Exepioa Chlde I
VoL 68, No.3, pp. 325344.
�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 higherlevel 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 tandardsdriven 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 longterm general education outcomes
(Nolet & McLaughlin, 2000; Sands, Adams, &
Stout, 1995; Smith, 1990). In the sections that
follow, the National Council of Teachers of
Exceptional Children
325
Mathematics (NCTM) Standards are discussed
relative to standardsbased 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 standardsdriven 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 problemsolving 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 ruledriven computation. Student
understanding of mathematical concepts is pro
moted via active engagement with manipulatives
or concrete objects, applying math to realworld
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 problemsolving.
The NCTM Standards are a critical
component of the Standardsdriven
reform movement.
The NCTM Standards are a critical com
ponent of the Standardsdriven 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 openended problemsolving 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 Standardsbased 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
lemsolving, may negatively impact these
students. Such ramifications may be observed
within subsequent classes where teachers utilize a
problemsolvingbased 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
fifthgrade 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 problemsolving. For instance, many
students with LD experience problems: (a) select
ing and employing appropriate operations during
problemsolving (Montague & Bos, 1990), (b)
representing problemsolving 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 Standardsbased ac
tivities. For example, Manouchehri (1998) noted
that teachers who lack familiarity with conceptu
allybased 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 standardsbased 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 Standardsbased 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
dardsbased activities. Nor is there research on
Exceptional Children
327
Many adolescents with LD experience
math difficulties, particularly in problem
application, and generally perform at the
fifthgrade 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 standardsbased 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 Standardsbased 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 Standardsbased activities,
teacher perception of student response to Stan
dardsbased activities), (c) barriers to implementa
tion of Standardsbased 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 openended 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 openended
questions) related to implementation of activities
based on the Standards.
The survey was developed via a fourstep
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
(0599, 600600, 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 617 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
612) 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 selfcontained
class). If more than two special education teacher
names and two general educator names were pro
vided per school, a twostage 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 followup 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 followup 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.
Exceptional Children
329
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
0599 83 (18) 52 (16)
600999 143 (32) 68 (21)
1,000 and more 131 (29) 69 (21)
Total Urban 357 (79) 139 (58)
Suburban
0599 6 (1) 12 (4)
600999 10 (2) 24 (7)
1,000 and more 4 (<1) 6 (2)
Total Suburban 20 (4) 42 (13)
Rural
0599 35 (8) 35 (11)
600999 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., 0599, 600999, 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 makeup
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 onethird of the 137 schools were in each
population category, with 32.1% (n = 44) having
up to 599 students, 32.8% (n = 45) with 600999
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 ttests 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
chisquare 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. Fortyeight 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 teachertype
(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 "15." The most common re
sponse to the range of students labeled ED with
no special services was "15 ." 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, coteaching) within general educa
tion math class, 43% of special educators (n = 15)
noted "None." The second most frequent re
sponse to this question was "610 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 "15 students." In terms of
students with ED receiving special services (e.g.,
consultative services and coteaching) within gen
eral education math class, 63% of special educa
tors (n = 22) noted "None." The second most
frequent response to this question was "15 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 "15 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 higherlevel 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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331
TABLE 2
Demographic Characteristics
No. (%) Significance
Characteristics Special Education Teachers General Education Teachers 2 p
Gender
Female
Male
Age
2029
3039
4049
5059
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
15
610
1115
1620
21 or >
Years of Experience
Teaching Math to Stu
dents with ED?
<1
15
610
1115
1620
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 12 34 56 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, MannWhitney 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.
Exceptional Children
333
TABLE 4
Nature j .U,',. , Courses
Mean Rating of Methods Courses Signcance
on a 5Point 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. Fiftyfive 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. Seventyone 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 MannWhit
A primary concern is that many special
education teachers indicated they were
unfamiliar with the goals of the NCTM
Standards.
Spring 2002
334
TABLE 5
Teacher Familiarity, Confidence, and Student Response
Mean Rating on 5Point 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 oneway
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
Exceptional Children
335
TABLE 6
Effect Barrier Has on NCTM Standards Implementation
Mean Rating of Barrier on 5Point 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 ttest 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 ttest 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 strongtomoderate
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.
Spring 2002
336
TABLE 7
NonHierarchical Regression Analysis for Teacher Perception of Confidence
Initial Entry of the Construct Construct Entered in Last Position
R Squared
Simple R R Squared pvalue revalue
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 ttest 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 ttest for
Beta weights was statistically significant for four
variables (i.e., confidence, familiarity, years teach
ing ED, and preparation);(see Table 9). The ttest
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
Standardsbased activities, (d) significant barriers
(i.e., lack of materials) to successful implementa
Exceptional Children
337
TABLE 8
NonHierarchical Regression Analysis for Teacher Perception of Familiarity
Initial Entry of the Construct Construct Entered in Last Position
R Squared
Variables Simple R R Squared pvalue 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 Standardsbased 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 standardsbased 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 concretesemiconcreteabstract phases
of instruction that are recommended
Spring 2002
338
TABLE 9
NonHierarchical Regression Analysis for Teacher Perception of Student Response
Initial Entry of the Construct Construct Entered in Last Position
Variables Simple R R Squared pvalue pvalue
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 onethird 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
concretesemiconcreteabstract phases of instruc
tion that are recommended (Maccini & Gagnon,
2000). Further, the highly conceptual and prob
lemsolving approach that is recommended by
Exceptional Children
339
NCTM contributes to the importance of ade
quate materials.
Having students with LD and ED learn to
solve complex, realworld 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 lowerlevel math courses to secondary
students with LD and ED (e.g., basic skills math,
middle school math), versus higherlevel 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 higherlevel 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
realworld 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 "renttoown" 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.
Higherlevel Mathematics. In the current
study, the most prevalent courses taught by re
spondents involved general/basic skills mathemat
ics, versus higherlevel 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 higherlevel 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
higherlevel 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 higherlevel
mathematics. Future research on combinations of
these supports within the context of higherlevel
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; 301/4057443
Email: 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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344
