DR. BELINDA EDWARDS
K E N N E S A W S TAT E
UNIVERSITY
JA N UA RY 2 013
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?
WHAT ARE STANDARDS (IN MATH ED)?
National Council of Teachers of Mathematics
 Curriculum and Evaluation Standards (1989)
 Professional Standards (1991)
 Mathematics Teaching Today (2007) – Revised
professional teaching standards
 Assessment Standards (1995)
 Principles and Standards for School Mathematics (2000)
6 Principles
5 Content Standards
5 Process Standards
NCTM PRINCIPLES AND STANDARDS
Principles
 Equity
 Curriculum
 Teaching
 Learning
 Assessment
 Technology
Process Standards
Communication
Connections
Representation
Content Standards
 Number and
Operations
 Measurement
 Geometry
 Algebra
 Data & Probability
Problem Solving
Reasoning & Proof
COMMON CORE GEORGIA
PERFORMANCE STANDARDS
•
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.
FROM PRESENTATION GIVEN BY SANDI WOODALL.
CCSSM CONCEPTUAL CATEGORIES AND
MATHEMATICAL PRACTICES
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
CCSS MATHEMATICAL PRACTICES
See Handout
GPS TASKS AND CCSSM
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
COMMON CORE GEORGIA PERFORMANCE
STANDARDS
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?
COLLEGE MATH PROFESSORS FEEL HS
STUDENTS TODAY ARE NOT PREPARED FOR
COLLEGE MATH
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Percent
HS-Math
College-Math
HSMathTchrs
College
Profs
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.
THE STANDARDS
Do…
Do Not . . .
•
Define what students
know
•
Determine how
teachers should teach
•
Articulate
fundamentals
•
Define all that should
be taught
•
Set grade-level
standards
•
Define intervention
methods or materials
TEACHERS ARE IMPORTANT DECISIONMAKERS!
“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)
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
What does the teacher do?
TRADITIONAL
STANDARDS-BASED
• teaches only
specific procedures
• encourages students to use
problem solving strategies
• discourages student
interaction/discussion
• encourages students’
questions, explanations, and
discussions
• asks mostly
knowledge-level
questions
• asks more high-level
questions
What does the teacher do?
TRADITIONAL
STANDARDS-BASED
• textbook guides
instruction
• standards and curriculum
map guide instruction
• spends most of the
time telling – whole
group
• spends most of the time
facilitating – small group
• seeks the “ONE”
right answer from
students
• asks more open-ended /
application questions
What do the students do?
TRADITIONAL
STANDARDS-BASED
• work alone
• work in flexible groups or pairs
• focus on only getting
the right answer
• use reasoning to justify their
answers and solutions
• memorize facts for
tests
• understand and apply
concepts, as well as, facts
• practice procedures
• solve problems and look for
real life connections
What do the students do?
TRADITIONAL
• use pencil, paper,
and worksheets
• show knowledge by
writing down numbers
• one way to show an
answer
STANDARDS-BASED
• use manipulatives, graphic
organizers, and games
• show knowledge both
orally and written
• 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
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/GeorgiaClassroom-Instructional-Videos.aspx
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)