Perceptions and application of NCTM's standards by special and general education teachers: Implications for practice for...
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Title: Perceptions and application of NCTM's standards by special and general education teachers: Implications for practice for secondary students with emotional and learning disabilities
Series Title: Maccini, P., & Gagnon, J. C. (2002). Perceptions and application of NCTM's standards by special and general education teachers: Implications for practice for secondary students with emotional and learning disabilities. Exceptional Children, 68, 325-344.
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Abstract: This study determined teachers’ perceptions related to application of, and barriers to implementation of the National Council of Teachers of Mathematics (NCTM) Standards with students labeled learning disabled (LD) and emotionally disturbed (ED). A stratified random sample of 129 secondary general education math and special education teachers responded to a mail survey. A majority of special education teachers indicated they had not heard of the NCTM Standards. Respondents reported teaching mostly basic skills/general math to secondary students with LD and ED, versus higher-level math, such as algebra and geometry. Teachers identified lack of adequate materials as a considerable barrier to successful implementation of activities based on the Standards. Implications for practice and future research are also provided.
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Exepioa Chlde I


VoL 68, No.3, pp. 325-344.
�2002 Council for Exceptional Children.


Perceptions and Application of

NCTM Standards by Special

and General Education Teachers


PAULA MACCINI
JOSEPH CALVIN GAGNON
University of Maryland, ( 1


ABSTRACT: This study determined teachers' perceptions related to application of, and barriers to
implementation of the National Council of Teachers of Mathematics (NCTM) Standards with
students labeled learning disabled (LD) and emotionally disturbed (ED). A stratified random
sample of 129 secondary general education math and special education teachers responded to a
mail survey. A majority of special education teachers indicated they had not heard of the NCTM
Standards. Respondents reported teaching mostly basic skills/general math to secondary students
with LD and ED, versus higher-level math, such as algebra and geometry. Teachers identified lack
of adequate materials as a considerable barrier to successful implementation of activities based on
the Standards. Implications for practice and future research are also provided.


W tandards-driven reform is the
primary approach to assuring
today's high school graduates
are internationally competitive.
Prompted by the public dissat-
isfaction and poor performance by U.S. students
on international assessments (McLaughlin, Shep-
ard, & O'Day, 1995), educators, curriculum spe-
cialists, and national organizations have focused
on development of challenging standards for over
a decade. Recent legislation (i.e., Goals 2000; Im-
proving America's Schools Act; Individuals with
Disabilities Education Act) has assisted these ef-
forts and assured that students with disabilities
are included, to the maximum extent possible.
Central to this notion of reform is the assertion
that all students are "entitled to instruction that is


grounded in a common set of challenging stan-
dards" (McLaughlin, 1999, p. 10).
Rigorous standards are especially crucial for
students with learning disabilities (LD) and emo-
tional disorders (ED), who compose 72% (n =
2,002,314); (U.S. Department of Education,
2000) of the secondary students in special educa-
tion and are commonly included in the general
education environment. These students have his-
torically been provided a less rigorous curriculum
with individualized education program (IEP)
goals that focus on computation (Shriner, Kim,
Thurlow, & Ysseldyke, 1993) and have minimal
linkage to long-term general education outcomes
(Nolet & McLaughlin, 2000; Sands, Adams, &
Stout, 1995; Smith, 1990). In the sections that
follow, the National Council of Teachers of


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Mathematics (NCTM) Standards are discussed
relative to standards-based reform efforts and stu-
dents with disabilities, followed by a review of
relevant characteristics of students with LD and
ED. Finally, the purpose of the study is delin-
eated.


NCTM AND REFORM EFFORTS
The NCTM is one of the national organizations
that have produced a comprehensive approach to
applying standards-driven reform. In 1989, a
community of math educators and other profes-
sionals developed the Standards in an effort to
address the low math performance of students in
the United States. The NCTM Standards are
guided by five main goals that encompass the
"spirit" of the Standards, wherein students (a) be-
come better problem solvers, (b) learn to reason
mathematically, (c) learn to value mathematics,
(d) become more confident in their mathematical
ability, and (e) learn to communicate mathemati-
cally (NCTM, 1989). These goals reflect changes
in math curriculum, assessment, and professional
teaching practices (NCTM 1989; 1991; 1995;
2000) to help all students achieve in mathemat-
ics. In contrast to past reform efforts (e.g., Back
to Basics) that narrowly focused on the acquisi-
tion and retention of basic math skills, NCTM
Standards address problem-solving and reasoning
skills deemed essential for an increasingly techno-
logical society and future employment.
Specifically, the focus of the Standards is on
conceptual understanding rather than procedural
knowledge or rule-driven computation. Student
understanding of mathematical concepts is pro-
moted via active engagement with manipulatives
or concrete objects, applying math to real-world
situations, group work and discussions, and
teacher facilitation. This approach to mathemat-
ics education is supported by recent analysis of
data from the Third International Mathematics
and Science Study (TIMSS). Based on the data,
researchers (National Institute on Educational
Governance, Finance, Policymaking, and Man-
agement, 1998) indicate that the problem with
U.S. student performance is not basic mathemati-
cal computation, but advanced mathematical
concepts and problem-solving.


The NCTM Standards are a critical
component of the Standards-driven
reform movement.



The NCTM Standards are a critical com-
ponent of the Standards-driven reform move-
ment. Although no current count exists that
identifies the number of states that have adopted
state standards consistent with those set forth by
NCTM, Blank and Dalkilic (1992);(as noted in
Thurlow, 2000) report that 42 states have used
the Standards as a guide to development of math-
ematics standards. Researchers (Rivera, Taylor, &
Bryant, 1994/1995) also assert that all students,
including those with disabilities, should be taught
areas identified in the Standards. This is becom-
ing more of a reality as students with disabilities
are being educated in the general education class-
room and are exposed to the same curricula as
their peers without disabilities. Further, it is a re-
quirement in some states for students to pass as-
sessments with open-ended problem-solving tasks
that are in line with the Standards in order to re-
ceive a diploma (e.g., Maryland State Depart-
ment of Education, 2000).
CHARACTERISTICS OF STUDENTS WITH LD
AND ED
Students with LD and ED exhibit several com-
mon academic and behavioral characteristics (An-
derson, Kutash, & Duchnowski, 2001; Scruggs
& Mastropieri, 1986) that may affect success in
NCTM Standards-based mathematics activities.
In addition to performing approximately two
grade levels behind peers without disabilities
(Wagner, 1995), significant characteristics affect-
ing performance for both groups include diffi-
culty attending to key dimensions of tasks
(Kauffman, 2001) and deficits employing
metacognitive strategies (Bricklin & Gallico,
1984; Gallico, Burns, & Grob, 1991). Also, typi-
cal instructional approaches may combine with
student learning and behavioral characteristics
and affect student academic success (Marolda &
Davidson, 1994). For example, the common em-


