Acknowledgements
The Committee would like to express its appreciation to
several members of the State Education Department who were extraordinarily
helpful, including Deputy Commissioner James Kadamus, Associate Commissioner
Thomas Sheldon, Assistant Commissioner Jean Stevens, Assistant Director of
Curriculum, Instruction and Instructional Technology Anne Schiano, Mathematics
Specialists Teri Calabrese-Gray and Michelle Kline, Administrative Assistant
Judi Golombiski, and Secretary to the
Associate Commissioner Maryann Jansen.
We were very impressed by their commitment and dedication to the public
schools of New York State, and to those for whom we are all here, the
children.
Table of
Contents
I.
Introduction...........................................................................................................................
1
A.
Background................................................................................................................
1
B.
Charge to the Committee.........................................................................................
3
C.
Committee’s Response to Its Charge.....................................................................
4
II.
Important Points Relative to Our Work..............................................................................
5
A.
Guiding Principles.....................................................................................................
5
B.
Time Constraints.......................................................................................................
6
C.
Field Review of Our Work is Recommended.........................................................
6
E.
The Importance of "The Power and Beauty of Mathematics"............................... 6
III.
Recommendations..............................................................................................................
8
A. The
Standards...........................................................................................................
8
1.
MST Standard 3..............................................................................................
8
2.
Key Ideas..........................................................................................................
8
3.
Detailed Performance Indicators...................................................................
9
4.
Implementation Timeline for 3-8 and High School.....................................
10
B.
High School
Mathematics Program, and Graduation Requirements................ 10
1.
Graduation Requirements and Regents Examinations.............................
10
2.
Course Content and Labels.........................................................................
11
3.
Additional High School Program Issues.....................................................
13
C.
Guidance to Classroom Teachers on the Standards..........................................
14
D.
Technology and Mathematics Instruction..............................................................
14
E. A
Capacity Issue – Adequately Prepared Teachers...........................................
16
IV.
Summary of
Changes to Performance Indicators..........................................................
17
V.
Summary............................................................................................................................
19
References
Attachment A. Current MST Standard 3 and Seven Key
ideas
Attachment B. Proposed Mathematics Standard,
Content Strands, Process Strands, and Grade-By-Grade Performance
Indicators (PDF File) (Word
File)
I.
INTRODUCTION
A.
Background
This
Mathematics Standards Committee was formed by the New York State Education
Department (SED) in response to a recommendation made to the Board of Regents in
October, 2003 by the Independent Math A Panel, a group formed to
investigate very high failure rates on the June, 2003 Math A Regents
Examination. The Panel’s findings
and recommendations included the following in the Executive Summary (p.
4):
Finding 1: The Math A standards lack clarity and
specificity.
Recommendation
1A:
Educationally
useful standards must be developed in mathematics for each grade, K-8, and for
Math A and Math B, that consist of a clear, well-defined set of skills, the
mastery of which is demonstrable.
Recommendation 1B:
SED should
establish a mathematics standards committee to rewrite the standards into
functional form, and to meet regularly in the future to analyze test results,
thus ensuring continuous relevance.
Recommendation
1C:
SED should
develop and disseminate suggested curricula for mathematics instruction for each
grade K-8, and for Math A and Math B (p.
19).
Recommendation
1D:
To benefit
from the extensive research and deliberation of the current Math A Panel, some
of the current Panel members should be included in both new committees
recommended in this report, i.e., the standards committee, and the curriculum
development committee.
The
establishment of this Committee was in response to the Panel's
Recommendation 1B. In
accordance with Recommendation 1D, several members of the original Panel were
appointed to this Committee, including both Co-Chairpersons. The Panel report
also stated:
This
committee should include a large cross section of adults including mathematics
teachers, university mathematicians, professors of mathematics education,
special education teachers, parents, and adults who work with mathematics in
real work applications, both in the professions (for example, engineers and
accountants) and in the trades (for example, carpenters and electricians). The Panel envisions that this group
would meet at least once a year to review the exams against the standards, in
order to provide continuity over time. (Page 19.)
