Nature and type of mathematics instructional approaches by special and general education teachers
CITATION
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/IR00000480/00001
 Material Information
Title: Nature and type of mathematics instructional approaches by special and general education teachers
Series Title: Maccini, P., & Gagnon, J. C. (2006). Nature and type of mathematics instructional approaches by special and general education teachers. Exceptional Children, 72, 217-234.
Physical Description: Journal Article
Creator: Gagnon, Joseph
 Notes
Abstract: A nationwide random sample of 179 secondary general education math and special education teachers completed a survey asking them about their use of specific instructional practices to help teach math to students with learning disabilities (LD) and emotional/behavioral disorders (EB/D) and their use of specific assessment accommodations with these students. Although general education teachers were generally more knowledgeable about higher level mathematics content (e.g., algebra) than special education teachers, they were less likely to report that they used specific instructional practices and testing accommodations. The number of methods courses taken by teachers and knowledge of course topics both contributed to the number of instructional practices and accommodations used by teachers.
Acquisition: Collected for University of Florida's Institutional Repository by the UFIR Self-Submittal tool. Submitted by Joseph Gagnon.
Publication Status: Published
 Record Information
Source Institution: University of Florida Institutional Repository
Holding Location: University of Florida
Rights Management: All rights reserved by the submitter.
System ID: IR00000480:00001

Full Text


1ExceptionalChldren.


Vol 72, No. 2, pp. 217-234.
�2006 Council fr Exceptional Children.


Mathematics Instructional

Practices and Assessment

Accommodations by Secondary

Special and General Educators


PAULA MACCINI
University ofMaryland, College Park
JOSEPH CALVIN GAGNON
George Mason University




ABSTRACT: A nationwide random sample of 179 secondary general education math and special ed-
ucation teachers completed a survey asking them about their use ofspecific instructional practices to
help teach math to students with learning disabilities (LD) and emotional/behavioral disorders
(EB/D) and their use of specific assessment accommodations with these students. Although general
education teachers were generally more knowledgeable about higher level mathematics content
(e.g., algebra) than special education teachers, they were less likely to report that they used specific
instructional practices and testing accommodations. The number of methods courses taken by
teachers and knowledge of course topics both contributed to the number of instructional practices
and accommodations used by teachers.


United States continue to place
increasingly higher demands on
youth with and without disabil-
ities. These demands are mea-
sured through mandatory district and state
assessments that directly affect whether or not stu-
dents graduate (Gagnon & McLaughlin, 2004).
For example, the No Child Left Behind Act


(NCLB, 2001) includes a focus on high standards
and accountability for student learning. The Indi-
viduals With Disabilities Education Act (1997) as-
sures that students with special needs are also
included in current educational reform via man-
dated access to the general education curriculum
to the greatest extent possible and participation in
assessments with accommodations, as needed.
Subsequently, general and special educators are


Exceptional Children







faced with the task of assisting youth with disabili-
ties, including those with learning disabilities
(LD) and emotional/behavioral disorders (E/BD),
to achieve maximum benefit from the curriculum
and progress toward academic goals.
Provisions within NCLB (2001) and IDEA
(1997) also increase the expectations of teachers.
To assist students with special needs, teachers
must have the knowledge and training to provide
effective instructional practices and assessment ac-
commodations. For example, in the area of math-
ematics, teachers are expected to provide effective
instruction on curriculum that addresses higher
level math skills and encompasses open-ended,
problem-solving tasks (see Maccini & Gagnon,
2000) as set forth by the National Council of
Teachers of Mathematics Standards (NCTM,
2000). Currently, 42 states (Blank & Dalkilic,
1992, as noted in Thurlow, 2000) have developed
state math standards consistent with NCTM.
The use of effective instructional proce-
dures and testing accommodations are critical be-
cause most youth with LD and E/BD experience
difficulty acquiring and retaining math skills,
such as algebraic reasoning skills (Maccini, Mc-
Naughton, & Ruhl, 1999) and basic skills/com-
putational skills (Algozzine, O'Shea, Crews, &
Stoddard, 1987). These students also have diffi-
culty passing math tests aligned with state stan-
dards (Thurlow, Albus, Spicuzza, & Thompson,
1998). For example, Thurlow and colleagues de-
termined that 83% of nondisabled eighth-grade
students passed a Basics Standards Math Test, in
comparison to 42% of students with E/BD and
34% of students with LD.
Given the difficulties that most students
with LD and E/BD experience with mathematics,
it is important to identify the instructional prac-
tices and- assessment accommodations that help
these students succeed in math. In this article, in-
structional practices refer to both empirically vali-
dated and recommended practices for teaching
math to students with LD and/or E/BD. Empiri-
cally validated and recommended instructional
practices and assessment accommodations are de-
fined and discussed relative to the literature and
the purpose of the current study.


