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Ohio. Pennsylvania. Mississippi. Tennessee. Utah. Maryland. District of ... American education is every bit as polarized, red and blue, as American politics. ... – PowerPoint PPT presentation

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Title: 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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Curriculum Focal Points - Timeline
  • Summer 2004 Park City, UT ASSM and NCTM
    Conference to analyze state standards and
    curriculum convened by Johnny Lott and Kathleen
    Nishimurra
  • April 2005 Release of Standards and Curriculum
    A View from the Nation (NCTM).
  • March 2005 Austin, TX NCTM Task Force created
    by Cathy Seeley, chaired by Barbara Reys
  • April 2005 NCTM Board Motion to write Curriculum
    Focal Points.
  • April 2005 Summer 2006 Writing, review, and
    NCTM Board Approval of the Curriculum Focal
    Points.
  • September 2006 Release of the Curriculum Focal
    Points PreK-8 A Quest for Coherence (NCTM).

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Number of 4th-Grade Learning Expectations per
State by Content Strand
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

This is NOT the next set of Standards!!!!!
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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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  • What can you say about
  • 24
  • 49
  • 57
  • How can we write
  • 23 20 3 30 7 25 - 2 etc
  • 109100 9 110 1 100 5 4

Fennell, 1999, 2001
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Linking Multiplication Facts and Geometry
5 X 3 equals 3 X 5
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Linking Multiplication Facts and Geometry
What are the factors of 12? How many different
rectangles can be made from 12 squares?
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Linking Multiplication Facts and Geometry
What are the factors of 11? How many different
rectangles can be made from 11 squares?
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http//illuminations.nctm.org/ActivityDetail.aspx?
ID29
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The Public Believes Mathematics is Just a Set of
Mechanical Procedures


  • 124 x13
    72
    24__ 312

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An Alternate Algorithm!
  • 20 4
  • x 10 3
  • 12
  • 60
  • 40
  • 200
  • 312

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( 20 4 )( 10 3)
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The Link to Area
3
10
4
  • 24
  • x 13
  • 12
  • 60
  • 40
  • 200
  • 312

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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 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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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)
  • Schmidt analysis

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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.
  • Over 600,000 downloads
  • Second printing

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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
  • West Virginia
  • Ohio
  • Pennsylvania
  • Mississippi
  • Tennessee
  • Utah
  • Maryland
  • District of Columbia
  • Kentucky

As of March 6, 2007
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Other Initiatives
  • National Math Panel Presentation September,
    2006
  • Capitol Senate and House Aides October, 2006
  • AMS, MAA October, 2006 and January, 2007
  • Major Publishers November, 2006
  • CBMS Presentation December, 2006
  • Department of Education MSP Meetings
  • National Title I meeting January, 2007
  • AMTE January, 2007
  • Curriculum Center Meeting February, 2007
  • Lieutenant Governors Retreat March, 2007
  • Others

NSTA Anchors Flattery is good!
We were first!!!!
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Concerns
  • Confusion Understanding what is meant by a
    focal point target, area of emphasis, a focus.
  • 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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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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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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