THE STRUGGLE FOR MATHEMATICS STANDARDS: TAKING A
CLOSER LOOK
Anthony D. Thompson
East Carolina University
thompsonant@mail.ecu.edu
Abstract: The development of Florida’s mathematics standards was researched from 1994-1996 using a symbolic interactionist perspective. In the first year of development, the writing team, consisting entirely of mathematics educators, strategically used the language and structure of the standards to convey their goals for reform in mathematics education. During the second year of development, as the standards underwent revision and non-mathematics educators entered the process, numerous debates erupted. Although debates occurred primarily over issues of language, it was the multiple and symbolic meanings of the language and structure of the standards that formed the basis for these debates.
Introduction
The publication
of the National Council of Teachers of Mathematics' [NCTM] Curriculum and Evaluation Standards for School Mathematics (1989)
set off a flurry of activity in the development of standards around the United
States not only in other national subject areas, but in the revision of
standards among the states (Ravitch, 1995).
Throughout the 1990s, mathematics standards became the basis of a
variety of state systemic reform initiatives including assessment and
accountability programs. The debates
over how to write these standards and who should write them have led to “math
wars” in numerous states (see Phi Delta
Kappan, February 1999). However,
despite their importance and controversy, little is known on how mathematics
standards are conceptualized, developed, and debated within political contexts.
Research Focus
Florida developed new mathematics standards from 1994 – 19961. The purpose of this research was to understand how participants conceptualized writing standards, why they conceptualized the standards in this way, and to uncover the meanings they ascribed to these experiences. An additional goal of this research was to place the development of the mathematics standards in the social, political and historical contexts within which they were developed. This paper explores the debates that erupted during the second year of development when the initial set of standards underwent revisions.
Data collection
included interviews, document analysis [e.g., memos / letters, drafts of the
standards, reviews, meeting artifacts (i.e., overheads, agenda sheets,
handouts, official state documents)], and field observations (e.g., writing,
editorial and advisory meetings). The
participants included members of the mathematics writing team, Department of
Education (DOE) officials, numerous reviewers, and a variety of other Florida
educators involved in writing, reviewing, or editing the new standards. Data were analyzed inductively (i.e.,
patterns, themes came from the data rather than being imposed on them prior to
data collection and analysis).
Triangulation, prolonged submersion / engagement at the research site,
negative case analysis, and extensive member checking were used to help ensure
the integrity of the research.
Theoretical Framework
Using a symbolic
interactionist framework, the focus of this research was on understanding the
intent of the writers as they developed the mathematics standards and to place
this within the larger historical and political context. A symbolic interactionist framework focuses
attention on how individuals interpret and give meaning to their experiences,
to other people, and to “objects” in their lives (in this case, mathematics standards),
and endeavors to understand how this process of interpretation leads to
particular behaviors. As Jacobs (1987) explains,
Symbolic interactionists’ assume that individuals’
experiences are mediated by their own interpretations of experience. These interpretations are created by
individuals through interaction with others and used by individual to achieve
specific goals. Symbolic
interactionists are interested in understanding how these interpretations are
developed and used by individuals in specific situations of interaction. (p.
27)
Symbolic
interactionism frames mathematics standards as social constructions that result
from the interplay of diverse political interests. This perspective encourages the collection of evidence that
reveals the differing intents / interests of the participants (Hall, 1997), and
focuses on the language and the politics of meaning in standards development
(Placier, 1998).
Major Findings
of the Study
Historical Background
Florida’s
systemic reform initiative for education, known as Blueprint 2000, was developed in 1991 and called for more local
control but greater state accountability.
However, what this should look like in practice and how it was to be
achieved politically were unclear. As a
result, the policy specifics of Blueprint
2000 were intensely debated between 1991 – 1994. In 1993, as these debates continued, the Florida DOE decided to
developed new standards in all subject areas.
Because of the uncertainties regarding the interpretation and
implementation of Blueprint 2000, the
new subject area standards were originally conceptualized as voluntary
standards that local districts could use to help design their own
curricula. It was unknown how or even
if these standards would be used for state level policies (e.g., state
assessment).
During the first year of development, the writing team consisted only of mathematics educators (K-12 / university teachers and district curriculum specialists) and was given considerable flexibility in how they could write the standards. Underlying the entire development process was the writing teams’ belief that any set of standards (even if only to delineate content to be learned) implicitly carries messages regarding curriculum and pedagogy based on how they are written. Therefore, since they believed that standards are naturally interpreted on multiple levels, they tried to “manage” these interpretations to be consistent with their own goals for reform and the role they wanted the standards to play in Florida’s systemic reform effort.
