ADDENDUM TO NOVEMBER 4, 2004
REPORT
I. INTRODUCTION
This
report is an addendum to the Committee's Report presented to the Board of
Regents on November 4, 2004. As
recommended by the Committee, the State Education Department went to great
lengths to open a public dialog on mathematics education for the children of New
York State. This period of open
comment lasted for a month, November 4 through December 4, 2005. The Committee was very pleased to see
that there were over 2,000 responses.
Some of these responses represented the work of school departments and/or
faculties, which means that there were many more than 2,000 people engaged in
this conversation. The Committee is
very pleased that thousands of people care this much about making sure that our
children have the best mathematics education anywhere. The Committee is also deeply grateful as
the responses have informed our work, have resulted in revisions and, we
believe, have resulted in a much stronger proposal. We turn first to the public
response.
II. PUBLIC COMMENT ON MATHEMATICS STANDARDS
COMMITTEE
NOVEMBER 2004 REPORT TO THE BOARD OF REGENTS
This summary of public testimony submitted to the New York
State Education Department regarding the November 2004 Mathematics Standards
Committee Report to the Board of Regents is organized into two sections:
a)
Summary of submissions made through the online survey;
b)
Summary of written testimony from
individuals/associations. (The full
list of individuals/associations that submitted written testimony is included as
Appendix A to this Addendum.)
a. Summary of submissions made
through the online survey
§
Two thousand
twenty one (2,021) online submissions were received
·
The majority
of respondents (1,448) were teachers:
o
552 elementary
o
433
middle
o
463 high
school teachers
·
The majority
of responses (1,880) came from those in public schools.
·
Half of the
respondents (1,014) were from suburban districts.
·
58% responded
that the proposed Mathematics Standard, Content Strands, Process Strands, and
Performance Indicators clearly communicate what PreK-12 students should know and
be able to do.
·
53% responded
that there is a clear continuum of concepts and skills across grade
levels.
·
53% responded
that the performance indicators are clearly written.
·
46% responded
that the performance indicators are specific enough to provide clear guidance to
educators.
·
55% responded
that the performance indicators focus on measurable concepts and skills at each
grade level.
·
36% responded
that the performance indicators balance mastery of skills with conceptual
understanding.
·
72% responded
that the performance indicators were rigorous at each grade
level.
·
32% responded
that the performance indicators are developmentally
appropriate.
·
27% responded
that the content was manageable within a given year.
b. Summary of written testimony
from individuals/associations.
§
Fifty six (56) written public comments were
received
§
Standard 3 as
rewritten is clear, concise and meaningful
§
Content and
process strands are aligned to NCTM
§
Concern
expressed regarding the developmental appropriateness of performance
indicators
§
More emphasis
is needed on higher level thinking skills and integration of process
strands
§
Grade by grade
performance indicators are more explicit
§
Great need for
professional development statewide
§
The timeline
for implementation is too tight
§
Enormous costs
for those who have just completed curriculum alignment, professional development
and text book adoption on existing mathematics standard
III.
COMMITTEE SUMMARY OF THE FEEDBACK
AND COMMITTEE ACTION TAKEN IN RESPONSE TO
THE FEEDBACK
The vast majority of the feedback was very
helpful to us as we embarked upon revisions to our work. Some feedback, while informative,
addressed issues beyond the purview of this committee, such as NCLB testing
implementation and what months in which to administer these tests. The Committee focused on those issues
related to its charge to develop standards for mathematics education in New York
State. As the Committee saw it,
much of its work was validated.
In general, the respondents liked:
- The proposed wording of Standard 3; they
see it as clearer than the current wording.
- The use of commonly understood
mathematical labels for the content strands.
- The grade by grade presentation of the
performance indicators.
- The specificity of the
language.
- The idea of three separate high school
courses, designed as one-year courses for the typical
student.
- The labels for the high school courses
being ones which are commonly understood mathematical term
Respondents did raise a number of concerns
with which we agreed, and the Committee designed and implemented an action plan
to respond to these concerns. These
are listed below.
Concern 1: Conceptual Understanding, Procedural
Understanding, and the Performance Indicators
A major theme of the responses was that
people interpreted our work as a return to a study of mathematical procedures
rather than a study of mathematical ideas.
This was never the intent of our work. Included in the original proposal was a
recommendation to adopt the NCTM process standards, and a recommendation that
curricula be developed as model curricula.