INSTRUCTIONAL PRACTICES
As mandated by IDEA (1997), students with dis-
abilities should have access to the general educa-
tion curriculum and are entitled to empirically
validated instructional practices that help them
succeed. Empirically validated practices refer to
research-based approaches to teaching math skills
(Wilson, Majsterek, & Jones, 2001). Maccini and
Gagnon (2000) determined that special and gen-
eral education teachers of secondary students with
LD and E/BD noted using a number of empiri-
cally validated approaches for teaching math to
these students. These approaches included the fol-
lowing: (a) use of objects for conceptual under-



Given the difficulties that most students
with LD and E/BD experience with
mathematics, it is important to identify
the instructional practices and assessment
accommodations that help these students
succeed in math.



standing; (b) peer or cross-age tutoring strategies;
and (c) organizational strategies for retention
(e.g., cue cards of strategy steps, graphic organiz-
ers, mnemonics, and time for additional practice).
Maccini and Gagnon (2000) also found
that teachers noted using other instructional prac-
tices with students with LD and E/BD in math:
(a) use of calculators; (b) assignment modifica-
tions (i.e., adjusted workloads); and (c) increased
time for activities and tests. Assignment modifica-
tions included reducing classwork problems and
homework problems and adjusting the workload
via color coding or circles for cuing. Although
these practices have yet to be validated with stu-
dents with LD and E/BD, they were frequently
noted, perhaps because they are recommended in
special and general education textbooks. For ex-
ample, in an introductory text for teaching math
to students with special needs, experts (Bley &
Thornton, 2001) recommend using visual cues
and reduced classwork and homework problems.
These recommended practices presumably help


Winter 2006







math teachers plan and implement instruction
that is beneficial for all students and help teachers
from "spending an inordinate amount of time
with one child to the exclusion of others" (Bley &
Thornton, p. 22). Though cited by teachers in a
statewide investigation (Maccini & Gagnon,
2002), no national studies exist that focus on
teachers' use of empirically validated and recom-
mended instructional practices to assist secondary
students with LD and E/BD in math.


ASSESSMENT
ACCOMMODATIONS
The National Council of Teachers of Mathemat-
ics (NCLB, 2001) mandates increased participa-
tion and accountability for all students, including
students with disabilities, on high-stakes assess-
ments that are tied to rigorous math standards.
Assessment accommodations are necessary for
some measures to help "level the playing field" for
students with special needs (Thompson, Blount,
& Thurlow, 2002). Experts define accommo-
dations as modifying assessment procedures (e.g.,
scheduling, timing, presentation) or materials
(e.g., setting, response) "that enable students with
disabilities to participate in an assessment in a
way that allows abilities to be assessed rather than
disabilities" (Thurlow, Elliott, & Ysseldyke, 1998,
pp. 28-29). In a statewide survey, Maccini and
Gagnon (2000) determined that special and gen-
eral education teachers of secondary students
with LD and E/BD reported using a number of
accommodations, including (a) presentation
(e.g., color coding); (b) response (e.g., using ref-
erence materials such as cue cards or charts of
strategy steps); (c) setting (e.g., behavioral modi-
fications such as seating accommodation); (d)
timing/scheduling (e.g., extended time on tests);
and (f) calculators. However, only timing accom-
modations (Helwig, Rozek-Tedesco, Tindal,
Heath, & Almond, 1999) and oral presentation
(Calhoon, Fuchs, & Hamlett, 2000) have been
empirically validated in math. The remaining ac-
commodations reported included those that are
commonly allowed on local and large-scale assess-
ments (Menikoff, 2004). To date, no national
studies exist that focus on teachers' use of empiri-
cally-validated and recommended assessment


accommodations to assist secondary students with
LD and/or E/BD in math.
Also lacking in the research on mathematics
instruction is the identification of factors that
may predict the number of instructional practices
and assessment accommodations made for stu-
dents with LD and E/BD. No information is
available concerning (a) the contribution of
teacher characteristics (e.g., number of years
teaching); (b) special and general education math
courses taken to teach math to students with LD
and E/BD); (c) knowledge (e.g., familiarity with
subject matter); (d) teacher type (e.g., general vs.
special education teacher); and (e) classroom vari-



To date, no national studies exist that
focus on teachers' use of empirically
validated and recommended assessment
accommodations to assist secondary
students with LD and/or E/BD in math.



ables (e.g., number of students per class that need
math assistance) in predicting the number of re-
search-based instructional adaptations and assess-
ment accommodations made by teachers.
However, in a related study, Graham, Harris,
Fink, and MacArthur (2003) found that, in addi-
tion to the amount of time spent writing, both
teacher variables (e.g., number of years teaching)
and classroom variables (e.g., number of students
needing special education services) predicted the
number of instructional practices teachers used
with students who experienced difficulty with
writing. Teacher type may also predict the num-
ber of instructional practices or assessment ac-
commodations made for students with LD and/or
E/BD. Researchers (Schumm et al., 1995) found
that general education teachers allow fewer assess-
ment accommodations. Also, as the number of
methods courses taken by teachers positively af-
fects student learning in secondary math courses
(Monk, 1994), it is possible that the number of
methods courses taken by teachers also influences
the number of instructional practices and assess-
ment accommodations.