The
writing team wanted the standards to reform mathematics education by
encouraging teachers to reconsider their views of mathematics and how it should
be taught. As a result, the writers
developed a set of strategies for writing standards based on how they felt
teachers might interpret and use them in their classrooms. Some of the strategies used by the writing
team to achieve these goals included:
a) using
“dynamic” verbs to encourage a more active pedagogy (e.g., verbs such as explore, investigate, and analyze
rather than “traditional” verbs such as solve,
compute, or factor).
b) integrating process strands such as problem solving and communication into the standards to encourage their integration into the curriculum;
c) integrating a
variety of activities and content into single standard statements in order to
encourage a more holistic and integrated view of mathematics, for example, a
standard in the September 1994 Draft included the following:
Recognize,
describe, extend, estimate, analyze, generalize, transform, and create a wide
variety of mathematical relationships by using models such as tables, graphs
(both one- and two-dimensional), matrices, verbal rules, expressions, equations,
and inequalities; and
d) writing broad
standards (lacking specifics) in order to provide both flexibility in classroom
practice and to encourage teachers to engage in curriculum development at the
local level (i.e., by requiring teachers and district curriculum specialist to
fill in the details).
In early 1995
the political context changed with the election of a new education commissioner
who called for a strong accountability system based on new content
standards. Analyzed from within this
new political context, the DOE officials felt it was unlikely that the new
standards – written more to reform teaching than delineating what students
should know and be able to do – could be used to guide the development of a new
state accountability and assessment program.
The Revision Process
In early 1995,
McREL Institute was hired to help the DOE facilitate the revisions. Since the standards were to be used for
state assessment, the mathematics writing team initially (and reluctantly) agreed
to make some changes. These included:
(a) adding more specificity, (b) removing non-assessable verbs (e.g.,
“explore,” “construct meaning for,” and “investigate”), (c) including language
more understandable to the general public, and (d) including additional “basic”
content (e.g., computational skills).
However, despite these changes, the mathematics standards continued to
be criticized throughout the revision process.
The standards were often characterized by McREL and DOE officials2
as (a) too broad and vague; (b) more like classroom activities than statements
of knowledge and skills; (c) “overloaded” (i.e., containing too much
information in single standard statements); (d) too sophisticated for grades
K-2; and (e) lacking clear and consistent distinctions between grade levels.
To the criticism that the standards were too broad and vague and lacking clear and consistent distinctions between grade levels, the writing team explained that although the standards were to be used as a basis for state assessment, the standards were also for classroom instruction, and they wanted to preserve a set of standards that provided for local flexibility. With respect to other criticisms, the writing team disagreed that including verbs such as “communicate,” “describe,” or “analyze” in the standards turned them into classroom activities instead of content standards. The writing team felt the use of these “dynamic” verbs encourages an active view of teaching mathematics (which was one of their original goals). With respect to some standards being “overloaded” with too much information, the mathematics writing team felt that these standards would help convey mathematics as integrated and holistic. To separate them, the writing team felt, would lead to a portrayal of mathematics as a set of isolated facts and topics.
Although compromising at times, the writing team used a variety of strategies to counter the pressure to make changes to the standards and to maintain as much of their original intent for the standards as possible. Strategies included: (1) keeping the number of standards to a minimum forcing the standards to be written at broader levels of generality; (2) agreeing to make more changes to the Number / Measurement standards than those in Geometry, Algebra and Data Analysis; and (3) using performance activities (examples that were included alongside the standards showing how they could be implemented in the classroom) to: (a) counter standards written in language more traditional than they wanted; (b) provide clarity to what the DOE felt were “vague” standards; (c) show increasing levels of sophistication for standards that were not significantly different across the grade levels; and (d) provide examples of how students could achieve standards deemed too sophisticated by reviewers (particularly for grades K-2). Despite the on-going debates and numerous concerns over the standards, DOE officials eventually acquiesced to the mathematics education community’s wishes and the new mathematics standards were officially adopted by Florida’s State Board of Education in May 1996.
In the first
year of development, the writing team, consisting entirely of mathematics
educators, strategically used the language and structure of the standards to
convey their goals for reform in mathematics education. During the second year of development, as
the standards underwent revision and non-mathematics educators entered the
process, numerous debates erupted.
Although debates occurred primarily over issues of language, it was the
multiple and symbolic meanings of the language and structure of the standards
that formed the basis for these debates.
Notes
1. In 1998,
Florida once again revised their mathematics standards by adding sample, grade-level
benchmarks; however, that effort was not included in this study.
2. “McREL”
and “DOE officials” as used here does not imply unanimity of opinions by the
various individual members within the DOE / McREL who participated in the
process to revise the standards.
References
Hall, P. (1997). “Policy as the transformation of intentions:
Producing program from statute.” The
Sociological Quarterly, 38(3), pp. 439-467.
NCTM (1989). The
Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.
Jacob, E.
(1987). “Qualitative Research
Traditions: A Review.” Review of Educational Research, 57 (1),
1-50.
Placier, M. (1998). The
Development of Missouri’s “Show Me” State Standards: The Politics of Language. Paper presented at the annual meeting of
AERA, San Diego, CA.
Ravitch, D. (1995). National
Standards in American Education: A Citizen’s Guide. Washington, DC: Brookings Institution.