SED's
efforts to include a large cross section of adults was, for the most part,
successful. The Committee included
mathematics educators from a wide range of grade levels, and from a wide range
school district types and geographic areas. The Committee also included an
accountant, an engineer and, as a tradesperson was not available, a BOCES
teacher of occupational education, with a background in mathematics. In addition, the Committee included
representatives from higher education, who are knowledgeable about mathematics,
mathematics education, and the pre-service and in-service preparation of
teachers. The Committee commends
SED for this broad effort, and believes this diversity was critically important
to our efforts.
The
Committee held 20 days of meetings, all in Albany:
January 8
January 29
January 30
February 26
February 27
March 16
March 17
April 29
April 30
May 24
May 25
June 29
June 30
July 19
July 20
July 21
August 9
August 10
September 27
September 28
The
Committee conducted an extensive review of standards from other states and
nations, as well as research reports.
A full list is enclosed in the list of References.
B.
Charge to the Committee
The
Committee's work has been guided by the Commissioner's
Charge:
Charge to the
Mathematics Standards Committee
The Committee will examine the existing
Regents standards in mathematics, consider relevant research and other standards
from the U.S. and other nations, and then propose modifications to the Regents
mathematics standards to improve clarity, specificity, and functionality. The
standards are to be challenging, and must represent a significant level of
achievement in mathematics. The standards will "consist of a clear, well-defined
set of skills, the mastery of which is demonstrable." (Math A Panel Report, page 4) The
Committee's recommendation will be consistent with the recommendations of the
Independent Math A Panel.
Specifically we ask that committee members
engage the following questions:
1.
Is standard 3 of the NYS Mathematics,
Science and Technology learning standards still sound? Are the seven key ideas embedded in the
mathematics standard all-inclusive?
Is there research/evidence to support modification of standard 3 and/or
the seven key ideas? (See Attachment A: Seven Key
Ideas.)
2.
There is a presumption that there are too
many performance indicators and that some should be consolidated and/or
eliminated. Are the current performance indicators appropriate and sufficient
for the developmental levels of elementary (grades K-4), intermediate (grades
5-8) and commencement (grades 9-12)?
Which performance indicators need to be added, revised, consolidated or
eliminated at each level?
3.
What additional information needs to be
provided to teachers to clarify the depth and breadth of understanding required
of students for particular performance indicators?
4.
What are the particular areas of study
that should be taught in greater depth for greater understanding? Are there
areas of study that should be eliminated?
5.
In response to the NCLB requirements for
grade-by-grade testing of mathematics in grades 3-8, the Standards Committee
will develop content standards for grade six which will help inform the test
development process for the new exams.
C.
Committee’s Response to its Charge
|
Charge
Element |
Committee’s Response |
|
1. Is standard 3 of the NYS Mathematics,
Science and Technology learning standards still sound? Are the seven key ideas embedded
in the mathematics standard all-inclusive? Is there research/evidence to
support modification of standard 3 and/or the seven key ideas? (See
Attachment A: Seven Key Ideas.)
|
The Committee’s
recommendations include modifying the wording of Standard 3, and replacing
the seven key ideas with five content strands and five process
strands. These
recommendations were reached based upon a review of standards from other
states and other nations, and also on extensive feedback from the field
regarding the clarity of the wording of the current
standards. |
|
2.
There is a presumption that there are too many performance
indicators and that some should be consolidated and/or eliminated. Are the
current performance indicators appropriate and sufficient for the
developmental levels of elementary (grades K-4), intermediate (grades 5-8)
and commencement (grades 9-12)?
Which performance indicators need to be added, revised,
consolidated or eliminated at each
level? |
The Committee is
recommending revisions to the performance indicators for all grade levels,
based on comparisons with other states and nations.
|
|
3. What additional information needs to
be provided to teachers to clarify the depth and breadth of understanding
required of students for particular performance
indicators? |
The Committee’s
recommendations address this question and focus on the need for
grade-by-grade curriculum guidance, as well as the need for additional
professional development. |
|
4. What are the particular areas of study
that should be taught in greater depth for greater understanding? Are
there areas of study that should be
eliminated? |
Based on its review of the
mathematics standards in other states and nations, the Committee concluded
that it is essential to revise the current program to enable students to
understand concepts at a deeper level of understanding. The recommended revisions reflect
that conclusion. |
|
5. In response to the NCLB
requirements for grade-by-grade testing of mathematics in grades 3-8, the
Standards Committee will develop content standards for grade six which
will help inform the test development process for the new
exams. |
The recommended revisions
encompass all grades, including grade six.
|
II.