Spring 2002


326










phases on computational skills and fact memo-
rization, coupled with a limited exposure to prob-
lem-solving, may negatively impact these
students. Such ramifications may be observed
within subsequent classes where teachers utilize a
problem-solving-based approach to math educa-
tion (Baroody & Hume, 1991; Bos & Vaughn,
1994; Salend & Hofstetter, 1996) and also in
contexts outside of school.
Researchers also note relevant characteris-
tics more specific to students labeled LD. Many
adolescents with LD experience math difficulties
(McLeod & Armstrong, 1982), particularly in
problem application, and generally perform at the
fifth-grade level in math (Cawley & Miller,
1989). These students typically approach com-
plex math tasks, such as multistep word prob-
lems, in a notably different way than students
proficient at problem-solving. For instance, many
students with LD experience problems: (a) select-
ing and employing appropriate operations during
problem-solving (Montague & Bos, 1990), (b)
representing problem-solving situations (Mon-
tague, Bos, & Ducette, 1991), and (c) selecting
relevant information in problems (Blankenship &
Lovitt, 1976).
Adolescents with ED also possess character-
istics that differentiate them from peers without
disabilities and, to a lesser extent, from students
with LD. For example, the academic success or
failure of students labeled ED is greatly affected
by the extent to which instruction is functional
and recognized by students as relevant (Bos &
Vaughn, 1994). In addition, these students often
exhibit a general lack of persistence and concen-
tration and have difficulties with independent
class work. Further, results of two studies (Carr &
Punzo, 1993; Hogan & Prater, 1993) indicate
that students with ED obtain a correct rate of be-
tween 20% and 76% on independent seatwork
(Guntner & Denny, 1998). The ability of stu-
dents to persist and work independently on open-
ended mathematical tasks could greatly affect the
level of success experienced in light of the more
constructivist approach that guides the NCTM
Standards.


TEACHER BELIEFS OF NCTM STANDARDS
WITH STUDENTS WITH LD AND ED
In addition to academic and behavioral character-
istics of students labeled LD and ED, certain
teacher beliefs, such as familiarity and confidence
with implementing the Standards, may also affect
successful implementation of Standards-based ac-
tivities. For example, Manouchehri (1998) noted
that teachers who lack familiarity with conceptu-
ally-based questioning techniques rarely expect
students to elaborate, justify their position, or
support students in the systematic testing of op-
posing approaches to mathematical problems.
Similarly, NCTM (1991) acknowledges that
teacher confidence affects both what is taught
and the instructional approach used by teachers.
Although there is widespread use of the NCTM
Standards (Parmer & Cawley, 1995), no informa-
tion is available that addresses secondary special
and general education teacher familiarity and
confidence with the standards with students with
disabilities.
To achieve a clear understanding of sec-
ondary general and special educator confidence
and familiarity with the NCTM Standards, stu-
dent response to standards-based activities and
barriers to implementation should also be consid-
ered. For example, Manouchehri (1998) noted
that teacher beliefs and practices are strongly in-
fluenced by leadership at the school and district
levels. Additionally, researchers (Reys, Reys,
Barnes, Beem, & Papick, 1998) have identified
obstacles to Standards-based reform efforts, in-
cluding (a) teacher views and beliefs of mathe-
matics that may influence practice (e.g.,
traditional view of math as facts and formulas,
tracking students in math by ability level), and
(b) initial student reactions to the new curricula
that require more critical thinking and problem-
solving skills than students may have experienced
in past math courses.


PURPOSE
To date, no studies investigate secondary teacher
familiarity with the NCTM Standards, confi-
dence with implementation, barriers to successful
implementation, and student response to Stan-
dards-based activities. Nor is there research on


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Many adolescents with LD experience
math difficulties, particularly in problem
application, and generally perform at the
fifth-grade level in math.



these topics for general and special educators who
teach students with LD and ED. This is unfortu-
nate given that common, rigorous standards are
the catalysts for improved educational outcomes
within standards-based reform (Gagnon,
McLaughlin, Rhim, & Davis, in press; McDon-
nell, McLaughlin, & Morison, 1997). Identifica-
tion of these factors is essential to assess teacher
perception of preparedness and ability to imple-
ment Standards-based activities within the school
context. Thus, our current study determined
teacher perceptions related to implementation of
the Standards with secondary students labeled LD
and ED. A survey for general and special educa-
tors in Maryland secondary schools was designed
to answer the following research questions:
1. How familiar are special and general education
teachers with the goals of the NCTM Stan-
dards?
2. How confident are special and general educa-
tion teachers in their ability to teach math rela-
tive to the goals of the NCTM Standards?
3. According to teachers, how favorably do stu-
dents with LD and ED respond to activities,
lessons, and strategies that incorporate the rec-
ommendations of the NCTM Standards?
4. What are perceived barriers to successful Stan-
dards implementation for students with LD
and ED?
5. Do teachers' responses differ according to age,
gender, years of teaching experience, grade lev-
els taught, training, locale, position, and teach-
ing load?


METHODOLOGY

INSTRUMENTATION
Based on a review of literature, the authors identi-
fied four central topics as the focus of the current


survey: (a) general background information (e.g.,
years teaching experience, type of mathematics
courses currently teaching, number of special edu-
cation methods courses taken), (b) implementa-
tion of the Standards with students labeled LD
and ED (e.g., familiarity with the Standards, con-
fidence implementing Standards-based activities,
teacher perception of student response to Stan-
dards-based activities), (c) barriers to implementa-
tion of Standards-based activities (e.g., lack of
materials, lack of administrative support), and (d)
nature of adaptations of the Standards to meet the
needs of students with LD and ED. In addition
to the categorical and ordinal questions contained
in each of the first four sections, the fourth and
fifth sections included open-ended questions
(e.g., list two advantages of implementing the
NCTM Standards with students with emo-
tional/behavioral disorders);(see Maccini and
Gagnon, 2000, for the results of the open-ended
questions) related to implementation of activities
based on the Standards.
The survey was developed via a four-step
process. Based on a review of literature an initial
version of the survey was constructed focusing on
teaching math to secondary students with LD and
ED. Second, a review board that included leaders
in the fields of special education and math educa-
tion examined the survey. Third, a focus group of
educators provided feedback on the survey ques-
tions and design. The authors made appropriate
revisions following each stage. To address issues
specific to general and special educators, two ver-
sions of the survey were constructed and mailed
to teachers. A majority of the questions on both
surveys were the same. However, the special edu-
cation survey included 14 questions that applied
solely to those teachers (e.g., number of students
on caseload). Similarly, the survey designed for
general educators also included questions (n = 12)
relevant only to them (e.g., average number of
students in your math classes).
Reliability. To address possible threats to re-
liability and enhance replicability of research find-
ings, survey data collection procedures were
closely followed (Fink, 1995; Yin, 1994). For ex-
ample, standardized directions were incorporated
into the survey instrument. Further, a reliability
check was conducted on 25% of survey questions
to assess the researchers' fidelity with data entry


