Dr. DeAnn Huinker University of Wisconsin-Milwaukee Journey to the Core This material was developed...

transcript

Dr. DeAnn HuinkerUniversity of Wisconsin-Milwaukee

Journey to the Core

This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission.

Shared, the

same for everyone

Essential, fundamental knowledge and skills

necessary for student success

Adopted and

maintained by States;

not a federal policy

Benchmarks of what

students are expected to learn in a

content area

45 states, D.C., & 3 territories

A Long Overdue Shifting of the Foundation

For as long as most of us can remember, the K-12 mathematics program in the U.S. has been aptly characterized in many rather uncomplimentary ways: underperforming, incoherent, fragmented, poorly aligned, narrow in focus, skill-based, and, of course, “a mile wide and an inch deep.”

---Steve Leinwand, Principal Research Analyst American Institutes for Research in Washington, D.C

But hope and change have arrived!

Like the long awaited cavalry, the new Common Core State Standards for Mathematics (CCSS) presents us a once in a lifetime opportunity to rescue ourselves and our students from the myriad curriculum problems we’ve faced for years.

---Steve Leinwand, Principal Research Analyst American Institutes for Research in Washington, D.C

Make no mistake,

for K-12 math in the

United States, this IS a

brave new world.

--Steve Leinwand

For over a decade, research of mathematics education in high-performing countries have pointed to the conclusion that the math curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country.

Focus: Unifying themes and guidance on “ways of knowing” the mathematics.

Coherence: Progressions across grades based on discipline of mathematics and on student learning.

Understanding (Rigor): Deep, genuine understanding of mathematics and ability to use that knowledge in real-world situations.

Make sense of problems

Reason quantitatively

Viable arguments & critique

Model with mathematics

Strategic use of tools

Attend to precision

Look for and use structure

Look for regularity in reasoning

K-8 Grade Levels

HS Conceptual Categories

Standards for Mathematical Practice

Standards for Mathematics Content

Standards

Domains

Clusters

Mathematics content Teaching of mathematics Student “knowing” of mathematics

Digging in…

Begin to unearth some discoveries:

2NBT9. Explain why addition and subtraction strategies work, using place value and the properties of operations.

3OA3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Reflecting…

4NF2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Reflecting…

4NF2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Reflecting…

Which is larger?

Find a common

numerator!

Rename

Focus and

Coherence

CCSS “design principles”

Focus Coherence

The Hunt Institute Video SeriesCommon Core State Standards: A New Foundation for Student Success

www.youtube.com/user/TheHuntInstitute#p

Helping Teachers: Coherence and Focus

Dr. William McCallum

Professor of Mathematics, University of Arizona

Lead Writer, Common Core Standards for Mathematics

Features of Focus and Coherence

“Give more detail than teachers were used to seeing in standards.”

Fewer Topics

Progressions

More Detail

Show how ideas fit with subsequent or previous grade levels.

“Free up time” to do fewer things more deeply.

Unifying Themes Details

Domains Clusters Standards

Grade Domains Clusters Standards

K 5 9 22

1 4 11 21

2 4 10 26

3 5 11 25

4 5 12 28

5 5 11 26

6 5 10 29

7 5 9 24

8 5 10 28

Grade Domains Clusters Standards

Conceptual Category

Domains Clusters StandardsAll

StandardsAdvanced

Number & Quantity

Algebra

Functions

Geometry

Statistics & Probability

Modeling

Conceptual Category

Domains Clusters StandardsAll

StandardsAdvanced

Number & Quantity 4 9 9 18

Algebra 4 11 23 4

Functions 4 10 22 6

Geometry 6 15 37 6

Statistics & Probability 4 9 22 9

Modeling * * * *

Content Standards: Reflect hierarchical nature & structure of the discipline.

– Progressions

– Ways of Knowing

Practice Standards: Reflect how knowledge is generated within the discipline.

Reflects what we know about how students develop mathematical knowledge.

Reflects the needs of learners to organize and connect ideas in their minds (e.g., brain research).

Discipline of mathematics

Research on students’ mathematics learning

Coherence

CCSSM Progression Documents (draft)

by The Common Core Standards Writing Team

ime.math.arizona.edu/progressions

Comprehensive discussions on:

• Intent of specific standards.

• Development within and across grades.

• Connections across domains.

• Suggested instructional approaches.

Domains and Clusters as unifying themes

within & across grades.

Domains and Clusters as unifying themes

within & across grades.

Detail in the standards give guidance on

“ways of knowing” the mathematics

Detail in the standards give guidance on

“ways of knowing” the mathematics

Focus and Coherence

Embedded progressions of

mathematical ideas.

Embedded progressions of

mathematical ideas.

Understandingthe Mathematics

“Rigor”

Understanding in CCSSM…

Word Number of instances

Understand(s) 147

Understanding 92

Understandings 21

Understood 3

TOTAL 263

These Standards define what students should understand and be able to do in their study of mathematics...

But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.

CCSSM, p. 4

Select a grade level.

Find the list of Clusters in CCSSM.

Read through the clusters and count the occurrences of “understand.”

Highlight one example of particular significance.

Mathematical understanding and

procedural skill are equally important, and

both are assessable using mathematical

tasks of sufficient richness.

CCSSM, p. 4

SBAC States…

PARCC States…

And so the journey begins…

I really hope these standards will help teachers be more creative in the classroom,

engender the mathematical practices, and free up time to really focus on

teaching mathematics.

--Bill McCallum

Progression

Progressio

Understanding

Coherence