Why?

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Why?
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Why Identify Focal Points?

• Address long lists of state learning expectations
• Address mile wide, inch deep math curriculum
• Identify the mathematics that should be the focus
  of instruction and student learning, preK-8
• Begin the discussion of appropriate curricular
  expectations
• Identify key mathematical ideas all others build
  on

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Number of 4th-Grade Learning Expectations per
State by Content Strand
Number Operation Geometry Measurement Algebra Data Analysis, Probability Statistics Total Number of Learning Expectations
California 16 11 4 7 5 43
Texas 15 7 3 4 3 32
New York 27 8 10 5 6 56
Florida 31 11 17 10 20 89
Ohio 15 8 6 6 13 48
Michigan 37 5 11 0 3 56
New Jersey 21 10 8 6 11 56
North Carolina 14 3 2 3 4 26
Georgia 23 10 5 3 4 45
Virginia 17 8 11 2 3 41
Reys, et al., 2006
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What?
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• Principles
• Equity
• Curriculum
• Teaching
• Learning
• Assessment
• Technology

• Content Standards
• Number/Operations
• Algebra
• Geometry
• Measurement
• Data/Probability

• Process Standards
• Problem Solving
• Reasoning
• Communication
• Connections
• Representation

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NCTM Curriculum Principle

• A curriculum is more than a collection of
  activities it must be
• coherent
• focused on important mathematics
• well articulated across the grades

Principles and Standards for School Mathematics,
page 14
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NCTM Curriculum Principle

• a well-articulated curriculum gives teachers
  guidance regarding important ideas or major
  themes, which receive special attention at
  different points in time. It also gives guidance
  about the depth of study warranted at particular
  times and when closure is expected for particular
  skills or concepts.
• Principles and Standards, p. 16

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What Are Curriculum Focal Points?

• Important mathematical topics for each grade
  level, preK-8
• Cohesive clusters of related ideas, concepts,
  skills, and procedures that form the foundation
  for higher-level mathematics

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What Are Curriculum Focal Points?

• More than a single objective, standard,
  expectation, or indicator
• Not discrete topics for teachers to present and
  check off as mastered by students

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The Product Process Standards

• Introductory statement for each level, PreK-8
• It is essential that these focal points be
  addressed in contexts that promote problem
  solving, reasoning, communication, making
  connections, and designing and analyzing
  representations.

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4 x 8
10 x 8
14 x 8 (10 x 8) (4 x 8)
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The Product Curriculum Focal Points

• Three per grade level, preK-8
• Often represent multiple content strands
• Describe the majority of instruction for a
  specific grade level
• Taken together across grade levels, provide the
  major components of a mathematically sound,
  coherent and cohesive preK-8 curriculum

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The Product Connections to the Curriculum Focal
Points

• Provide meaningful contexts for the focal points
• Identify connections between strands and across
  grade levels
• Round out a well-balanced curriculum

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The Process Incorporating a Research Base

• Content- and pedagogy-related studies
• (found in publications such as JRME, AERJ, and
  those from NAEYC)
• National and international measures of students
  mathematical proficiencies
• (e.g., NAEP, TIMSS, PISA)

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How?
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Curriculum Focal Points and State and District
Leaders

• As a framework for future development of
  mathematics curriculum
• To identify grade-level targets

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Curriculum Focal Points and Teachers

• To design instruction around the question, What
  are the most important ideas at my grade level?
• To provide information about how ideas at one
  grade level fit with the important ideas in
  previous and following grades
• To prioritize uses of activities, assessments and
  other published materials

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Curriculum Focal Points and Publishers

• As an example for guiding the next generation of
  instructional materials and related assessments

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Curriculum Focal Points and Teacher Educators

• To organize preservice and inservice education
  for developing teachers knowledge of critical
  mathematics understandings across the grades

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Who did this?
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Participation

• Writing group
• Mathematicians
• Mathematics educators
• Teachers
• Outside reviewers
• Mathematicians and mathematics educators
• Teachers and supervisors
• Policymakers

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Curriculum Focal Points Whats New

• Priorities - focus
• Grade-by-grade descriptions
• Descriptive clusters of content
• More clarification
• Connections

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Curriculum Focal PointsWhats Not New

• Alignment with Principles and Standards for
  School Mathematics, particularly the Curriculum
  Principle
• Well-balanced curriculum
• Strong attention to number and operations
• Commitment to problem solving, processes and
  content
• Understanding math, doing math, using math

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Then What?
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• September 12, 2006
• Arithmetic Problem
• New Report Urges Return to Basics in Teaching
  Math
• By JOHN HECHINGER
• Critics of Fuzzy Methods Cheer Educators
  Findings Drills
• Without Calculators
• The nations math teachers, on the front lines
  of a 17-year Curriculum war, are getting some new
  marching orders Make sure students learn the
  basics.

