2011 MEA-MFT Educators'
Barbara J. Reys
Conference October 20-21, Missoula
University of Missouri - Columbia
Barbara Reys
University of Missouri
Center for the Study of Mathematics Curriculum
About this Session
5 Challenges
and
1 Opportunity (CCSS)
Challenge #1:
Widespread perception that mathematics
is a set of facts, rules, and procedures to
be mastered.
This perception leads to:
•teaching that focuses on presentation rather
than student engagement.
•a general public which values math but doesn’t
like it or feel comfortable using it.
Is there room in today’s curriculum (or
classroom) for exploration?
Challenge #2:
Many current textbooks reinforce
the perception of mathematics as a
set of rules, procedures.
• They don’t offer teachers good
guidance for engaging students.
Challenge #3:
Lack of student interest in and
motivation to learn mathematics.
• Many students don’t think that learning
mathematics is important.
• Some students are not willing to work hard
to learn mathematics.
Challenge #4:
There is no coherent system for
improving teaching practices (
professional development).
• The teacher work day lacks “space” for
continual professional development OR for
serious collaboration with colleagues.
U.S. teachers spend about 80 percent
of their total working time engaged in
classroom instruction, as compared to
about 60 percent for teachers in many
other nations.
Professional Learning in the Learning Profession (2009)
National Staff Development Council
Challenge #5:
Annual high-stakes assessments are
currently the primary tool for gauging
school/teacher success
(accountability).
An opportunity to focus on
improvement:
Common Core State Standards Initiative
Common Core State Standards (CCSSM)
Initiated by:
National Governor’s Association
and
Council of Chief State School Officers
How much do you know about CCSSM?
1 – Nothing (except the last slide), that’s why
I’m here.
2 – A little (I know what “CCSSM” stands for and
I’ve been introduced to it).
3 – Some – I’ve read/reviewed some or all of it.
4 – A lot, I’ve thought about implications for my
classroom/work.
5 – A whole lot – I could facilitate this session.
Common Core State Standards Initiative
• State consensus on learning goals
(standards) for mathematics, K-12
• State collaboration to develop and use
improved assessments to monitor
student learning
Common Core State Standards (Math)
Adopted by all but 6 states (as of 9/20/11)
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• The 2011 Montana draft standards
are the CCSSM with the addition
of embedded Indian Education
statements.
• Public Hearing: Oct. 24, 2011
• Action on Adoption (Montana
Board of Public Education):
Nov. 4, 2011
Common Core State Standards (Math)
Adopted by all but 6 states (as of 9/20/11)
16
Why a common core curriculum?
Potential to increase the quality of …
- instructional materials
- high stakes assessments
Common standards address one cause
of the U.S. “mile-wide, inch-deep”
curriculum.
Are/were state standards alike or
different (many were based on the
NCTM Standards of 2000)?
Example:
4th grade mathematics standards
10 largest states.
- 108 “unique” standards
Gr. 4 mathematics standards common
across 10 largest states in 2006:
• Read, write, compare, and order whole
numbers.
• Read, write, compare and order decimals.
• Add and subtract decimals.
• Solve problems involving whole number
multiplication and division.
(4 of 108 learning goals)
Gr. 4 standards unique to only one of ten
states (examples):
• Use concrete materials and symbolic notation to
represent numbers in bases other than base ten,
such as base five.
• Compare decimal number system to the Roman
numeral system (using the Roman numerals I, V,
X, L, C, D, and M.)
• Use models to identify perfect squares to 100.
(28 of 108 learning goals)
The differences across state standards
(and related assessments) regarding what
to teach and when to teach particular
mathematics topics practically guarantees
curriculum materials that are “a mile wide
and an inch deep.”
• What are the CCSS and
how are they
organized?
• How are they different
from current state
standards?
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Standards for Mathematical Practice
 Carry across all grade levels
 Describe habits of mind of a mathematically expert
student
Standards for Mathematical Content
 K-8 standards presented by grade level


Organized into domains that progress over several grades
Grade introductions give 2–4 focal points at each grade level
 High school standards presented by conceptual themes
(two “pathways” included in Appendix – single subject
and integrated)
The standards are not intended to define HOW to teach.