Spring 2002


328










and was determined to have a 99% reliability rate.
This agreement was calculated by the following
formula: number of agreements divided by num-
ber of agreements and disagreements times 100.
To further establish reliability, Cohen's Alpha was
calculated to determine the internal consistency
of items addressing barriers to implementation of
the NCTM Standards (n = .724).
Validity. Threats to validity were addressed
to maximize the quality of the surveys and im-
prove the generalizability of findings. To address
construct validity, a focus group and advisory
panel were developed prior to study implementa-
tion. The focus group consisted of secondary gen-
eral and special education math teachers. These
professionals offered feedback and recommenda-
tions in three areas: (a) accuracy of targeted objec-
tives, (b) necessary question additions/deletions,
and (c) clarification of questions and format. The
advisory panel included experts in the fields of
math education, statistics, and learning disabili-
ties. This panel examined the survey instruments
and also reviewed the methodology of the study.
Modifications were made based on the recom-
mendations of these two groups.
SAMPLE
Survey Sampling Procedures. The state of
Maryland was selected for the study as the 24
school districts are representative of a national
range of geographical locations (urban, suburban,
and rural), as well as student population densities
(0-599, 600-600, and 1,000 or more students).
For example, 88% of students in Maryland are
served in urban schools and 3% in suburban
schools versus national averages of 71% and 12%,
respectively. Also, the percentages of identified
students in Maryland approach national statistics.
For example, 11% (n = 4,933) of students in
Maryland were labeled with serious emotional
disturbance versus 11% (n = 275,485) nationally.
Further, 5.19% of children ages 6-17 in Maryland
were labeled with a specific learning disability
during the 1997/1998 school year. This was close
to the national average of 5.61%.
The following sampling procedures were
followed for inclusion in this study: (a) a list of all
Maryland school districts was identified using the
Common Core of Data (National Center for Ed-
ucation Statistics, 1995); (b) initial contact was


made via phone with administrators and supervi-
sors of special education from each of 24 Mary-
land districts; and (c) the administrators in the
districts willing to participate (n = 17) were
mailed a description of the study, survey, and a re-
quest for all public school secondary (i.e., Grades
6-12) mathematics teachers and special educators
who were currently teaching mathematics in the
general education setting or in exclusionary pro-
grams (i.e., resource room and self-contained
class). If more than two special education teacher
names and two general educator names were pro-
vided per school, a two-stage cluster procedure
(Fink, 1995; Fowler, 1988) was used. Teacher
names were randomized and chosen in sequential
order, and surveys were mailed to the targeted
teachers, with 143 mailed to special educators and
182 to general educators, for a total of 325.
Response Rate. A total of 39 surveys were ex-
cluded from the analysis due to one of five con-
cerns: (a) teachers were not instructing students
labeled LD or ED (n = 4), (b) teachers changed
schools from the initial to follow-up mailings (n =
29), (c) incorrect school address (n = 3), (d) the
wrong survey was mailed to the teacher (n = 1), or
(e) the survey was returned with the code number
and name removed (n = 2). With the noted ex-
ceptions, a total of 286 teacher surveys met the
criteria for inclusion. Of these, 129 teachers re-
turned the survey for a response rate of 45%. The
response rate remained low despite four survey
mailings and follow-up phone calls. Although the
return rate does not approach the common stan-
dard of 70% and could be considered a limita-
tion, it is acknowledged that 50% is a typical
return rate for mail questionnaires (Weisberg,
Krosnick, & Bowen, 1989). No statistically sig-
nificant differences were found between respon-
dents and nonrespondents for level of teaching
(i.e., middle school and high school);(x2 = .945,
p = .623), school size (x2 = 2.365, p = .306), and
number of general and special education teachers
(X2 = 3.745, p = .053). However, a significant dif-
ference was determined between school locales of
respondents and nonrespondents (i.e., urban,
suburban, and rural);(2 = 8.786, p = .012), with
a larger percentage of respondents represented in
each category. Thus, in relation to these variables,
respondents and nonrespondents were generally
more similar than different.


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TABLE 1
Comparison of the Number and Percentage of Schools by Locale and Student I


and the Survey Sample

No. (%)
Locale/Population Maryland Total Sample

Urban
0-599 83 (18) 52 (16)
600-999 143 (32) 68 (21)
1,000 and more 131 (29) 69 (21)
Total Urban 357 (79) 139 (58)

Suburban
0-599 6 (1) 12 (4)
600-999 10 (2) 24 (7)
1,000 and more 4 (<1) 6 (2)
Total Suburban 20 (4) 42 (13)

Rural
0-599 35 (8) 35 (11)
600-999 25 (6) 39 (12)
1,000 and more 16 (4) 20 (6)
Total Rural 76 (17) 94 (29)


School Selection. A stratified random sample
of schools was selected across population density
(i.e., urban, suburban, and rural), enrollment
(i.e., 0-599, 600-999, 1,000 and greater), and
school levels (i.e., middle school, and high
school). Percentages of schools across population
density and enrollment were established to main-
tain a sample consistent with the overall make-up
of schools within Maryland (see Table 1). While
the return rate resulted in minor differences in
these percentages, surveys were distributed with
the intention of approximating the general char-
acteristics of the state. Additionally, an approxi-
mate equal number of surveys were distributed to
both middle and high schools.
A total of 137 schools refused to participate
and of these, 73.7% (n = 101) were from urban
locales, 21.9% (n = 30) from rural locales, and
4.4% (n = 6) from suburban locales. In contrast,
student population of the schools refusing to par-
ticipate was more equally distributed. Approxi-
mately one-third of the 137 schools were in each
population category, with 32.1% (n = 44) having
up to 599 students, 32.8% (n = 45) with 600-999
students, and 35.0% (n = 48) with 1,000 or more
students.