IMPORTANT POINTS RELATIVE TO OUR WORK
A.
Guiding Principles
This
Committee’s work was guided by a review of standards from a number of states in
our nation, as well as standards and curricula from other nations of the
world. We were impressed by the
focus of the mathematics programs in some other nations as compared with our
current New York State standards.
Our standards include several topics each year, causing teachers and
children to jump from topic to topic, with rarely enough time to cover material
in any great depth. We worked very
hard to rewrite the performance indicators to provide teachers with sufficient
time to focus on important areas of mathematics, so that children will be able
to reach deep levels of understanding, and become mathematically proficient,
which is so essential for future success.
The
Mathematics Standards Committee based its work and recommendations upon a number
of guiding principles:
- The
performance indicators must be presented on a grade-by-grade basis, rather
than in bands of grades, as was previously the case. The purpose is to provide vitally
important information to classroom teachers across New York State, and to
clarify the expectations for parents and students for each grade.
- The
number of performance indicators in each given year should be developed with
the goal of enabling teachers to focus on important areas of mathematics, so
that they can be sure the children have reached deep levels of
understanding.
- The
language should be clear for teachers, parents, students and test developers,
both in terms of the expectations, and in terms of the depth of understanding
of each expectation. If everyone
understands the expectations, then everyone will be working toward the same
goal.
- The
performance indicators need to be sequenced appropriately across the grades,
so that knowledge and skills grow from year to year.
- The
performance indicators must be developmentally appropriate at each grade
level.
The
result of our work is a draft of a set of performance indicators in mathematics
that the committee believes delineates the levels all students should
attain.
B.
Time Constraints
The
Committee has been concerned about the tight time constraints under which we
have worked. The development of
standards for mathematics instruction at all grade levels, pre-K–12, is an
enormous task. Standards committees
typically have two or three years to complete their work. Our timeline, though, was "squeezed" by
two events. At the front end was
the large failure rate on the June 2003 Math A Regents exam, which resulted in
the appointment of the Math A Panel. The Panel presented its report in October
2003, at which time our formation was recommended. At the back end is the federal “No Child
Left Behind” law (NCLB), which requires that all school districts in the country
test every child in mathematics in grades 3 – 8 beginning in the 2005-2006
school year. For a test to be
administered in March 2006, the test development work should have started around
March 2004. At that point, though,
our group had just started its work. The Committee and the State Education
Department were left with a difficult choice: either take more time than we did to
develop the new standards – which would have caused the new NCLB tests to be
based on the old standards, or move as quickly as possible and work with the
testing company to delay its timeline for test development. Our preference is
the latter; the response from the field, and the Math A Panel report, dictate
revisions to the current standards.
C.
Field Review of Our Work is Recommended
The
Committee believes the standards we have developed, in addition to meeting all
of the guiding principles, will be very helpful to teachers because of their
simplicity and clarity. However,
from our first meeting, and to this day, we have felt that statewide review is
essential before finalization of the document. Such public review can only strengthen
our work which, in turn, will strengthen mathematics education for New York
State's children.
D.
The Importance of "The Power and Beauty of
Mathematics"
The
Committee anguished over whether to include wording in MST Standard 3 that would
communicate the importance of children learning to appreciate the power and
beauty of mathematics. This should
be the goal of every person who teaches mathematics, from the early childhood
teacher to the high school calculus teacher. Excitement in any classroom is
contagious; and mathematics is fun and exciting to study. Children should learn that mathematics
is elegant and beautiful. Helping
children see this beauty is as important as helping children see the beauty of a
daVinci painting or a Beethoven Symphony.
We
considered including language in the standards establishing this
expectation. We were dissuaded
because we were informed that any statement in a standard could be assessed, and
children could be held accountable for meeting the standard. We know of no way to assess the “power
and beauty” of mathematics; and even if there is a way to assess it, we do not
believe children should be denied a high school diploma for failing to
appreciate this "power and beauty."