Exceptional Children


219







TABLE 1
Participant Characteristics
No. (%) Significance
Special General
Education Education
Characteristics Teachers Teachers df X2 p
Gender
Female 69 (39) 53 (30) 1 .124 .725
Male 29 (17) 25 (14)

Age
20-29 7 (4) 6 (3) 3 2.570 .463
30-39 18(10) 19(11)
40-49 42 (24) 24 (14)
50-or > 32(18) 28(16)

Educational Level
Undergraduate 36 (21) 31 (18) 1 .317 .574
Graduate 61 (35) 44 (26)


PURPOSE
Provisions within NCLB (2001) and IDEA
(1997) require that students with special needs be
exposed to the same curriculum as their nondis-
abled peers, to the greatest extent possible. Also,
as mandated by IDEA, all students are required to
participate in state assessments (with the excep-
tion of those that participate in alternate assess-
ments) that are linked to the general education
curriculum. The challenge, then, is to help educa-
tors provide effective instructional practices and
appropriate assessment accommodations to help
all students achieve within the general education
mathematics curriculum and meet high stan-
dards. Using a nationwide sample, the current
study was designed to answer three research ques-
tions. First, what specific instructional practices
do special and general education teachers report-
edly use for students with LD and E/BD during
instruction on basic math computation skills and
problem-solving tasks? Second, what specific ac-
commodations do special and general education
teachers reportedly make for students with LD
and E/BD when assessing basic math skills and
when assessing problem-solving tasks? Third,
what factors predict the number of instructional
practices and assessment accommodations general
and special education teachers reportedly make
for students with LD and E/BD?


METHOD


SURVEYS
A survey of secondary general and special educa-
tors teaching math to students with LD and
E/BD was developed across three central topics:
(a) teacher background information, (b) teacher
perceived knowledge of secondary math topics,
and (c) specific instructional practices and accom-
modations teachers use for students with LD and
E/BD during instruction and when assessing basic
math/computation skills and problem-solving
tasks (see Tables 1, 2, and 3). For teacher back-
ground information, respondents were asked to
provide information on their age, gender, educa-
tional level, years teaching students with LD
and/or E/BD, teaching credentials, math methods
courses taken, and type of math courses currently
taught (e.g., prealgebra, algebra, algebra II, alge-
bra II/trigonometry, geometry, statistics/probabil-
ity, general mathematics or basic skills
mathematics, integrated/unified high school
mathematics, other). In addition, teachers com-
pleted a 4-point Likert-type scale to indicate their
level of preparation for teaching math to students
with LD and/or E/BD after completing their
methods courses (ranging from very prepared to
very unprepared = 4).
The second portion of the survey focused
on teacher perceived knowledge of secondary


Winter 2006


220







TABLE 2
Participants' Credentials and Current Teaching Responsibilities
No. (%) Significance
Special General
Education Teachers Education Teachers df x2 p ES
Characteristics Yes No Yes No

Secondary math teaching
credential 7 (4) 94 (52) 76 (43) 2 (1) 1 144.966 .000 .90
Elementary math teaching
credential 18 (10) 83 (46) 9 (5) 69 (39) 1 1.357 .244 -.09
Special education teaching
credential 97 (54) 4 (2) 5 (3) 73 (41) 1 144.238 .000 -.90
Teaches Prealgebra 62 (34) 39 (22) 21 (12) 57 (32) 1 21.020 .000 -.34
Teaches Algebra 46(26) 55 (31) 45 (25) 33 (18) 1 2.599 .107 .12
Teaches Geometry 27(15) 74(41) 25(14) 53(30) 1 .604 .437 .06
Teaches General
Mathematics or Basic
Skills (HS) 65(36) 36 (20) 13 (8) 65 (36) 1 40.710 .000 -.48
Teaches Algebra II 6 (3) 95 (53) 13 (8) 65(36) 1 5.377 .021 .17
Teaches Algebra II/
Trigonometry 1 (0) 100 (56) 4 (2) 74 (42) 1 - .169a .13
Teaches Statistics/
Probability 3 (2) 98 (55) 6 (3) 72(40) 1 - .181a .11
Teaches Integrated/Unified
High School Math 6 (3) 95 (53) 7 (4) 71 (40) 1 .601 .438 .06
Note. ES = coefficient phi; - = Insufficient cell size to calculate 2; a = Fisher's exact test value.