Data Analysis Procedures. Data analysis for
the survey included descriptive statistics and addi-
tional statistical methods, such as t-tests or Analy-
sis of Variance (ANOVA) to compare group
means. Given the ordinal data and the fact that
some of the variables were not normally distrib-
uted (i.e., kurtosis or skewness greater than 1.0),
nonparametric statistics were also calculated, with
the alpha level set at .01 to reduce possible Type
II errors. These nonparametric statistics included
chi-square tests to compare proportions, Mann-
Whitney U tests to compare medians between
groups, and nonhierarchical regression analyses to
determine how well certain variables (e.g., age,
level, and number of methods courses) predict
teacher familiarity, confidence, and favorable stu-
dent response. Results were reported for the sec-
ond analyses whenever differences existed with
parametric statistics.


RESU LTS

DEMOGRAPHICS
Analysis of demographics included both teacher
and student information. Approximately 45% of
general education (n = 65) and special education


Spring 2002


.. . . for Maryland


330










teachers (n = 64) responded for a total of 129
teachers. Forty-eight percent of these teachers (n =
62) were from urban school districts, followed by
36% rural (n = 46) and 16% suburban (n = 21)
(see Table 1). Responses to demographic ques-
tions were further analyzed across teacher-type
(special versus general education math teachers)
(see Table 2). The majority of general education
(n = 44) and special education (n = 51) teachers
were female (69% and 80%, respectively).
Further, general education teachers taught
for more years than the participating special edu-
cators (see Table 2). A significant difference was
determined across general and special educators
and years of experience teaching students with
LD and ED. Compared to special educators, gen-
eral education teachers had more years of experi-
ence teaching students with LD (X2 = 12.872, p =
.025) and ED (x2 = 15.763, p = .008). Regarding
the types of math courses currently being taught
to students with LD and ED, teachers were asked
to indicate "All that apply." The most commonly
marked course for both general and special educa-
tors was middle school math for students with
LD.
Teachers were questioned on pertinent stu-
dent information, such as services provided and
student achievement level. When asked the num-
ber of students with LD that were provided in-
struction in the general education math class with
no special services provided, 29% of responding
special education teachers (n = 10) indicated
"None," and 40% of general education teachers
(n = 10) indicated "1-5." The most common re-
sponse to the range of students labeled ED with
no special services was "1-5 ." Specifically, 71% of
special educators (n = 25) and 48% of general ed-
ucation teachers (n = 29) noted this range. Fur-
ther, when asked the number of students with LD
that were receiving special services (e.g., consulta-
tive services, co-teaching) within general educa-
tion math class, 43% of special educators (n = 15)
noted "None." The second most frequent re-
sponse to this question was "6-10 students" by
29% (n = 10) of special education teachers. Also,
33% of general education teachers (n = 20) indi-
cated that no students were receiving additional
special education services (e.g., resource support),
followed by 25% of general education teachers
(n= 15), indicating "1-5 students." In terms of


students with ED receiving special services (e.g.,
consultative services and co-teaching) within gen-
eral education math class, 63% of special educa-
tors (n = 22) noted "None." The second most
frequent response to this question was "1-5 stu-
dents" by 26% of special education teachers. Also,
48% of general education teachers (n = 29) indi-
cated that no students were receiving additional
special education services (e.g., resource support),
followed by 37% of general education teachers
(n = 22), indicating "1-5 students."
Researchers also analyzed general and spe-
cial educator ratings of the achievement level
common for students labeled LD and ED in
math relative to peers without disabilities (1 =
well above average, 2 = above average, 3 = about
class average, 4 = below class average, 5 = well
below class average, 6 = not applicable). Both
groups of teachers reported the mean achievement
level for students with LD more closely ap-
proached the performance of unlabeled students
than did the achievement of students labeled ED.
Further, special educators reported slightly higher
achievement for students with LD (M= 3.85)
versus general education teachers (M= 3.92). In
contrast, general educators noted a higher-level of
achievement for students with ED (M= 4.42), as
compared to the responses of special educators
(M= 4.73).
Methods Courses. Teachers also responded to
questions concerning their prior methods courses
that addressed, at least in part, teaching math to
students with LD or ED. As reported in Table 3,
a significant difference was found (X2 = 37.424,
p = .000), with general education teachers indicat-
ing having taken more math methods courses. No




A significant difference was determined
across general and special educators and
years of experience teaching students with
LD and ED.



significant differences were determined among
special and general education teachers with regard
to the number of special education math courses


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TABLE 2
Demographic Characteristics

No. (%) Significance
Characteristics Special Education Teachers General Education Teachers 2 p


Gender
Female
Male

Age
20-29
30-39
40-49
50-59
60 or >


Educational Level
BA
MA


Level of Teaching
High School
Middle School
Combination

Years of Experience
Teaching Math to Stu-
dents with LD?
<1
1-5
6-10
11-15
16-20
21 or >

Years of Experience
Teaching Math to Stu-
dents with ED?
<1
1-5
6-10
11-15
16-20
21 or >


taken for teaching math to students with LD or
ED (see Table 3).
Also computed were teachers' perceptions
of their preparation resulting from math and spe-
cial education methods courses, which focused on
teaching math to students with disabilities. Fol-
lowing special education methods courses, a sta-
tistically significant difference was determined


across teachers' perceptions (t= 1.982, p= .050),
with special education teachers (M= 2.44) noting
greater preparation than general education teach-
ers (M= 3.76);(see Table 4). In addition, special
education teachers (M= 2.13) noted significantly
greater preparation (t= 3.222, p= .002) as a re-
sult of taking math education content methods


Spring 2002


51 (80)
12 (19)


9 (14)
19 (30)
24 (38)
12 (19)
0 (0)


16 (25)
47 (75)



32 (50)
26 (41)
6 (9)


44 (69)
20 (31)


14 (22)
14 (22)
21 (33)
13 (20)
1 (2)


26 (41)
38 (60)



31 (48)
28 (43)
6 (9)


3.516 .172



4.085 .537


3.326 .068


.082 .960


12.872 .025


4 (6)
24 (38)
22 (35)
2 (3)
8 (13)
4 (6)


5 (8)
25 (39)
10 (15)
6 (9)
5 (8)
14 (22)


15.76 3.008


12 (20)
21 (34)
17 (28)
3 (5)
7 (12)
1 (2)


12 (19)
23 (37)
7(11)
7(11)
3 (5)
11 (18)


332










TABLE 3
Nature j.1 ,.-',., , Courses

No (%) Significance
Survey Item None 1-2 3-4 5-6 7or > X 2 p

How many math methods courses
have you taken?
37.424 .000
Special Education Teachers 18 (29) 31 (50) 12 (19) 0 1 (2)
General Education Teachers 1 (2) 19 (31) 24 (39) 7(11) 11 (18)

Number of special education
methods courses taken that
addressed, at least in part, teaching 6.490 .167
math to students with LD?

