COMMON CORE

MATHEMAT

ICS G

EORGIA

PERFO

RMANCE

STANDARDS

DR. BEL INDA EDWARDS

KENNES AW STATE UNIVERS ITY

JANUARY 2013

AGENDA

• Getting to Know Each Other

• Discuss the Common Core Georgia Performance Standards—focus on Math

• Review background knowledge about the Common Core Standards

• Gain an Understanding of the approach to implementation

• Provide an introduction to each of the Instructional Shifts

• Observe a Standards-based Mathematics Classroom via video

GETTING TO KNOW EACH OTHER

Share your thoughts on at least one of these questions, in addition to your name .

What is the purpose of school mathematics?What mathematics is most essential for secondary students to learn? Why?

What aspects of supervising student teachers are you most concerned about?

National Council of Teachers of MathematicsCurriculum and Evaluation Standards (1989)Professional Standards (1991)Mathematics Teaching Today (2007) – Revised

professional teaching standardsAssessment Standards (1995)Principles and Standards for School Mathematics (2000)

6 Principles5 Content Standards5 Process Standards

WHAT ARE STANDARDS (IN MATH ED)?

PrinciplesEquityCurriculumTeachingLearningAssessmentTechnology

Content StandardsNumber and

OperationsMeasurementGeometryAlgebraData & Probability

NCTM PRINCIPLES AND STANDARDS

Process StandardsCommunication Problem SolvingConnections Reasoning & ProofRepresentation

• Previous work with the GPS has prepared Georgia for the implementation of the CCSS.

• Prior teacher and administrator GPS training ensures a smooth transition.

• Although some content may be in different grade levels in the CCSS, all of the standards are addressed in the GPS.

• CCSS expectations are consistent with a single/high-rigor diploma requirement for all students.

F R O M P R E S E N TAT I O N G I V E N BY S A N D I W O O D A L L .

COMMON CORE GEORGIA PERFORMANCE STANDARDS

Counting and Cardinality K

Operations and Algebraic Thinking K – 8

Number and Operations in Base Ten K – 5

Measurement & Data K – 5

Geometry K – High

The Number System 6 – 8

Ratios & Proportional Reasoning 6 – 7

Statistics & Probability 6 – High

Expressions & Equations 6 – 8

Number & Quantity High

Algebra High

Functions 8 – High

Modeling High

CCSSM CONCEPTUAL CATEGORIES AND MATHEMATICAL PRACTICES

CCSS MATHEMATICAL PRACTICES

See Handout

Alignment of present GPS tasks with CCSSM standards has been completed.

Gaps have been noted.

Should be able to use many of the same tasks in the CCSSM, possibly in different grades.

Frameworks

GPS TASKS AND CCSSM

Implementation begins during the 2012-2013 school year.Assessments begin in 2014

“The Georgia Performance Standards (GPS) for mathematics was one of the state curricula used to inform the creation of the CCSS for mathematics. So, it is no surprise that 90% of the GPS align with the CCSS. Therefore, when Georgia teachers are teaching GPS mathematics, in essence they are teaching CCSS mathematics. The rigor and relevance, as well as the balance of skills, concepts, and problem solving found in GPS mathematics is mirrored in the CCSS.

The CCSS, like the GPS, is evidence and/or research based, vertically aligned, and internationally benchmarked so that all students are prepared to succeed in our global economy and society.”

Why did GA switch to Common Core Standards?

COMMON CORE GEORGIA PERFORMANCE STANDARDS

COLLEGE MATH PROFESSORS FEEL HS STUDENTS TODAY ARE NOT PREPARED FOR COLLEGE MATH

HS-MathTchr

s

College Profs

0%10%20%30%40%50%60%70%80%90%

100%

PercentHS-MathCollege-Math

WHAT THE DISCONNECT MEANS FOR STUDENTS

• Nationwide, many students in two-year and four-year colleges need remediation in math.

• Remedial classes lower the odds of finishing the degree or program.

• Need to set the agenda in middle and high school math to prepare more students for postsecondary education and training.

COMMON CORE GEORGIA PERFORMANCE STANDARDS FOR MATHEMATICS

Focus, Coherence, and Rigor

www.youtube.com/watch?v=dnjbwJdcPjE

THE CCSS REQUIRES THREE SHIFTS IN MATHEMATICS

1.Focus: Focus strongly where the standards focus.

2.Coherence: Think across grades, and link to major topics.

3.Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application.

SHIFT#1: FOCUS STRONGLY WHERE THE STANDARDS FOCUS• Significantly narrow the scope of content and

deepen how time and energy is spent in the math classroom.

• Focus deeply on what is emphasized in the standards, so that students gain strong foundations.

• Move away from “mile wide, inch deep” curricula identified in TIMSS and Learn from international comparisons.

• Teach less, learn more

• “Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught.

Ginsburg et al., 2005

FOCUS MEANS FEWER PRIORITIES FOR EACH GRADE

Grade

6 Ratios and Proportional relationships; early expressions and equations.

7 Ratios and Proportional relationships; arithmetic of rational numbers.

8 Linear Algebra

9-12 Modeling of Mathematics in the areas of number, algebra, geometry, and statistics.