There was strong sentiment from several of our members that it is sad
that the current national focus on assessment prevents us from including
language stating this as an expectation for students. Let there be no misunderstanding; we
unanimously and strongly support the notion that an overarching goal of all
mathematics instruction must be to help children appreciate the power, the
beauty, and the elegance of mathematics, and we urge teachers to do all that
they can to inspire their students to acquire this
appreciation.
III.
RECOMMENDATIONS
A.
The Standards
1.
MST Standard 3
Discussion.
The charge to our Committee asked us to
". . . propose modifications to the Regents mathematics standards to improve
clarity, specificity, and functionality."
As we reviewed the wording of MST Standard 3, which articulates the
mission of mathematics education in our state, we felt that changes would
improve clarify and functionality.
This leads to our first recommendation.
Recommendation 1. The Committee recommends that MST
Standard 3 be rewritten as follows:
Students
will:
·
understand the concepts of, and
become proficient with the skills of, mathematics
·
communicate and reason
mathematically
·
become problem solvers by using
appropriate tools and strategies
through the integrated study of
number sense and operations, algebra, geometry, measurement, and statistics and
probability.
2.
Key Ideas
Discussion.
The
current seven key ideas form the framework for the performance indicators. As we reflected upon the current key
ideas, we saw that they attempted to interweave content standards and process
standards. Our Committee felt it
would be helpful to distinguish between the two types of standards to give
clearer guidance to the field. As
we embarked upon this work, we concluded that the content standards would be
most useful if they reflected the commonly understood branches of
mathematics. Regarding the process
standards, we felt the NCTM (National Council of Teachers of Mathematics)
statements were very clear, and we felt New York State should adopt these. As we envision this, we see the two sets
of standards being applied simultaneously, for example, while teachers work to
help students attain mastery of the content of algebra, the five process strands
(Problem solving, Reasoning and Proof, Communication, Connections and
Representation) should be part of the instruction and of the assessment. This leads to our second
recommendation.
Recommendation 2. The Committee recommends that the
current seven key ideas be replaced with the following five content strands and
five process strands:
Content
Strands
- Number Sense and
Operations
- Algebra
- Geometry
- Measurement
- Statistics and
Probability
Process
Strands
o
Problem
solving
- Reasoning and Proof
- Communication
- Connections
- Representation
3.
Detailed Performance Indicators
Discussion.
Once
MST Standard 3 and the ten strands (five content and five process) are
determined, the work moves into great detail, too much detail for this report
introduction. The Committee spent
enormous time developing the grade-by-grade detail which we believe will give
clear direction to the field. This
work is included as Attachment B to this introduction.
Recommendation 3. The Committee recommends that the
standards document accompanying this report as Attachment B be adopted as a
draft. This document includes
definitions of each content strand, definitions of each process strand, the
division of each content strand into bands, and grade-by-grade performance
indicators keyed to the strand., We further recommend that this document be made available
to the field for review and feedback before finalization.
4.
Implementation Timeline for 3-8 and High School
Discussion. The new standards and performance indicators will guide both the curriculum and the state
assessments for mathematics in grades 3-8.
Under NCLB, these new assessments must first be administered in school
year 2005-2006. The committee
believes that additional time would enable more reflection and review, and
ultimately, in an improved product.
More time would also allow additional time for curriculum development,
professional development and program transition, thus, Recommendation
4.
Recommendation 4. The Committee recommends that the State
Education Department consider requesting from the federal government a waiver
for a one-year postponement of the NCLB math tests in grades 3-8. If this is not possible, the Committee
feels it is imperative that all accountability measures be adjusted or delayed
so that there is ample phase in time for these revised
standards.
Discussion. The Committee further believes that a
phase-in approach for the high school program is important. Because success in the high school
courses will depend on the skills and knowledge learned in grades 3–8, we
believe the high school changes should not be implemented until a year after the
3-8 program. Also, the Committee
believes, because Math B depends on Math A, and because the changes recommended
herein will change these programs, the implementation of the new Math B should
be made the year after the implementation of the new Math A. Recommendation 5 addresses this, and
includes a table illustrating the timelines with or without the waiver
recommended in Recommendation 4.
Recommendation 5. The Committee
recommends that the high school program be phased in over a three year period,
following the implementation of the 3-8 program by one year.
|
|
Implementation Year
With
One Year Waiver |
Implementation Year
Without
One-Year Waiver |