Special Education Teachers 9 (15) 42 (68) 8 (13) 2 (3) 1 (2)
General Education Teachers 20 (32) 32 (51) 6 (10) 4 (6) 1 (2)

Number of special education
methods courses taken that
addressed, at least in part, teaching 3.030 .391
math to students with ED?

Special Education Teachers 25 (42) 31 (52) 3 (5) 1 (2) 0
General Education Teachers 36 (58) 24 (38) 2 (3) 1 (2) 0


courses versus general education teachers (M=
3.76).
TEACHER FAMILIARITY, CONFIDENCE, AND
STUDENT RESPONSE
Respondents were queried on whether they knew
about the goals of the NCTM Standards. Ninety-
five percent (n = 62) of general education teachers
responded "Yes," versus 55% (n = 35) of special
educators. Participants who answered "No" (i.e.,
never heard of the NCTM Standards) were
deleted from analysis in questions pertaining to
the implementation of and barriers to the imple-
mentation of the Standards. In closer analysis, re-
spondents who had never heard of the NCTM
Standards (n = 31) were mostly high school spe-
cial education teachers from rural school districts
(n = 8). The three general education teachers that
had not heard of the NCTM Standards taught
middle school from mostly urban school districts.
Mean ratings of teacher familiarity with the
Standards (see Table 5) across general and special
education teachers were nonsignificant using
parametric statistics. General education teachers


noted greater familiarity as compared to special
education teachers. Specifically, 73% (n = 44) of
general education teachers responded either
"Strongly Agree" or "Agree" regarding familiarity
with the goals of the Standards, versus 50% (n =
17) of special education teachers. However, results
from a more sensitive measure, Mann-Whitney U
test, revealed significant differences in teacher fa-
miliarity of the Standards across general and spe-
cial education teachers (p = .002).
General and special education teachers were
asked to rate their perceived level of confidence
implementing the goals of the NCTM Standards
with students labeled LD and ED (see Table 5).



Perceptions of favorable student response
toward activities, lessons, and strategies
that incorporate the recommendations of
the Standards were determined to be non-
significant across general and special edu-
cation teachers.


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TABLE 4
Nature j .U,-',. , Courses

Mean Rating of Methods Courses Signcance
on a 5-Point Scale Signi nce

General Educa- Special Educa-
Survey Quesons tion Teachers tion Teachers

What is true regarding your
prior math education con- 3.04 2.13 3.222 .002
tent area courses that fo-
cused on teaching math?

What is true regarding your
prior special education
courses that focused on 3.76 2.44 1.982 .050
teaching math?

al = very prepared; 2 = somewhat prepared; 3 = no opinion; 4 = somewhat unprepared; 5 = very unprepared.


There was a significant difference across teachers
(t = 2.950, p = .004), with general education
teachers reporting greater confidence. For in-
stance, 78% (n = 47) of general education teach-
ers marked "Strongly Agree" or "Agree" versus
59% (n = 20) of special education teachers.
Perceptions of favorable student response
toward activities, lessons, and strategies that in-
corporate the recommendations of the Standards
were determined to be nonsignificant across gen-
eral and special education teachers. Fifty-five per-
cent (n = 32) of general and 58% (n = 19) of
special educators rated, "Strongly Agree" or
"Agree" that student response was favorable, ver-
sus only 10% (n = 6) of general educators and 6%
(n = 2) of special education teachers who rated
"Disagree" or "Strongly Disagree."
BARRIERS
Special educators were queried regarding the ex-
tent to which a lack of support from the general
educators was a barrier. Seventy-one percent (n =
25) of the respondents answered "Sometimes"
and "Rarely," and the mean was 3.61. For general
education teachers, the issue of support from spe-
cial educators was less pronounced, with a mean
score of 3.8 (n = 58). Specifically, 60% (n = 39) of
general educators noted that this issue was
"Rarely" or "Never" a barrier, and an additional


15.4% (n = 10) responded "Somewhat."
Analysis of perceived barriers to implemen-
tation of the NCTM Standards was conducted
across two general grade level categories (i.e., mid-
dle school and high school) and across special and
general educators (see Table 6). When comparing
the views of teachers concerning barriers across
middle and high school, no significant differences
were observed. However, it is interesting to note
that, on average, both groups identified a lack of
administrative support as the barrier least affect-
ing successful implementation. In contrast, a lack
of materials was considered the greatest barrier.
Significant differences do exist (t= 2.17,
p = .033) between the overall means for special
and general educator responses on the extent to
which they view a lack of administrative support
as a barrier toward successful implementation of
the Standards. However, use of the Mann-Whit-




A primary concern is that many special
education teachers indicated they were
unfamiliar with the goals of the NCTM
Standards.


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TABLE 5
Teacher Familiarity, Confidence, and Student Response

Mean Rating on 5-Point Scalea Significance

Teacher Perceptions General Education Special Education t P
I feel familiar with the goals of 2.15 2.88 1.470 .145
the NCTM Standards for teach-
ing mathematics.


I feel confident in my ability to 1.97 2.59 2.950 .004
teach mathematics relative to the
goals of the NCTM Standards.


My students with special needs 2.57 2.82 1.599 .113
respond favorably when I work
on activities/lessons that apply
these goals.

al = strongly agree; 2 = agree; 3 = undecided; 4 = disagree; 5 = strongly disagree.


ney U test did not show significant differences
across teachers (p = .372). General education
teachers reported this issue was more frequently a
barrier than their special education counterparts.
Despite this significant difference, 66.6% of gen-
eral educators (n = 38) and 78.2% of special edu-
cators (n = 25) reported administrative support
was "Rarely" or "Never" an issue.
Important information on teacher percep-
tions of barriers is also available through an evalu-
ation of the group means. For example, on
average both general and special educators indi-
cated that a lack of materials was a relatively fre-
quent barrier (see Table 6). Approximately 76%
(n = 44) of general educators and 88% (n = 29) of
special educators responded that this issue is a
barrier "Always," "Frequently," or "Sometimes."
In contrast, the district curriculum was less often
seen as a barrier, with group means of 3.98 and
3.48 for general and special educators, respec-
tively. Specifically, 80.7% (n = 45) of the general
education teachers and 51.6% (n = 16) of special
educator respondents noted the occurrence of the
issue "Rarely" or "Never." While a lower percent-
age of special educators responded "Rarely" or
"Never," an additional 35.5% (n = 11) of these
teachers commented that the district curriculum
was a barrier "Sometimes."