These are the priority /concepts/emphases at each grade level in the common core.

ALL standards are taught, but some standards receive more time and attention.

SHIFT #2: COHERENCE: THINK ACROSS GRADES, AND LINK TO MAJOR TOPICS WITHIN GRADES• Carefully connect the learning within and across

grades so that students can build new understanding on foundations built in previous years.

• Begin to count on solid conceptual understanding of core content and build on it.

• Each standard is not a new event, but an extension of previous learning.

SHIFT #3: RIGOR

• The CCSSM require a balance of:

• Solid conceptual understanding

•Procedural skill and fluency

• Application of skills in problem solving situations.

• Pursuit of all three requires equal intensity in time, activities, and resources.

Rigor: “the quality of being extremely thorough, exhaustive or accurate”.

SOLID CONCEPTUAL UNDERSTANDING

• Teach more than “how to get the answer: and instead support students’ ability to access concepts from a number of perspectives.

• Students are able to see math as more than a set of mnemonics or discrete procedures.

• Conceptual understanding supports the other aspects of rigor (fluency and application)

FLUENCY• The standards require speed and

accuracy in calculation.• Teachers structure class time and/or

homework time for students to practice core functions such as operating with integers so that they are more able to understand and manipulate more complex concepts.

APPLICATION

• Students can use appropriate concepts and procedures for application even when not prompted to do so.

• Teachers provide opportunities at all grade levels for students t apply math concepts in “real world” situations, recognizing this means different things in k-5, 6-8, and HS.

CCGPS MATHEMATICS STANDARDS CODES

Common Core Domain

Math MCC6.RP.1a Standard #

Grade

READING THE MATH CCGPS

Standards define what students should understand and be able to do.

Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connect subject.

Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.

Do…• Define what

students know• Articulate

fundamentals• Set grade-level

standards

Do Not . . .• Determine how

teachers should teach

• Define all that should be taught

• Define intervention methods or materials

THE STANDARDS

“A school mathematics curriculum is an abstraction that can only be glimpsed through such means as examining statements of goals, analyzing mathematical and pedagogical features of materials, observing lessons, finding out how teachers understand the curriculum, and assessing what students have learned.” (Kilpatrick, 2003, p. 473)

“Teachers don’t merely deliver the curriculum. They develop, define it and reinterpret it too. It is what teachers think, what teachers believe and what teachers do at the level of the classroom that ultimately shapes the kind of learning that young people get.” (Hargreaves, 1994, p. ix)

TEACHERS ARE IMPORTANT DECISION-MAKERS!

HOW DOES A STANDARDS-BASED MATHEMATICS CLASSROOM LOOK?

Flexible cooperative groups of students Hands-on learning experiences “Productive” noise Differentiation of processes and products is encouraged within

tasks Student works, with teacher commentary, are available for

student reference (if using performance tasks) Multiple representations of solutions are valued Balanced approach to concepts, skills, and problem solving

TRADITIONAL STANDARDS-BASED

What does the teacher do?• teaches only specific procedures

• discourages student interaction/discussion• asks mostly knowledge-level questions

• encourages students to use problem solving strategies• encourages students’ questions, explanations, and discussions

• asks more high-level questions

TRADITIONAL STANDARDS-BASED

What does the teacher do?

• textbook guides instruction

• spends most of the time telling – whole group

• seeks the “ONE” right answer from students

• standards and curriculum map guide instruction• spends most of the time facilitating – small group

• asks more open-ended / application questions

TRADITIONAL STANDARDS-BASED• work alone

• focus on only getting the right answer

• practice procedures

• memorize facts for tests

• work in flexible groups or pairs• use reasoning to justify their answers and solutions

• understand and apply concepts, as well as, facts• solve problems and look for real life connections

What do the students do?

TRADITIONAL STANDARDS-BASED

What do the students do?

• use pencil, paper, and worksheets

• show knowledge by writing down numbers

• use manipulatives, graphic organizers, and games • show knowledge both orally and written

• one way to show an answer

• use multiple representations for solutions (pictures, models, diagrams, words, etc.

A TALE OF TWO CLASSES-- A VIDEO

Observation of each class What is the teacher doing? What are the students doing? Note how the teacher begins and ends class. Note any interesting interactions between the teacher and students.

Compare and contrast the two classes What was similar in the two classes? What was different in the two classes? How was the lesson structure similar or different? How were the teacher-student interactions similar or different?

Common Core State Standards for Mathematics: http://www.corestandards.org/the-standards/mathematics

Suggested Pathways: http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

SMARTER Balanced Assessment Consortium (SBAC) & the Partnership for the Assessment of Readiness for College and Career (PARCC)

https://www.georgiastandards.org/resources/Pages/Videos/Georgia-Classroom-Instructional-Videos.aspx

COMMON CORE STATE STANDARDS

REFERENCES

Transitions to Common Core Georgia Performance Standards in the Atlanta Public Schools

http.achievethecore.org

www.youtube.com/watch?v=dnjbwJdcPjE

Third International Mathematics and Science Study (TIMMS)