math topics. Teachers completed a 4-point Likert-
type scale (ranging from great deal = 1 to very little
or nothing = 4) to indicate their level of perceived
knowledge to teach the eight math topics. For the
final section of the survey, teachers indicated if
they used specific instructional practices to help
students with LD and/or E/BD with basic
skills/computation and problem-solving tasks
from a list of 14 choices (see Tables 4 and 5).
Teachers also indicated if they used specific assess-
ment accommodations to help students with LD
and/or E/BD with basic skills/computation and
for problem solving tasks from a list of eight
choices (see Tables 4 and 5).
One version of the survey was constructed
for general educators and another for special edu-
cation teachers to address their unique teaching
situations. The survey questions were identical,
with the exception of three questions that applied
solely to special education teachers (number of


years as a special education teacher, number of
students on caseload, current teaching position)
and one question for general education teachers
(number of years as a math teacher). Finally, it
should be noted that coding for data entry was
conducted for 25% of the responses. Data was
entered accurately as the obtained reliability was
95%.
SAMPLE
Survey Sampling Procedures. The target pop-
ulation for the current study consisted of two
groups of secondary teachers: (a) general educa-
tion math teachers who teach students with LD
and/or E/BD, and (b) special education teachers
who teach math to students with LD and/or
E/BD and/or collaborate with the general educa-
tion math teachers. First, a random sample of 750
special and general educators from all public high
schools in the United States was obtained from


Exceptional Children


221







TABLE 3
Years Teaching and Number and Nature ofMethods Courses
Mean Rating ofMethods
Courses on a 4-Point Scalea Significance
Special General
Education Education
Survey Questions Teachers Teachers df t p ES

How many years have you taught 12.36 1.15 176 -12.433 .000 .68
students with LD and/or E/BD?
How many general education math 1.61 3.16 91 3.719 .000 .36
methods courses have you taken?
How many special education math 1.27 .56 163 -4.309 .000 .32
methods courses have you taken that
addressed teaching math to students
with LD and E/BD?
How prepared were you to teach 2.28a 2.75a 123 2.852 .005 .25
math to students with LD and/or
E/BD after completing your math
education methods courses?
How prepared were you to teach 2.34a 1.74a 111 -4.171 .000 .37
math to general education students
after completing your math
education methods courses?
How prepared were you to teach 1.94a 2.07 a 88 -.868 .388 .09
math to students with LD and/or
E/BD after completing your special
education courses that focused on
teaching math?

Note. LD = learning disabilities; E/BD = emotional/behavioral disorders; ES = Cohen's d.
a4-point scale ranging from 1 = very prepared to 4 = very unprepared.


Quality Education Data (QED School Personnel
Data Base, 2000/2001). Approximately 40% (n =
325) of the teachers sampled were general educa-
tors listed as having a special education class and
currently teaching (a) algebra, (b) business/
consumer math, (c) general/applied math, (d) ge-
ometry, (e) prealgebra, or (f) remedial math. Ap-
proximately 60% of the total sample (n = 425)
were special educators. These teachers were listed
as currently teaching students who were emotion-
ally challenged, learning challenged, or had spe-
cial needs and a special needs resource. The
percentage of special educators sampled was
greater than general educators, as the list of spe-
cial educators was not limited to those teachers
who teach only mathematics. Thus, more special
educators needed to be sampled to account for in-


eligibility (e.g., special education teachers who
teach students with learning challenges but do
not teach math). Surveys were then mailed to the
targeted teachers.
Response Rate. Of the 750 surveys mailed,
257 surveys were excluded from the analysis be-
cause of concerns about (a) ineligibility (teachers
either returned surveys with a note or made con-
tact by phone saying they do not teach relevant
courses; n = 250), or (b) incorrect school address
(n = 7). Thus, a total of 493 (278 special educa-
tion; 215 general education) teacher surveys met
the criteria for inclusion. Of these, 101 special ed-
ucation teachers returned the survey for a response
rate of 36%, and 78 general education teachers re-
turned the surveys for a return rate of 36%. The
response rate remained below a common survey


Winter 2006







return rate of 50% (Weisberg, Krosnick, &
Bowen, 1989). This occurred even though there
were two mailings, a follow-up postcard sent be-
tween the mailings, and a phone call to all eligible
participants after the second mailing.

DEMOGRAPHICS
Of the 176 teachers that responded to the ques-
tion (3 were missing), 44% (n = 78) were general
education teachers and 56% (n = 98) were special
education teachers who teach math to students
with LD and/or E/BD (see Tables 1 and 2). Fur-
ther, 69% (n = 122) of the total respondents were
female, most of whom were special education
teachers (n = 69, 57%). The majority of respon-
dents noted being 40 years of age or older (n =
126, 72%) and holding graduate degrees (n =
105, 61%). No significant differences were deter-
mined among general and special educators with
regard to gender, age, or educational level.
To determine if there were statistical differ-
ences between general and special education
teachers on the variables included in Tables 2 and
3, chi square and t-tests were conducted. If statis-
tically significant differences were found, the
magnitude of the effect, or effect size (ES), was
computed (Cohen's d for the t-test; coefficient phi
for chi square analysis). Cohen's d values range
from .2 (small), .5 (medium), to .8 (large). For
coefficient phi, the range is 0 (proportions of the
sample are equal to the hypothesized proportions)
to 1 (proportions of the sample are as divergent as
possible to the hypothesized proportions).
As can be seen from Tables 2 and 3, there
were a number of differences between general and
special education teachers. Special education
teachers were almost 11 times more likely to teach
students with LD and/or E/BD, than general ed-
ucation teachers. In addition, special education
teachers were almost 20 times more likely to have
special education credentials than general educa-
tion participants, but more than 10 times less
likely to hold secondary math credentials. As ex-
pected, no significant difference was determined
among general and special educators with regard
to holding an elementary math credential.
Statistical significance (t= -7.001, df= 89,
p = .000; ES = .60) was determined across teacher
type and the average number of students with LD