FACTORS AFFECTING TEACHER RESPONSE

First, a correlation table was constructed to deter-
mine variables that were significantly correlated
with one another. Results of the correlational
analysis between the criterion variables (i.e.,
teacher confidence, favorable student response,
and familiarity) and predictor variables (i.e., age,
level, teacher type, school population, locale,
years of teaching, highest degree earned, student
achievement, number of methods courses, gender,
course preparation, familiarity with the Standards,
confidence implementing the Standards, or favor-
able student response) included moderate to
strong correlations. To further examine the rela-
tionships across variables, a series of one-way
analyses of variance were conducted across depen-
dent variables (i.e., familiarity, confidence, and fa-
vorable student response) and predictor variables.
No significant differences were determined
among these variables. Finally, nonparametric sta-
tistics were used to determine the contribution of
the predictor variables on various criteria (i.e.,
teacher confidence, favorable student response,
and familiarity).
Teacher Confidence. Teacher confidence in
their ability to teach math relative to the goals of
their NCTM Standards was strongly correlated
with familiarity of the goals (r = .74). The authors


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TABLE 6
Effect Barrier Has on NCTM Standards Implementation

Mean Rating of Barrier on 5-Point Scalea Significance

General Education Special Education
Barrier Teachers Teachers
Lack of materials 2.98 2.58 1.06 .290

District's curriculum 3.98 3.48 1.74 .085

Current textbook 3.38 2.97 .17 .863

Lack of administrative support 3.77 4.03 2.17 .033

Lack of information/knowledge 3.64 3.41 .48 .630


al= always; 2 = frequently; 3 = sometimes; 4 = rarely; 5 = never.

used nonhierarchical regression analysis to deter-
mine the contribution of 10 variables (i.e., years
of teaching ED, years of teaching LD, number of
methods courses, preparation, teacher type, famil-
iarity, favorable student response, achievement,
lack of administrative support, and lack of infor-
mation) to predict the level of teacher confidence
when teaching math activities that reflect the
goals of the NCTM Standards. The total contri-
bution of these variables was determined for an
"overall" predictor variable contribution to
teacher confidence. This accounted for 61% of
the variance for overall teacher confidence.
To determine the contribution of each,
variables were entered into the first position of the
linear equation. Then, each variable was entered
in the last position to determine if the variable
significantly contributed to teacher confidence
beyond the contribution of the other variables. As
shown in Table 7, when entered in the first posi-
tion, the t-test for Beta weights was statistically
significant for six variables (i.e., teacher familiar-
ity, favorable student response, number of meth-
ods courses, lack of information, years of teaching
ED, and teacher type), thus contributing to
teacher confidence. However, the t-test for Beta
weights was significant for only two variables (i.e.,
familiarity and years of teaching ED), when en-
tered in the final position of the linear equation.
It was determined that familiarity accounted for


10% of the variance and years of teaching ED 3%
beyond the contribution of the other variables.
Teacher Familiarity. Lack of information/
knowledge as a barrier affecting successful Stan-
dards implementation had a strong-to-moderate
negative correlation with familiarity of the Stan-
dards (r= -.67) and confidence level (r= -.46).
Thus, teachers who indicated that a lack of infor-
mation was a barrier to successful Standards im-
plementation were generally unfamiliar with the
Standards and did not feel confident implement-
ing the Standards.
A nonhierarchical regression analysis was
also used to determine the contribution of seven
variables (i.e., years of teaching ED, years of
teaching LD, number of methods courses, prepa-
ration, confidence, teacher type, and favorable
student response) to predict the level of teacher
familiarity with the goals of the NCTM stan-
dards. Sixty percent of the variance for overall
teacher familiarity with the Standards was deter-
mined with the noted variables entered into the



Although there are a number of effective
resources for teachers, one consideration
should be the use of materials that have
been empirically validated.


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TABLE 7
Non-Hierarchical Regression Analysis for Teacher Perception of Confidence

Initial Entry of the Construct Construct Entered in Last Position

R Squared
Simple R R Squared p-value re-value
Variables Increment
Years Teaching ED .350 .130 .001 .030 .044

Years Teaching LD .140 .019 .185 .016 .126

Number of Methods Courses .480 .231 .000 .038 .148

Preparation .140 .018 .438 .009 .522

Teacher Type .330 .107 .001 .004 .437

Familiarity .740 .551 .000 .100 .000

Student Response .570 .322 .000 .015 .014

Achievement .230 .053 .106 .014 .358

Lack of Administrative Support .111 .012 .314 .005 .414

Lack of Information .460 .213 .000 .000 .924


regression equation. As shown in Table 8, the t-
test for Beta weights was statistically significant
for five variables (i.e., confidence, favorable stu-
dent response, number of methods courses,
teacher type, and years teaching ED) when each
was entered in the first position. The t-test for
Beta weights was significant for two variables (i.e.,
confidence and favorable student response), when
entered in the final position. Teacher confidence
accounted for 18% of the variance, and favorable
student response accounted for 2% of the vari-
ance beyond the contribution of the other vari-
ables.
Favorable Student Response. Teacher percep-
tions of favorable student response to activities
that incorporate the goals of the Standards were
moderately correlated with teacher familiarity of
the goals of the Standards (r= .54) and teacher
confidence in their ability to teach math relative
to the goals of the Standards (r= .57). Results of
the nonhierarchical regression analysis showed
that 41% of the variance for overall favorable stu-
dent response was determined with the noted
variables entered into the regression equation.


When entered in the first position, the t-test for
Beta weights was statistically significant for four
variables (i.e., confidence, familiarity, years teach-
ing ED, and preparation);(see Table 9). The t-test
for Beta weights was significant for two variables
(i.e., confidence and familiarity) when entered in
the final position of the linear equation. It was
determined that confidence accounted for 4% of
the variance and familiarity 4% beyond the con-
tribution of the other variables.


