathematics Project

UCLA

The Common Core is not just a list of topics to teach in a given grade, but rather a description of the mathematics students are expected to accomplish. Current courses titled "Algebra" or "Geometry" will very likely not provide opportunities for students to accomplish the mathematics described in the Common Core. We will discuss significant changes in expectations in algebra and geometry and practical steps that teachers, schools, and districts can start doing immediately to transition towards these new expectations.

I heard you have fully implemented the common core in your district!

That’s right! We chose to go Traditional.

We used to teach Algebra 1, Geometry, and Algebra 2.

Now we are teaching Algebra 1, Geometry, and Algebra 2.

Doing Common Core is a lot easier than I thought it’d be!

“fully implemented?”

From a student’s perspective the first time the Common Core could be fully implemented is a student graduating in 2024.

Before that time every student will experience a hybrid of Common Core and previous mathematics.

“fully implemented?”

From a student’s perspective the first time the Common Core could be fully implemented is a student graduating in 2024.

Before that time every student will experience a hybrid of Common Core and previous mathematics.

You have experienced about 7.692% Common Core!

Congrats Class of 2014 !

Implementation vs Transition

The word “implementation” tends to refer to the policy aspects of adopting the Common Core.

In a policy sense you can be “fully implemented” right away.

Another, more student-centric, approach is to think in terms of “transition” rather than “implementation”.

This is a pragmatic approach that acknowledges that student, teachers, and systems are where they are now and that it will take time to move the system to the Common Core.

I encourage thinking strategically about at minimum a three-year transition plan.

Don’t try to do everything at once. Have focus and purpose!

Transition to What?

We use the phrase

“implement the Common Core”

or

“transition to the Common Core”

but what does that mean?

What exactly are the Common Core Standards?

Common Core Standards, what they are NOT and what they ARE:

The Common Core standards are not a list of topics to be covered.

The Common Core State Standards are a description of the mathematics students are expected to understand and use, not a curriculum. The standards are not the building blocks of curriculum, they are the achievements we want students to attain as the result of curriculum. To quote page 5 of the Common Core State Standards for Mathematics (Common Core):

“Just because topic A appears before topic B in the standards for a given grade, it does not necessarily mean that topic A must be taught before topic B. A teacher might prefer to teach topic B before topic A, or might choose to highlight connections by teaching topic A and topic B at the same time. Or, a teacher might prefer to teach a topic of his or her own choosing that leads, as a byproduct, to students reaching the standards for topics A and B.”

How are the CCSS different?

The CCSS are reverse engineered from an analysis of what students need to be college and career ready.

The design principals were focus and coherence. (No more mile-wide inch deep laundry lists of standards)

The CCSS in Mathematics have two sections:

CONTENT and PRACTICES

The Mathematical Content is what students should know.

The Mathematical Practices are what students should do.

Real life applications and mathematical modeling are essential.

Mathematical Practice

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

CCSS Mathematical Practices

REASONING AND EXPLAINING

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

OVERARCHING HABITS OF MIND

1. Make sense of problems and persevere in solving them

6. Attend to precision

MODELING AND USING TOOLS

4. Model with mathematics

5. Use appropriate tools strategically

SEEING STRUCTURE AND GENERALIZING

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Shifts in Content

Because the Common Core were reverse engineered from a definition of Career and College Ready, there were shifts in content.

How is Algebra different?

More applications, modeling, equivalence

Less algorithms, answer-getting, simplifying

HS Algebra Families of Function Cycle

CONTEXTS

ABSTRACTION

(structure, precision)

FUNCTIONS

(modeling)

EQUATIONS

(solving, manipulations

- Families of Functions:
- Linear (one variable)
- Linear (two variables)
- Quadratic
- Polynomial and Rational
- Exponential
- Trigonometric

Conrad Wolfram’s TED Talk:

What is math?

Posing the right questions

Real world math formulation

Computation

Math formulation real world, verification

Conrad Wolfram’s TED Talk:

What is math?

Posing the right questions

Real world math formulation

Computation

Math formulation real world, verification

Humans are vastly better than computers at three of these.

Conrad Wolfram’s TED Talk:

What is math?

Posing the right questions

Real world math formulation

Computation

Math formulation real world, verification

Yet, we spend 80% or more of math instruction on the one that computers can do better than humans

Conrad Wolfram’s TED Talk:

What is math?

Posing the right questions

Real world math formulation

Computation

Math formulation real world, verification

Note: The CCSS would indentify Wolfram’s description of math in terms of Mathematical Practices: make sense of problems, model, use tools strategically.

Sample Algebra Worksheet

This should look familiar.

What do you notice?

What is the mathematical goal?

What is the expectation of the student?

A sample Algebra Exam

I typed #16 into Mathematica

What do you notice?

“Answer Getting”

As Phil Daro has mentioned:

There is a difference between using problems to “get answers” and to learn mathematics.

This algebra exam sends a clear message to students:

Math is about getting answers.

Note also that there is no context, just numbers and expressions

Changing expectationsThe trouble with course names

In the particular case of mathematics, there is a “vocabulary” around the names of mathematics courses that is likely to cause confusion not only for educators, but also for parents. “Algebra 1” is a course that, prior to CA CCSSM, has been taught in 8th grade to an increasing number of students. That same course name will be the default for ninth grade for most students who moving forward will complete the CA CCSSM for grade eight – a course that is more rigorous and more demanding than the earlier versions of “Algebra 1.” Even so, we expect the changes to cause confusion. The single most practical solution is to describe detailed course contents, in addition to course names, as a way of clearing up confusion until “Algebra I” as commonly used, refers to a ninth grade and not an eighth grade course

Changing expectations:Middle School is key

When the expectations for middles school mathematics were about speed and accuracy of computations it made sense to accelerate in middle school, and even skip grades.

This no longer makes sense.

Middle school mathematics is the key to success for all students. Rushing or skipping is a bad idea for almost all students.

Common Core Grade 8 Curriculum Plan

Common Core is much more rigorous than previous middle school expectations.

CA Framework on Acceleration

Decisions to accelerate students into the Common Core State Standards for higher mathematics before ninth grade should not be rushed.

Placing students into an accelerated pathway too early should be avoided at all costs. It is not recommended to compact the standards before grade seven to ensure that students are developmentally ready for accelerated content. In this document, compaction begins in seventh grade for both the traditional and integrated sequences.

CA Framework on Acceleration

2. Decisions to accelerate students into higher mathematics before ninth grade must require solid evidence of mastery of prerequisite CA CCSSM.

3. Compacted courses should include the same Common Core State Standards as the non-compacted courses.

4. A menu of challenging options should be available for students after their third year of mathematics—and all students should be strongly encouraged to take mathematics in all years of high school.

Transitioning to Common Core:Focus and Purpose

Advice: Don’t try to do everything at once!

Start supporting the mathematical practices immediately. Focus on one or so per semester.

Consider a three-year roll out for the content.

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