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• September 21, 2006
• Latest new math idea gets back to the basics
• By Stephanie Banchero
• For nearly two decades, a battle has raged over
  the best ways to teach elementary and high school
  math.
• On one side sit fundamentalists, who prefer
  old-fashioned drilling and a focus on the basics.
  On the other side are the so-called new math
  proponents, who care more about understanding the
  concepts than performing the calculations.

1202!!!
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• April 13, 2000
• Math Teachers Back Return Of Education in Basic
  Skills
• By ANEMONA HARTOCOLLIS
• In an important about-face, the nation's most
  influential group of mathematics teachers
  announced yesterday that it was recommending, in
  essence, that the arithmetic be put back into
  mathematics, urging teachers to emphasize the
  fundamentals of computation rather than focus on
  concepts and reasoning.

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• Children should master the basic facts of
  arithmetic that are essential components of
  fluency with paper-pencil and mental computation
  and with estimation.
• It is important for children to learn the
  sequence of steps and the reason for them in
  the paper-and-pencil algorithms used widely in
  our culture.

PreK-4 Curriculum and Evaluation Standards,
NCTM, 1989, p.47
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• Knowing basic number combinations the single
  digit addition and multiplication pairs and their
  counterparts for subtraction and division is
  essential.
• Equally essential is computational fluency
  having and using efficient and accurate methods
  for computing. Fluency may be manifested in
  using a combination of mental strategies and
  jottings on paper or using an algorithm with
  paper and pencil, particularly when the numbers
  are large, to produce accurate results quickly.
  Regardless of the particular algorithm used,
  students should be able to explain their method,
  understand that many methods exist, and see the
  usefulness of methods that are efficient,
  accurate, and general.

Number Operations, Principles and Standards for
School Mathematics, NCTM, 2000, p. 32
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And then.
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• States who have met or will meet to consider
  using the Curriculum Focal Points to assist in
  revising their state standards
• Florida
• Maine
• North Carolina
• South Carolina
• Minnesota
• New York
• Pennsylvania
• Mississippi
• Tennessee
• Utah
• Maryland
• District of Columbia

As of December 6, 2006
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Other Initiatives

• National Math Panel Presentation
• Capitol Senate and House Aides
• AMS, MAA October and January
• Major Publishers
• CBMS Presentation - December
• Department of Education MSP Meetings
• Brookings Institution Meeting
• Curriculum Center Meeting February
• Others

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Concerns

• Confusion Concept vs Content
• Will states and school districts drop topics?
• When will the tests change?
• Push back internally
• Why this topic at this grade level (see above)?
• Should NCTM have taken more time?

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Comic relief?
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The Good Stuff
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Sunday, Nov. 19, 2006How to End the Math WarsWe
have a new formula for teaching kids. Don't let
ideology ruin it this timeBy CLAUDIA WALLIS