DISCUSSION

The results of this study indicate that, according
to general and special educator perceptions, sev-
eral issues must be considered for successful im-
plementation of activities based on the goals of
the NCTM Standards. Specifically, five central
themes come to light: (a) teacher unfamiliarity
with the Standards, (b) variables that affect
teacher confidence in implementing Standards-
based activities, (c) favorable student response to
Standards-based activities, (d) significant barriers
(i.e., lack of materials) to successful implementa-


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TABLE 8
Non-Hierarchical Regression Analysis for Teacher Perception of Familiarity

Initial Entry of the Construct Construct Entered in Last Position
R Squared
Variables Simple R R Squared p-value Incrementvalue
Variables Increment
Years Teaching ED .31 .094 .004 .000 .865

Years Teaching LD .12 .015 .232 .000 .985

Number of Methods Courses .44 .191 .002 .003 .921

Preparation .09 .009 .674 .012 .342

Confidence .74 .551 .000 .183 .000

Teacher Type .31 .093 .003 .006 .308

Student Response .54 .295 .000 .022 .054


tion of Standards-based activities, and (e) level of
math courses typically taught by teachers of stu-
dents with LD and ED.
A primary concern is that many special ed-
ucation teachers indicated they were unfamiliar
with the goals of the NCTM Standards. This is of
concern given that the Standards were first pub-
lished in 1989 and were also revised in April
2000. Further, as more students with LD and ED
are educated in general education math classes,
special education teachers need greater familiarity
with the Standards to accommodate and adapt to
individual learning needs.
For teachers who are familiar with the Stan-
dards, certain variables influenced teacher confi-
dence with the Standards. Specifically, teacher
confidence was influenced by familiarity, student
response, number of methods courses, a lack of
information, years of teaching ED, and teacher
type. The overall contribution of all variables ac-
counted for 61% of the variance. Two of these
variables were uniquely and significantly related
to teacher confidence (familiarity and years of
teaching ED), when all other variables were con-
trolled. Thus, teacher confidence in the ability to
teach math consistent with goals of the Standards,
significantly relates to familiarity with the Stan-
dards. However, it should be noted that this rela-
tionship does not necessarily imply actual teacher


implementation of activities consistent with the
NCTM Standards. As Batchelder (1998) deter-
mined, " ... teachers may be familiar with the
language of standards-based strategies, but not
understand the implications of these strategies for
teaching and learning" (p. 12). To identify the
link between teacher confidence, familiarity with
the Standards, and classroom practices, future re-
search should include the addition of observation
to validate teacher perceptions.
Researchers also determined that more than
half of general and special educators indicated
students responded favorably to activities, lessons,
and strategies that incorporate the recommenda-
tion of the Standards. This is consistent with past
research on students' views of mathematics when
taught in classes that are in line with Standards-


The lack ofsuitable materials is especially
disconcerting for students with LD and
ED who require manipulatives, multiple
representations, and varied examples and
nonexamples as teachers progress through
the concrete-semi-concrete-abstract phases
of instruction that are recommended


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TABLE 9
Non-Hierarchical Regression Analysis for Teacher Perception of Student Response
Initial Entry of the Construct Construct Entered in Last Position

Variables Simple R R Squared p-value p-value
Increment

Years Teaching ED .28 .080 .008 .005 .437

Years Teaching LD .13 .017 .215 .001 .716

Number of Methods Courses .27 .065 .137 .004 .925

Preparation .26 .070 .045 .027 .209

Confidence .57 .322 .000 .038 .039

Teacher Type .10 .010 .338 .000 .853

Level of Teaching .00 .000 .994 .010 .284

Familiarity .54 .295 .000 .035 .047


based reform efforts. Specifically, Brown, Kreis-
man, & Noble (1999) determined that students
had a more positive view of math, stated greater
confidence in the ability to be successful in math,
and wanted to learn more about math. However,
as Brown et al. caution, "It is important to keep
in mind that although students may have more
positive attitudes toward mathematics, this does
not automatically indicate they will have in-
creased achievement" (p. 19). In fact, recent re-
search (Papanastasiou, 2000) from the TIMSS
indicates no significant relationship between stu-
dent attitude and achievement. Thus, conclusions
based on teacher perception of student favorable
response should be made with caution.
Four variables (i.e., confidence, familiarity,
years of teaching ED, and preparation) signifi-
cantly related to favorable student response. Fur-
ther, two variables (confidence and familiarity)
uniquely and significantly contributed to this cri-
terion variable when all other variables were con-
trolled. Relatedly, Meyen, Vergason, and Whelan
(1993) noted that a positive attitude toward
teaching math and enthusiasm toward the subject
matter positively impacts student attitudes. How-
ever, this link between teacher confidence, famil-
iarity with the Standards, and favorable student
response requires further study.


In addition, barriers exist that impede suc-
cessful implementation of the Standards by spe-
cial and general educators when instructing
students with LD and ED. Teachers identified ad-
ministrative support and district curricula as rela-
tively minor issues. This indicates that within the
district and school levels, there is a general accep-
tance and adherence to the NCTM Standards.
However, teachers did note that a lack of ade-
quate materials was a considerable barrier to suc-
cessful implementation of activities based on the
Standards. The issue of inadequate materials has
also been noted in the literature as hindering
other teacher practices. For instance, in their
analysis of 28 surveys on general education teach-
ers' attitudes toward inclusion, Scruggs and Mas-
tropieri (1996) determined that only one-third of
teachers felt they had resources to adequately ad-
dress student needs. The lack of suitable materials
is especially disconcerting for students with LD
and ED who require manipulatives, multiple rep-
resentations, and varied examples and nonexam-
ples as teachers progress through the
concrete-semi-concrete-abstract phases of instruc-
tion that are recommended (Maccini & Gagnon,
2000). Further, the highly conceptual and prob-
lem-solving approach that is recommended by