Our thinking was that the curriculum developers would incorporate the
process strands into the course of study, to ensure that children are taught in
a way which connects the content strands and the process strands. It became clear to us, though, because
of the large numbers of people who responded with this concern, that we had not
clearly communicated our intent. To
respond to this concern, members of the committee developed process performance
indicators as well as content performance indicators to show the integration of
process and content. These
performance indicators have been incorporated into the revised standards
document proposed herein. Lest
there be any doubt, we want to make our intention very
clear:
The study of mathematics is a study of ideas
and concepts. Yes, students need to
know the procedures, but the knowledge of those procedures without understanding
is surface knowledge that is virtually meaningless.
It is the Committee's fervent hope that the
revision of the document to include process standards makes our intention very
clear.
Concern 2: Curriculum Guidance and ongoing
professional development
Many respondents indicated a need for
further curriculum guidance and ongoing professional development. The Committee
agrees with this and so stated in our original report. Teachers need more than written
standards to guide their work; they need ongoing support through curriculum
guidance and embedded professional development. It is our understanding that SED will be
providing additional resources to support teacher practice. This includes
revisions of its Resource Guide with Core Curriculum for Mathematics and a
“Toolkit” for teachers of mathematics. This toolkit will provide guidance for
local school districts in aligning local curriculum with the new
standards.
Concern 3: K-4 is too light
The Committee heard concerns that there are
too few performance indicators in the early grades, and that there should be more. The reduction of performance indicators
in K-4 was a deliberate change based on our study of the mathematics programs in
the highest performing nations. The
typical mathematics program in our nation contains many topics, and often causes
teachers to have to "jump" from topic to topic. In the highest performing nations, the
youngest children are given the gift of time – time to explore numbers, to
develop deep understanding of what numbers mean and how they interact. This was our intent. After reviewing the concerns, we
realized how our initial report could be interpreted this way. To address this, we did two things. First, we reviewed all of the indicators
K-4 and made adjustments where we felt it was appropriate and, second, we added
process performance indicators to communicate more clearly that, while the
breadth has narrowed, the depth must deepen. It is critically important for their
future success in mathematics for children to understand what numbers are, how
they relate to each other, and what happens when operations are applied to
them.
Concern 4: 5-8 is too
heavy
The Committee reviewed the performance
indicators and the concerns, and decided that it agreed with many of these
concerns. The Committee revised the
indicators. The Committee did not,
though, agree with all of the concerns.
For example, some respondents objected to polynomials being in eighth
grade. The Committee, which
includes classroom teachers of eighth graders, strongly feels that eighth
graders can, and should, be able to handle this material. In short, the Committee did make major
adjustments, to the extent that we agreed with these
concerns.
Concern 5: Calculator Use/Technology
Use
Some respondents raised questions about the
Committee's recommendation on calculator use. The Committee stands by its original
recommendation. The use of
technology should not replace the learning of essential skills; however, the use
of appropriate technology is an essential part of high quality mathematics
instruction. The Committee believes
the original recommendation, including the recommended review every few years by
a group to ensure technology remains current.
Concern 6: Document
Structure
We received a number of suggestions about
the structure of the document and the presentation of the material. We made a number of revisions, including
grouping some of the performance indicators into broader concepts, adding
process performance indicators, adding an introduction tying the process and
content performance indicators together, and reinforcing scaffolding.
Concern 7: High School
Standards
A number of respondents raised concerns
about the high school performance indicators. The Committee agrees more work needs to
be done, and requests additional time to complete this
work.
IV.
RECOMMENDATIONS
Recommendation 1. The Committee recommends that the revised
standards and performance indicators, included herein, which encompasses grades
Pre-Kindergarten through 8, be adopted.
Recommendation 2.
The Committee recommends that work continue on the high school program
and that we be permitted to bring forth recommendations as soon as possible,
with the goal being before the February Board of Regents
meeting.
Recommendation 3.
The Committee continues to support its original Recommendation 11 (grade
by grade curricula), Recommendations 12A, B, C and D (Technology) and
Recommendation 13 (teacher preparation and training) which is originally from
the Independent Math A report. (9A, B, C, D)
The Committee also wishes to state its
continuing support for the statement in the original report for every teacher to
set as a goal, inspiring their students to appreciate the “Power and Beauty” of
mathematics.
V. SUMMARY
The Mathematics Standards Committee believes
that the changes made as a result of field input have greatly strengthened this
work. We believe these revised
standards are challenging and appropriate for all children of New York State,
Pre-K – 8. We look forward to finishing the high school work. On the following
pages are the proposed standards, including the process strands and content
strands, as revised after field input. We hope our work will raise the mathematical
knowledge, skill, and opportunity of all children.