and/or E/BD who are provided assistance (e.g., in
class support, resource room), with special educa-
tion teachers noting a greater average of students
who are provided assistance (M= 13.73, SD =
10.89) than general education teachers (M'I
3.08,. = 3.51). Concerning current teaching
position, 60% (n = 61) of special educators taught
full time in either a resource room or segregated
classroom setting. Only 12% of special educators
(n = 12) reported being a full-time consultant or
team teaching on a full-time basis.
Teachers also reported the type of math
courses they currently teach to students with LD
and/or E/BD. Special education teachers were five
times more likely to teach general math or basic
skills classes and three times more likely to teach
prealgebra classes to students with LD and/or
E/BD than were general education participants.
There was insufficient cell size to calculate chi-
square statistics for the number of teachers teach-
ing algebra II/trigonometry classes and
statistics/probability classes. However, general ed-
ucation teachers were twice as likely to teach alge-
bra II to students with LD and/or E/BD than
were special education teachers. No statistically
significant differences were found across teacher
type for algebra, geometry, and integrated/unified
mathematics.
Teachers were asked to indicate the number
of general and special education methods courses
taken that addressed teaching matlV to students
with LD and E/BD and their level of preparation
for teaching math to these students. GCeneral edu-
cation teachers were almost twice as likely to take
general education riethods courses than were spe-
cial education participants. Special education
teachers were more than twice as likely to take
special education methods courses than were geni
eral education participants.
For teachers who noted taking at least'one
special or general education methods course (n
187), respondents also reported their level qf
preparation for teaching math to students with
LD and/or E/BD as a result of the metho.ds
courses they had completed. For general educa-
tion methods courses completed, special eduica-
tion teachers indicated feeling more prepared to
teach math to students with LD and/or E/BD (M
= 2.28, SD = .95) than were general education
teachers (M = 2.75, SD = .92); whereas general


Exceptional Children


223







education teachers felt more prepared to teach
math to general education students (M = 1.74,
SD = .69) than were special education teachers
(M= 2.34, SD = .93). There were no statistically
significant differences in teachers' perceptions to
teach math to students with LD and E/BD as a
result of taking special education methods courses
(M =2.07, SD = .72 for general educators; M =
1.94, SD = .67 for special educators).


RESULTS

RESEARCH QUESTION 1:
INSTRUCTIONAL PRACTICES
Teachers were queried on their use of 14 instruc-
tional practices with students with LD and/or
E/BD during instruction of basic math
skills/computational tasks (see Table 4) and multi-
step problem-solving tasks (see Table 5). Overall,
the mean number of instructional practices on
basic math skills/computational tasks they re-
ported using was 9.13 (SD = 2.86) for special ed-
ucators and 6.17 (SD = 2.89) for general
education teachers. The mean number of instruc-
tional practices they reported using on multistep
problem-solving tasks was 8.46 (SD = 3.08) for
special educators and 9.09 (SD = 2.57) for gen-
eral education teachers. A statistically significant
difference existed 1Letween the groups on the aver-
age number of instructional practices used with
basic math facts (t = -6.860, df= 177, p = .000;
ES = .46), with special educators reporting using
more instructional practices than general educa-
tors. No statistically significant differences were
noted between special and general educators for
the overall use of these procedures with problem-
solving tasks.
Basic Skills/Computational Tasks. As can be
seen in Table 4, special educators were more likely
to report that they used the following instruc-
tional procedures with students with LD and/or
E/BD when teaching basic skills/computational
tasks: individualized instruction by teacher, addi-
tional practice, reduced classwork problems, ex-
tended time on assignments, problems read to
students, cue cards of strategy steps, individual-
ized attention given to student by classroom aide,
and graphic organizers. Across special education