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NCTM contributes to the importance of ade-
quate materials.
Having students with LD and ED learn to
solve complex, real-world math problems can
promote generalization to other real world tasks,
application of skills across time (Bottge & Hassel-
bring, 1993), and conceptual understanding of
mathematics (Van De Walle, 1994). This is im-
perative given that the Individuals with Disabili-
ties Education Act (IDEA, 1997) calls for all
students to have access to the general education
curriculum to the greatest extent possible and ac-
countability for learning the same material as
their peers without disabilities. However, in the
current study, respondents generally reported
teaching lower-level math courses to secondary
students with LD and ED (e.g., basic skills math,
middle school math), versus higher-level math
courses. This may have detrimental effects for stu-
dents with LD and ED as the lack of challenging
math content may hinder student achievement
and possibly limit future career choices in mathe-
matics. Additional research is necessary to identify
the extent to which students with LD and ED
have access to higher level math courses with ap-
propriate academic supports.
LIMITATIONS AND FUTURE RESEARCH
Although important results emanated from the
current study, caution must be made when gener-
alizing results beyond Maryland. Future studies
should include a national sample of general and
special education teachers' perceptions related to
implementation of the Standards with secondary
students with LD and ED. In addition to modifi-
cations in sampling procedures, future studies
should also include different research methods to
determine teachers' perspectives and behaviors.
One such method is triangulation, which com-
bines quantitative and qualitative research meth-
ods to investigate the variables of interest
(Campbell & Fiske, 1959). These methods repre-
sent different roles in data interpretation that will
be essential to the integration of information in-
volving various perspectives and behaviors (Sieber,
1973). For example, as "lack of materials" was tar-
geted as a common barrier, teachers should be in-
terviewed and observed regarding the types and
uses of materials perceived as necessary for effec-
tive implementation of activities based on the


Standards. Recommendations for future courses
of action can then be delineated.


IMPLICATIONS FOR PRACTICE
Important implications for both general and spe-
cial education teachers based on the current re-
search include the need to educate and support
teachers in their efforts to teach mathematics to
students with LD and ED in light of the goals of
the NCTM Standards. Such supports include:
TRAINING AND DISSEMINATION
Given that 55% of special educators indicated
they had not heard of the Standards, intensive
teacher training via workshops and inservices are
needed. This issue is particularly critical for high
school special education teachers in rural areas. It
is from this locale that the largest percentage of
respondents (28%, n = 8) had not heard of the
Standards. Thus, it is imperative that schools train
special education teachers on the revised Stan-
dards (NCTM, 2000) and approaches to meeting
the needs of students with disabilities in general
education classes. Additionally, information pro-
vided in teacher training programs is vital to help
educate teachers on the latest reform efforts.
Adequate Resources. Special and general edu-
cators both indicated the lack of materials as a
barrier to successful Standards implementation.
Teachers have consistently cited inadequate mate-
rials as a barrier to successful implementation of
educational reform (Scruggs & Mastropieri,
1996). However, the availability of resources does
not "reveal how these resources are used" or by
whom. And they say nothing about the quality of
that use (McLaughlin et al., 1995, p. 46).
Notwithstanding, adequate materials are one es-
sential component to successful implementation
of activities based on the Standards.
Teachers in the current study did not iden-
tify which materials were lacking. However, ade-
quate manipulatives are essential for students with
LD and ED when completing higher-level math
tasks. Although there are a number of effective re-
sources for teachers, one consideration should be
the use of materials that have been empirically
validated. For example, the Algebra Lab Gear
(colored blocks that represent numeric and vari-


Spring 2002


340










able amounts; Picciotto, 1990) is one validated
tool teachers may use to help students visualize a
problem and follow logical steps during activities
focusing on algebraic reasoning. This representa-
tion is supported within the goals of the Stan-
dards (NCTM, 2000). Additionally, students and
teachers could benefit from varied texts and re-
sources that present math activities embedded in
real-world problems. For example, the Connected
Math Series (Lappan, Fey, Fitzgerald, Friel, &
Phillips, 1998), which has an orientation and or-
ganization consistent with the NCTM Standards,
can be used as a supplement to traditional texts
(Reys et al., 1998).
One creative approach to a lack of materials
is currently being implemented within some sec-
ondary schools in Maryland. Students are allowed
to borrow or "rent-to-own" graphing calculators
that have been procured through donations or
agreements with local companies. This approach
assures that students have equal access to current
technology and can participate fully in math ac-
tivities within and outside of school.
Higher-level Mathematics. In the current
study, the most prevalent courses taught by re-
spondents involved general/basic skills mathemat-
ics, versus higher-level math, such as algebra and
geometry. Approximately an equal number of
middle and high school teachers responded to the
survey. It could be assumed that middle school
math would typically be taught by middle school
teachers. However, it is becoming more common
for nonlabeled students to take algebra in the sev-
enth or eighth grades and one would certainly ex-
pect a majority of students with LD and ED to be
enrolled in algebra by the high school level. As
IDEA assures students with disabilities have ac-
cess to the general education curriculum, it is im-
portant to consider whether these students are
enrolled in higher-level math courses with appro-
priate academic supports. Thus, there is a need
for future research to examine the placement of
students with LD and ED in math classes and
whether these students would be successful in
higher-level mathematics with supports that have
been empirically validated. For example, manipu-
latives (Huntington, 1994; Maccini, & Hughes,
2000) and cognitive strategy instruction
(Hutchinson, 1993) have been determined to
help students with mild disabilities in higher-level


mathematics. Future research on combinations of
these supports within the context of higher-level
mathematics courses is crucial to assist students in
meeting district and state requirements for gradu-
ation and for future occupations.
To assure positive academic outcomes, stu-
dents with LD and ED must have access to the
general education curriculum and rigorous stan-
dards, such as those set forth by NCTM. How-
ever, to meet the unique needs of these students,
and better prepare students for their "next envi-
ronment," it is imperative that teachers are given
adequate supports, training, and resources. As
stated by the National Research Council (2001),
"For people to participate fully in society, they
must know basic mathematics. Citizens who can-
not reason mathematically are cut off from whole
realms of human endeavor" (p. 1). This can be re-
alized with knowledgeable and empowered teach-
ers who are provided the necessary tools and
information to implement math instruction con-
sistent with the most recent reform movements
and empirically validated instructional ap-
proaches.


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ABOUT THE AUTHORS

PAULA MACCINI, Assistant Professor; and
JOSEPH CALVIN GAGNON, Faculty Research
Assistant, Department of Special Education, Uni-
versity of Maryland, College Park.

Please address all correspondence to Paula Mac-
cini, University of Maryland, Department of Spe-
cial Education, 1308 Benjamin Building, College
Park, MD 20742; 301/405-7443
E-mail: pm147@umail.umd.edu


This research was supported by Grant
#H324N990029, CFDA #84.324N Office of
Special Education Programs, U.S. Department of
Education, Office of Special Education and Reha-
bilitative Services. The views expressed herein do
not necessarily represent those of the U.S. De-
partment of Education.

Manuscript received January 2001; accepted Oc-
tober 2001.




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Spring 2002


344




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