Improving K-12 Mathematics Education: Challenges

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Improving K-12 Mathematics Education Challenges
Opportunities
2011 MEA-MFT Educators' Conference?October 20-21,
Missoula Barbara Reys University of
Missouri Center for the Study of Mathematics
Curriculum

• Barbara J. Reys
• University of Missouri - Columbia

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About this Session
5 Challengesand1 Opportunity (CCSS)
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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 doesnt
  like it or feel comfortable using it.

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Is there room in todays curriculum (or
classroom) for exploration?
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Challenge 2

• Many current textbooks reinforce the perception
  of mathematics as a set of rules, procedures.

• They dont offer teachers good guidance for
  engaging students.

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Challenge 3

• Lack of student interest in and motivation to
  learn mathematics.

• Many students dont think that learning
  mathematics is important.
• Some students are not willing to work hard to
  learn mathematics.

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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.

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• 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
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Challenge 5

• Annual high-stakes assessments are currently the
  primary tool for gauging school/teacher success
  (accountability).

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An opportunity to focus on improvement
Common Core State Standards Initiative
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Common Core State Standards (CCSSM)
Initiated by National Governors Association
and Council of Chief State School Officers
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How much do you know about CCSSM?
1 Nothing (except the last slide), thats why
Im here. 2 A little (I know what CCSSM
stands for and Ive been introduced to it). 3
Some Ive read/reviewed some or all of it. 4
A lot, Ive thought about implications for my
classroom/work. 5 A whole lot I could
facilitate this session.
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• 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

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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

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Common Core State Standards (Math) Adopted by all
but 6 states (as of 9/20/11)
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• 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.

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Are/were state standards alike or different (many
were based on the NCTM Standards of 2000)?
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• Example
• 4th grade mathematics standards
• 10 largest states.

- 108 unique standards
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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)
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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)
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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.
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• 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 24 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.
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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.

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Mathematical Processes/Proficiencies/Practices
NCTM (2000) Adding it Up (2001) CCSSM (2010)
Problem Solving Strategic competence 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
Communications Procedural 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)

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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.

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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.

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Emphasis on particular models (e.g., number line)

• 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.

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Montana Standards (2009)

• 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)

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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.

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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.

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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
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Textbooks aligned to CCSS
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http//www.inkling.com/
The next generation of curriculum materials
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• 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.

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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//illustrativem
athematics.org/
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CCSSM Curriculum Analysis Tool Set of
mathematics curriculum analysis tools that allow
K12 textbook adoption committees, school
administrators, and K12 teachers to analyze
mathematics curriculum materials with regard to
their alignment to the Common Core -
http//commoncoretools.wordpress.com/2011/04/14/ma
thematics-curriculum-analysis-project/
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Inside Mathematics http//www.insidemathematics.o
rg/
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• Barbara J. Reys
• reysb_at_missouri.edu