transitioning to the common core rigorous mathematics: all roads lead to calculus and statistics dr....

Transitioning to the Common CoreRigorous Mathematics:

All Roads lead to Calculus and Statistics

Dr. Patrick CallahanStatewide Co-Director, California Mathematics Project, UCLA

Huntington Beach Unified High School DistrictJanuary 26, 2015

Why Common Core?

Where did the CCSS Come From?

Overriding question:What do we want HS graduates to know and be able to do?

Current Adoptions of CCSS

CCSS Adoptions as of 11/3/2014

43 State are currently implementing the CCSS

When will we be fully implemented?

“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.

CONGRATS CLASS OF 2014 !

You have experienced about 7.692% Common Core!

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, parents, teachers, and systems are where they are now and that it will take time to move the system to the Common Core.

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 or taught.

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.

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, coherence, and rigor. (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.

1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of

others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Mathematical Practice

CCSS Mathematical PracticesO

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REASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others

MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically

SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

What is rigor?

CONCEPTS

PROCEDURES

APPLICATIONS

What is rigor?

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

A sample Algebra Exam

I typed #16 into Mathematica

Look at the circled answers.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 that there is no context, just numbers and expressions.

Getting correct answers is necessary, but students must also understand, and be able do applications

CONCEPTS

PROCEDURES

APPLICATIONS

Previous Expectations for Mathematics

California STAR test released items 5th Grade

Students will NOT be given this type of assessment anymore.

Why not?This test is not rigorous!It is essentially all procedures and no conceptual understanding or applications.

The definition of RIGOR in the Common Core is equal intensity of all three!

Fortune 500: Most Valued Skills

Getting into Elite Universities

Getting into Elite Universities

Getting into Elite Universities

rigor of courses taken and grades earned

What is rigor?

CONCEPTS

PROCEDURES

APPLICATIONS

Key IdeaThe Common Core is NOT just about shuffling topics around.

The Common Core is fundamentally about changing the definition of what it means to be mathematically proficient.

The Common Core is a response to demands from colleges and the business sector to change what is meant by rigor.

The Target has Changed!OLD DEFINITION OF

PROFICENCYNEW DEFINITION OF

PROFICENCY

Procedural Fluency

Procedural Fluency+Applications+Conceptual Understanding

SBAC Claims

SAT Redesign (2016)

Focus on Math that Matters Most

The exam will focus in depth on three essential areas of math:

• Problem Solving and Data Analysis

• Heart of Algebra

• Passport to Advanced Math

New SAT items

New expectations require new Pathways

Changing expectations:The 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 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

An important equation:

Algebra 1 ≠ Algebra 1

Previous 8th grade CA standards

Crosswalks are not the answer

Changing expectations:Middle School is key

When the expectations for middles school mathematics were mostly 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.

Sample Common Core Grade 8 Curriculum

Plan

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

CA Framework on Acceleration

1. 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

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

What it means to be successful at mathematics

It’s not rushing to get as far ahead as you can.

It means mastering rigorous mathematics.

CONCEPTS

PROCEDURES

APPLI-CATIONS

OLD vs. CC: Same Advanced Options for Students(A POSSIBLE SET OF CC PATHWAYS)

OLD GRADE

6

OLD GRADE

7

OLD ALG

1

OLD GEOM

OLD ALG

2

AP CALC

OLD PRE-CALC

Grade 6 Grade 7 Grade 8 Grade 9

OLD GRADE

6

OLD ALG

1

OLD GEOM

OLD ALG

2

OLD PRE-CALC

APCALC

BC

APCALC

AB

Grade 10 Grade 11 Grade 12

CC6

CC 7

CC8

CCALG

1

CCGEOM

YR 4or

AP C/S

CC ALG

2

CC7

CC 8

CCALG

1

CCGEOM

CCALG

2

APCALC

BC

APCALC

AB

OLD vs. CC: Same Advanced Options for Students(A POSSIBLE SET OF CC PATHWAYS)

OLD GRADE

6

OLD GRADE

7

OLD ALG

1

OLD GEOM

OLD ALG

2

AP CALC

OLD PRE-CALC

Grade 6 Grade 7 Grade 8 Grade 9

OLD GRADE

6

OLD ALG

1

OLD GEOM

OLD ALG

2

OLD PRE-CALC

APCALC

BC

APCALC

AB

Grade 10 Grade 11 Grade 12

CC6

CC 7

CC8

CCALG

1

CCGEOM

YR 4or

AP C/S

CC ALG

2

CC6

CC 7/8

CCGEOM

CCALG

2

APCALC

BC

APCALC

AB

CC8/

CCALG 1

Transitioning to Common Core:Focus and Purpose

Transitions are like home remodels: they take time and they can be messy along the way, but it is worth the effort if you have a vision for improving mathematics for all students.

Resources for Parents

Achieve the Core: http://achievethecore.org/common-core-intro-for-parents

Inside Mathematics: http://www.insidemathematics.org/

Illustrative Mathematics: https://www.illustrativemathematics.org/