teachers, the four most reported applied instruc-
tional practices during basic skills/computational
tasks included: calculators, individualized instruc-
tion by teacher, extended time on assignments,
and problems read to students. General education
teachers reported using the following most fre-
quent instructional practices: calculators, ex-
tended time on assignment, individualized
instruction by teacher, and peer or cross-age tu-
toring.
Problem-Solving Tasks. As shown in Table 5,
special educators were more likely to report that
they used the following instructional procedures
with students with LD and/or E/BD when teach-
ing multistep problem-solving tasks: individual-
ized instruction by teacher, additional practice,
reduced classwork problems, extended time on as-
signments, reduced homework problems, prob-
lems read to students, cue cards of strategy steps,
use of concrete objects, and graphic organizers.
Across special education teachers, the four most
reported applied instructional practices during
multistep problem-solving tasks included: prob-
lems read to students, individualized instruction
by teacher, extended time on assignments, and
calculators. General education teachers reported
most frequent use of the following instructional
practices: calculators, individualized instruction
by teacher, extended time on assignment, and
peer or cross-age tutoring.
RESEARCH QUESTION 2:
ASSESSMENT ACCOMMODATIONS
Teachers were queried on their use of eight assess-
ment accommodations with students with LD
and/or E/BD while assessing student knowledge
of basic math skills/computational tasks (see Table
4) and multistep problem-solving tasks (see Table
5). Overall, the mean number of assessment ac-
commodations on basic math skills/computa-
tional tasks they reported using was 4.52 (SD =
1.75) for special educators and 3.14 (SD = 1.36)
for general education teachers. The mean number
of assessment accommodations they reported
using on multistep problem-solving tasks was
4.54 (SD = 2.05) for special educators and 3.18
(SD = 1.40) for general education teachers. Statis-
tically significant differences existed between the
groups for the average number of assessment
accommodations used with basic math facts


Winter 2006








TABLE 4
Instructional Practices and Assessment Accommodations Used During Instruction on Basic Math
Skills/Computational Tasks

No. (%) Significance
Special General
Education Teachers Education Teachers df X2 p ES
Characteristics Yes No Yes No


Type of Instructional Practices
Individualized
instruction by teacher 93 (52) 8 (4) 57 (32) 21 (12)
Additional practice 83 (47) 18 (10) 31 (17) 47 (26)
Reduced classwork
problems 74 (41) 27 (15) 33 (19) 45 (25)


Extended time on
assignments
Reduced homework
problems
Color coding
Peer or cross-age
tutoring
Problems read to
students


93 (52) 8 (4) 61 (34) 17 (10)

58 (33) 43 (24) 31 (17) 47 (26)
23 (13) 78 (44) 9 (5) 69 (38)

64 (36) 37 (20) 48 (27) 30 (17)

93 (52) 8 (5) 40 (22) 38 (21)


Cue cards of strategy
steps 44 (25) 57 (32) 8 (4) 70 (39)
Use of concrete objects 66 (37) 35 (20) 38 (21) 40 (22)


Individualized attention
by class aide
Calculators
Graphic organizers
Mnemonics


55 (30) 46 (26) 21(12) 57 (32)
98(54) 3 (2) 71 (40) 7 (4)
36 (20) 65 (36) 13 (8) 65 (36)
42(24) 59(33) 20(11) 58(32)


1 11.706 .001 .26
1 34.268 .000 .44

1 17.545 .000 .31

1 7.050 .008 .20

1 5.504 .019 .18
1 3.783 .052 .15

1 .063 .802 .02

1 38.364 .000 .46

1 23.690 .000 .36
1 4.999 .025 .17

1 13.655 .000 .28
1 - .106a .13
1 7.972 .005 .21
1 4.941 .026 .17


Type of Assessment Accommodations
Reduced problems on
tests 60 (34) 41 (23) 18 (10) 60 (33)
Extended time on tests 94 (53) 7 (4) 67 (37) 11 (6)
Calculators 93 (52) 8 (4) 69 (39) 9 (5)
Cue cards of strategy
steps 28 (15) 73 (41) 7 (4) 71 (40)
Color coding 13 (7) 88 (50) 4 (2) 74 (41)
Use of concrete objects 39 (22) 62 (35) 20 (11) 58 (32)


Problems read to
students
Individualized attention
given by class aide


86(48) 15 (8) 37(21) 41(23)

44(24) 57(32) 23 (13) 55 (31)


1 23.624 .000 .36
1 2.503 .114 -.12
1 .670 .413 .06

1 9.835 .002 .23
1 3.070 .080 .13
1 3.352 .067 .14

1 29.117 .000 .40

1 3.724 .054 .14


Note. ES = coefficient phi; - = Insufficient cell size to calculate x2; = Fisher's exact test value.