Standards for Mathematical Practice
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 Processes/Proficiencies/Practices
NCTM (2000)
Adding it Up (2001)
Problem Solving Strategic competence
CCSSM (2010)
Make sense and persevere in
problem solving
Reasoning
Adaptive reasoning
Reason abstractly and
quantitatively
Express regularity in repeated
reasoning
Construct viable arguments
Connections
Conceptual
understanding
Look for and use structure
CommunicationsProcedural fluency
Use tools strategically
Attend to precision
Representations Productive disposition
Model mathematics
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Opportunity of Common Core
The standards:
 Attention to mathematical practices/processes
 Focus on understanding
 Some attention to learning progressions
More generally:
 Energy and activity focused on same learning goals:
 Curriculum development
 Professional development
 Assessments (high stake)
How is the Common Core different from
previous state Standards?







Use of precise mathematical language to convey
learning goals.
Increased emphasis on some models
Some content moved to earlier grades
Less emphasis on data analysis and probability in K-5
More emphasis on transformational geometry in high
school.
Little attention to or acknowledgement of technology as
a tool for doing or learning mathematics
At high school level, standards are listed by “conceptual
category” - not by course.
Example of grade level shift
Topic: Fluency with basic facts for multiplication and
division.
Current MT standard:
Recall basic multiplication facts to products up to 100 and
related division facts. (Grade 4)
CCSSM standard:
By the end of Grade 3, know from memory all products
of two one-digit numbers. (Grade 3)
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Use of precise mathematical language
Grade 3: “Understand a fraction 1/b as the
quantity formed by 1 part when a whole is
partitioned into b equal parts; understand a
fraction a/b as the quantity formed by a parts of
size 1/b.”
Grade 3:
“Represent a fraction 1/b on a number line diagram by
defining the interval from 0 to 1 as the whole and
partitioning it into b equal parts. Recognize that each
part has size 1/b and that the endpoint of the part
based at 0 locates the number 1/b on the number line.”
“Represent a fraction a/b on a number line diagram by
marking off a lengths 1/b from 0. Recognize that the
resulting interval has size a/b and that its endpoint
locates the number a/b on the number line.”
 Use models to represent equivalent fractions.
Represent fractions using an area model, and/or
parts of a set model and locate points on a
number line model. (Gr. 3)
 Use models to identify equivalent symbolic
representations of improper fractions and mixed
numbers. (Gr. 4)
 Compare and order fractions using area, set, and
linear models. (Gr. 5)
Teachers need many opportunities to
study, discuss, and plan for the changes in
approach, sequence or intended models in
the Common Core State Standards.
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Standards: Important but not sufficient
The Standards must be partnered with a
content-rich curriculum, focused professional
development and robust assessments aligned
to the Standards.
CCSS-aligned Assessment
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SMARTER Balanced
Assessment Consortia
(SBAC)
$160 million
31 states, including MO
Washington – lead state
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“SBAC will create state-of-the-art adaptive online exams, using
“open source” technology. The online system will provide
accurate assessment information to teachers and others on the
progress of all students, including those with disabilities, English
language learners and low- and high-performing students. The
system will include:
•the required summative exams (offered twice each school
year);
•optional formative, or benchmark, exams; and
•a variety of tools, processes and practices that teachers may
use in planning and implementing informal, ongoing assessment.”
37
Partnership for Assessment of Readiness for
College and Careers (PARCC) Consortia:
$170 million
26 states
Florida – Lead state
Achieve
“The proposed assessment system will be computer-based and will
measure student progress at key times during the school year, rather
than on one test at the end, to allow for instructional adjustment
and extra support to students who need it.”
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Work underway to support
implementation of CCSSM
Textbooks ‘aligned’ to CCSS
http://www.inkling.com/
The next
generation
of
curriculum
materials
Gates Foundation Project
Provided $3 million to support a joint effort with
Pearson Foundation to develop curriculum centered on
Common Core
-Instructional system of 24 online courses covering K-12
English/language arts and K-10 math.
-One course for each grade level.
-Four of the courses - two in each subject area in the
early to middle high school grade levels - will be
contributed as free and open resources.
42
Illustrative Mathematics Project
Set of activities/tasks/problems that illustrate
the type of mathematical work that students
will experience in a faithful implementation of
the Common Core State Standards.
http://illustrativemathematics.org/
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CCSSM Curriculum Analysis Tool
Set of mathematics curriculum analysis tools that
allow K–12 textbook adoption committees, school
administrators, and K–12 teachers to analyze
mathematics curriculum materials with regard to
their alignment to the Common Core
http://commoncoretools.wordpress.com/2011/04/14/m
athematics-curriculum-analysis-project/
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Inside Mathematics
http://www.insidemathematics.org/
Barbara J. Reys
reysb@missouri.edu