• American education is every bit as polarized,
  red and blue, as American politics. On the
  crimson, conservative end of the spectrum are
  those who adhere to the back-to-basics credo
  Kids, practice those spelling words and times
  tables, sit still and listen to the teacher
  school isn't meant to be fun--hard work builds
  character. On the opposite, indigo extreme are
  the currently unfashionable "progressives," who
  believe that learning should be like
  breathing--natural and relaxed, that school
  should take its cues from a child's interests. As
  in politics, good sense lies toward the center,
  but the pendulum keeps sweeping sharply from
  right to left and back again. And the kids end up
  whiplashed.
• Since the Reading Wars of the '90s, the U.S. has
  largely gone red. Remember the Reading Wars? In
  the '80s, educators embraced "whole language" as
  the key to teaching kids to love reading. Instead
  of using "See Dick and Jane run" primers,
  grade-school teachers taught reading with
  authentic kid lit storybooks by respected
  authors, like Eric Carle (Polar Bear, Polar
  Bear). They encouraged 5- and 6-year-olds to
  write with "inventive spelling." It was fun.
  Teachers felt creative. The founders of whole
  language never intended it to displace the
  teaching of phonics or proper spelling, but
  that's what happened in many places. The result
  was a generation of kids who couldn't spell,
  including a high percentage who had to be turned
  over to special-ed instructors to learn how to
  read. That eventually ushered in the current
  joyless back-to-phonics movement, with its
  endless hours of reading-skill drills. Welcome
  back, Dick and Jane.
• Now we're into the Math Wars. With American kids
  foundering on state math exams and getting
  clobbered on international tests by their peers
  in Singapore and Belgium, parents and
  policymakers have been searching for a culprit.
  They've found it in the math equivalent of whole
  language--so-called fuzzy math, an object of
  parental contempt from coast to coast. Fuzzy
  math, properly called reform math, is the bastard
  child of teaching standards introduced by the
  National Council of Teachers of Mathematics
  (N.C.T.M) in 1989. Like whole language, it was a
  sensible approach that got distorted into a
  parody of itself. The reform standards, for
  instance, called for teaching the uses of a
  calculator and estimation, but some educators
  took that as a license to stop drilling the
  multiplication tables, skip past long division
  and give lots of partial credit for wrong
  answers. "Some of the textbooks and materials
  were absolutely hideous," says R. James Milgram,
  a professor of mathematics at Stanford.
• Adding to the math morass was the fact that 49
  states (all but Iowa) devised their own math
  standards, with up to 100 different goals for
  each grade level. Textbook publishers responded
  with textbooks that tried to incorporate every
  goal of every state. "There are some 700-page
  third-grade math books out there," says
  N.C.T.M.'s current president Francis (Skip)
  Fennell, professor of education at Maryland's
  McDaniel College.
• Now the N.C.T.M. itself has come riding to the
  rescue. In a notably slim document, it has
  identified just three essential goals, or "focal
  points," for each grade from pre-K to eighth,
  none of them fuzzy, all of them building blocks
  for higher math. In fourth grade, for instance,
  the group recommends focusing on the quick recall
  of multiplication facts, a deep understanding of
  decimals and the ability to measure and compute
  the area of rectangles, circles and other shapes.
  "Our objective," says Fennell, "is to get
  conversations going at the state level about what
  really is important." In recent weeks, that's
  begun to happen. Florida and Utah and half a
  dozen other states are talking about revising
  their math standards to match the pared-down
  approach. That pleases academic mathematicians
  like Milgram, who notes that this kind of
  instruction is what works in math-proficient
  nations like Singapore.
• So do we have a solution to the national math
  problem? We certainly have the correct formula.
  The question is, Can we apply it? Already the
  N.C.T.M.'s focal points are being called a
  back-to-basics movement, another swing of the
  ideological pendulum rather than a fresh look at
  what it would take to get more kids to calculus
  by 12th grade. If the script follows that of the
  Reading Wars, what comes next will be dreary
  times-tables recitals in unison, dull new books
  that fail to inspire understanding, and drill,
  drill, drill, much like the unhappy scenes in
  many of today's "Reading First" classrooms. And
  that would be just another kind of math
  fiasco--of the red variety. Kids will learn their
  times tables for sure, but they'll also learn to
  hate math.

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November 27, 2006

• Problem solved
• School surveys show that more American students
  are taking math courses such as algebra and
  calculus
• but what are they learning? A kind of phony
  debate has sprung up about whether they need more
  basics,
• such as multiplication and long division, or more
  so-called creative applications such as problem
  solving. The
• sensible answer, according to the nation's math
  teachers, is both. If more students understand
  the basics,
• they can apply that knowledge to solving complex
  problems. And they can also help keep America
  globally
• competitive. The importance of understanding
  basic math shouldn't be in question. But some
  parents and
• school districts think there was too much
  emphasis on so-called reform math after a 1989
  report by the
• Influential National Council of Teachers of
  Mathematics seemed to encourage students to
  tackle math
• problems - and deal with their intimidation by
  the subject - through pictures, writing or other
  methods. But
• two more recent NCTM reports, in 2000 and earlier
  this all, try to give more clarity to important
  principles and
• standards related to math instruction,
  particularly as more and more goals, assessments
  and other layers of
• accountability have been added by federal and
  state education officials.
• NCTM's most recent report in September rightly
  re-emphasizes "coherence" in math curriculums,
  outlining
• essential concepts and skills that students
  should be able to master from pre-kindergarten
  through eighth
• grade. The idea is to encourage states to refocus
  attention on fundamental and common lessons and
  skills,
• from whole numbers to linear equations, that
  highly mobile students will understand wherever
  they attend
• school. Maryland State Department of Education
  officials think the state's math curriculum
  already strikes a

