Title: Why
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3Why?
4Why 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
5Curriculum 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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7Number of 4th-Grade Learning Expectations per
State by Content Strand
Reys, et al., 2006
8What?
9- 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!!!!!
10NCTM 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
11NCTM 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
12What 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
13What 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
14The 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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16- 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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18Linking Multiplication Facts and Geometry
5 X 3 equals 3 X 5
19Linking Multiplication Facts and Geometry
What are the factors of 12? How many different
rectangles can be made from 12 squares?
20Linking Multiplication Facts and Geometry
What are the factors of 11? How many different
rectangles can be made from 11 squares?
21http//illuminations.nctm.org/ActivityDetail.aspx?
ID29
22The Public Believes Mathematics is Just a Set of
Mechanical Procedures
23An Alternate Algorithm!
- 20 4
- x 10 3
- 12
- 60
- 40
- 200
- 312
24( 20 4 )( 10 3)
25The Link to Area
3
10
4
20
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27The 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
28The 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
29Incorporating 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
30How?
31Curriculum Focal Points and State and District
Leaders
- As a framework for future development of
mathematics curriculum - To identify grade-level targets
32 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
33Curriculum Focal Points and Publishers
- As an example for guiding the next generation of
instructional materials and related assessments
34Curriculum Focal Points and Teacher Educators
- To organize preservice and inservice education
for developing teachers knowledge of critical
mathematics understandings across the grades
35Who did this?
36Participation
- Writing group
- Mathematicians
- Mathematics educators
- Teachers
- Outside reviewers
- Mathematicians and mathematics educators
- Teachers and supervisors
- Policymakers
37Curriculum Focal Points Whats New
- Priorities - focus
- Grade-by-grade descriptions
- Descriptive clusters of content
- More clarification
- Connections
38Curriculum 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
39Then What?
40- 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.
41- 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!!!
42- 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.
43- 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
44- 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
45And then.
- Over 600,000 downloads
- Second printing
46- 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
47Other 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!!!!
48Concerns
- 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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50The Good Stuff
51Sunday, 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.
52Local 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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55Questions
- 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?
56The 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
57Your Questions?
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