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Local Schools to Study Whether Math -- Topics
Better InstructionBy Daniel de ViseWashington
Post Staff WriterTuesday, December 5, 2006 A01

• Advocates of new math and old math,
  back-to-basics math and "fuzzy" math might be
  shelving their
• differences to collectively focus on what many
  consider a more pressing problem too much math.
• Maryland math leaders meet today -- and D.C. math
  educators gather tomorrow to discuss
• Curriculum Focal Points, a new document from the
  influential National Council of Teachers of
• Mathematics that could profoundly influence math
  instruction in the region and nationwide. It
  says the
• typical state math curriculum runs a mile wide
  and an inch deep, resulting in students being
  introduced
• to too many concepts but mastering too few, and
  urges educators to slim down those lessons.
• Some are calling Focal Points the most
  significant publication in the field since the
  1980s. R. James
• Milgram, a Stanford University math professor who
  is among the harshest critics of U.S. math
• instruction, said the 41-page report aligns
  teaching "with what is being done with
  unbelievable
• success" in other countries.
• What lies ahead, all agree, is a comparison of
  Focal Points and state math curricula. Critics of
  math
• education hope that process will lead some states
  to delete entire sections of their lesson plans.
• Most of the topics listed in Maryland's math
  curriculum and Virginia's math standards can be
  found in
• the Focal Points document. But Focal Points is
  far more selective in identifying the essential
  math
• topics for each grade.

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Questions

• Can curriculum/standards designed around a few
  key ideas structure a comprehensive program?
• Can assessments focus on priorities and problem
  solving?
• How might textbooks/materials look different if
  structured around focal points?
• How can state/federal policies best support rich,
  deep appropriate mathematics for every student?

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The Goal Curriculum Focal Points and Improved
Mathematics Education

• Guidance for schools and states in the design of
  curricula and assessment that target the most
  important topics
• Focus for teachers that gives sufficient time for
  students to understand concepts and develop and
  apply skills necessary for future mathematics
• Clear direction for students and parents on the
  importance of deep understanding of particular
  topics at each grade level

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Your Questions?
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• Children should master the basic facts of
  arithmetic that are essential components of
  fluency with paper-pencil and mental computation
  and with estimation.
• It is important for children to learn the
  sequence of steps and the reason for them in
  the paper-and-pencil algorithms used widely in
  our culture.

PreK-4 Curriculum and Evaluation Standards,
NCTM, 1989, p.47
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• Knowing basic number combinations the single
  digit addition and multiplication pairs and their
  counterparts for subtraction and division is
  essential.
• Equally essential is computational fluency
  having and using efficient and accurate methods
  for computing. Fluency may be manifested in
  using a combination of mental strategies and
  jottings on paper or using an algorithm with
  paper and pencil, particularly when the numbers
  are large, to produce accurate results quickly.
  Regardless of the particular algorithm used,
  students should be able to explain their method,
  understand that many methods exist, and see the
  usefulness of methods that are efficient,
  accurate, and general.

Number Operations, Principles and Standards for
School Mathematics, NCTM, 2000, p. 32
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• Number and Operations and Algebra Developing
  Quick Recall of Multiplication Facts and Related
  Division Facts and Fluency with Whole Number
  Multiplication
• Students use understandings of multiplication to
  develop quick recall of the basic multiplication
  facts and related division facts. They apply
  their understanding of models for multiplication
  (i.e., equal-sized groups, arrays, area models,
  equal intervals on the number line), place value,
  and properties of operations, in particular the
  distributive property, as they develop, discuss,
  and use efficient, accurate, and generalizable
  methods to multiply multi-digit whole numbers.
  They select and accurately apply appropriate
  methods to estimate products and mentally
  calculate products depending upon the context and
  the numbers involved. They develop fluency with
  efficient procedures, including the standard
  algorithm, for multiplying whole numbers
  understand why the procedures work based on place
  value and properties of operations and use them
  to solve problems.

Curriculum Focal Points for PreK through Grade 8
Mathematics, NCTM, 2006, p.16
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