Exceptional Children


225








TABLE 5
Instructional Practices Used During Instruction on Multistep Problem-Solving Tasks
No. (%) Significance
Special General
Education Teachers Education Teachers df x2 p ES
Characteristics Yes No Yes No


Type of Instructional Practices
Individualized
instruction by teacher 90 (51) 11 (6) 56 (31) 22 (12)
Additional practice 77 (43) 24 (13) 34 (19) 44 (25)


Reduced classwork
problems
Extended time on
assignments
Reduced homework
problems
Color coding
Peer or cross-age
tutoring
Problems read to
students
Cue cards of strategy
steps
Use of concrete objec


Individualized attention
by class aide
Calculators
Graphic organizers
Mnemonics


62 (35) 39 (22) 29 (16) 49 (27)

87 (49) 14 (8) 53 (29) 25 (14)

58 (33) 43 (24) 22 (12) 56 (31)
17 (10) 84 (47) 5 (3) 73 (41)

57 (32) 44 (25) 46 (25) 32 (18)

91 (51) 10 (6) 45 (25) 33 (18)

48 (27) 53 (30) 13 (7) 65(36)
ts 63 (35) 38 (21) 28 (15) 50 (28)


50 (28) 51 (29) 25(14) 53 (29)
87 (49) 14 (8) 66 (36) 12 (7)
34 (19) 67 (37) 9 (5) 69 (38)
33 (18) 68 (38) 16 (9) 62 (35)


1 8.774 .003 .22
1 19.913 .000 .33

1 10.318 .001 .24

1 8.545 .003 .22

1 15.203 .000 .29
1 4.434 .035 .16

1 .116 .733 -.03

1 25.324 .000 .38

1 18.655 .000 .32
1 12.346 .000 .26

1 5.507 .019 .18
1 .082 .774 .02
1 11.804 .001 -.26
1 3.274 .070 -.14


Type of Assessment Accommodations
Reduced problems on
tests 66 (37) 35 (20) 22 (12) 56 (31)
Extended time on tests 90 (50) 11 (6) 63 (35) 15 (9)
Calculators 89 (50) 12 (7) 67 (37) 11 (6)
Cue cards of strategy
steps 30 (17) 71 (40) 8 (4) 70 (39)
Color coding 13 (8) 88 (49) 6 (3) 72 (40)
Use of concrete objects 49 (28) 52 (29) 17 (9) 61 (34)


Problems read to
students
Individualized attention
by class aide


82(46) 19 (11) 41(23) 37(20)

40(22) 61(34) 24 (14) 54 (30)


1 24.292 .000 .37
1 2.465 .116 .12
1 .194 .660 .03

1 9.953 .002 .24
1 1.244 .265 .08
1 13.500 .000 .28

1 16.774 .000 .31

1 1.495 .221 .09


Note. ES = coefficient phi.


Winter 2006


226







(t = -5.753, df= 177, p = .000; ES = .40) and
problem-solving tasks (t = -5.044, df= 177, p =
.000; ES = .35), with special educators reporting
using more assessment accommodations than
general educators.
Basic Skills/Computational Tasks. As can be
seen in Table 4, special educators reported that
they more likely used the following accommoda-
tions with students with LD and/or E/BD when
assessing knowledge on basic skills/computational
tasks: reduced problems on tests, cue cards of
strategy steps, and problems read to students.
Across special education teachers, the four most
reportedly applied accommodations provided
when assessing knowledge of basic math
skills/computational tasks included: extended
time on tests, calculators, problems read to stu-
dents, and reduced problems on tests. General ed-
ucation teachers reported using the following
accommodations most frequently: calculators, ex-
tended time on assignment, problems read to stu-
dents, and individualized attention given to
student by classroom aide.
Problem-Solving Tasks. As shown in Table 5,
special educators reported that they were more
likely to use the following accommodations with
LD and/or E/BD when assessing knowledge of
multistep problem-solving tasks: reduced prob-
lems on tests, cue cards of strategy steps, use of
concrete objects, and problems read to students.
Across special education teachers, the four most
reported applied accommodations when assessing
knowledge of multistep problem-solving tasks in-
cluded: extended time on tests, calculators, prob-
lems read to students, and reduced problems on
tests. General education teachers reported using
most frequently the following accommodations:
calculators, extended time on tests, problems read
to students, and individualized attention given to
student by classroom aide.
RESEARCH QUESTION 3: FACTORS
AFFECTING TEACHER RESPONSE
Four nonhierarchical regression analyses were
conducted to examine the contribution of three
predictor variables on the number of instructional
practices and assessment accommodations re-
ported by general and special education teachers.
This was done separately for general and special
education teachers for the following two indices:


total number of reported instructional practices
and total number of reported accommodations.
First, each predictor variable was entered into the
first position of the linear equation to determine
if it was significantly related to the outcome vari-
able (e.g., total number of reported instructional
practices). In addition, each variable was entered
into the last position to determine if it con-
tributed to the prediction of the outcome variable
(e.g., total number of reported accommodations)
beyond the contribution of the other two vari-
ables. The predictor variables were (a) years teach-
ing students with LD and/or E/BD; (b) number
of methods courses completed; and (c) knowledge
of math topics (i.e., prealgebra, algebra, geometry,
general or basic skills math, algebra II, and alge-
bra II/trigonometry). Data for knowledge of math
topics is included in Table 6. It is interesting to
note that general education teachers were more
familiar than were special education teachers with
the topics of prealgebra, algebra, geometry, alge-
bra II, algebra II/trigonometry, statistics/probabil-
ity, and integrated/unified high school math.
INSTRUCTIONAL PRACTICES
Special Education Teachers. The three pre-
dictor variables accounted for 11.7% of the vari-
ance in the total number of instructional practices
special education teachers noted using with stu-
dents with LD and/or E/BD on basic math/com-
putational skills and problem-solving tasks (see
Table 7). The t-test for Beta weights was statisti-
cally significant for two predictor variables
(knowledge of math topics and number of meth-
ods courses) when entered into the first position
of the regression model. When entered into the
last position, one variable (knowledge of math
topics) contributed significantly to the prediction
of instructional practices above and beyond the
other predictor variables. Knowledge of math top-
ics accounted for 6.1% of the total variance after
the other variables were controlled.
General Education Teachers. The three pre-
dictor variables accounted for 12.5% of the vari-
ance in the total number of instructional practices
general teachers reported using with students with
LD and/or E/BD on basic math/computational
skills and problem-solving tasks (see Table 7). The
t-test for Beta weights was statistically significant
for the first predictor variable (number of meth-


Exceptional Children







TABLE 6
Teacher Perceived Knowledge of Secondary Math Topics
Significance
Special General
Education Education
Teacher Perceptions Teachers Teachers df t p ES

How much do you feel you know
about each of the math topics listed
below?
Prealgebra 1.53 (.70) 1.06 (.30) 134 -5.497 .000 .43
Algebra 2.07 (.84) 1.12 (.40) 143 -9.153 .000 .61
Geometry 2.54 (.86) 1.49 (.70) 169 -8.590 .000 .55
General Mathematics or Basic
Skills (HS) 1.14 (.38) 1.08 (.32) 167 -1.117 .265 .09
Algebra II 2.92 (.82) 1.35 (.60) 166 -13.958 .000 .74
Algebra II/Trigonometry 3.37 (.80) 1.62 (.76) 164 -14.464 .000 .75
Statistics/Probability 3.07 (.80) 2.01 (.84) 157 -8.275 .000 .55
Integrated/Unified High School
Math 2.98 (1.03) 2.14 (1.06) 152 -5.095 .000 .38
Note. ES = Cohen's d. Ratings based on a 4-point scale with 1 = a great deal; 2 = quite a lot; 3 = some;
4 = very little or nothing.


ods courses) when it was entered into the first and
last position of the regression model. For general
education teachers, the number of methods
courses taken accounted for 9.6% of the variance
after the other variables were controlled.
ASSESSMENT ACCOMMODATIONS
Special Education Teachers. The three pre-
dictor variables (years teaching students with LD
and/or E/BD, knowledge of math topics, and
number of methods courses) accounted for 4.7%
of the variance in the number of assessment ac-
commodations used by special educators (see
Table 8). The t-tests for Beta weights were not
statistically significant for any of the predictor
variables when they were entered into the first po-
sition or the last position of the regression model.
General Education Teachers. The three pre-
dictor variables accounted for 12.5% of the
variance in the number of assessment accommo-
dations made by general educators (see Table 8).
The t-test for Beta weights was statistically signifi-
cant for one predictor variable (total number of
methods courses) when entered into both the first
and last position. For general education teachers,


the number of methods courses taken accounted
for 11.1% of the total variance above and beyond
the other variables.


DISCUSSION

This study provides a national picture of sec-
ondary general and special educator views con-
cerning their reported level of preparation to
teach math and their perceived knowledge of
math. We also examined teacher use of specific
instructional practices and assessment accommo-
dations. In addition, we examined the contribu-
tion of experience, knowledge, and preparation in
predicting teachers' reported use of instructional
practices and testing accommodations.
We found that special education teachers
indicated they were less familiar with secondary
math knowledge than were general educators (the
only exception involved general mathematics or
basic skills). Furthermore, both general and spe-
cial education teachers take few methods courses
that focus on teaching math to students with LD
and/or E/BD. Only one of every two general


Winter 2006


228







TABLE 7
Nonhierarchical Regression Analysis for General Education and Special Education
Teachers' Instructional Approaches

Construct Entered
Initial Entry of the Construct in Last Position
Variables Simple R R2 p-value R2 Increment p-value
General Education Teachers
Mean perceived knowledge .090 .008 .444 .009 .488
Total number of methods courses .368 .136 .006 .096 .025
Total years teaching LD and/or E/BD .124 .015 .279 .007 .533

Special Education Teachers
Mean perceived knowledge .234 .055 .031 .063 .030
Total number of methods courses .247 .061 .023 .031 .124
Total years teaching LD and/or E/BD .055 .003 .587 .026 .157


education teachers took such a course, whereas educators for computational and problem-solving
special educators averaged only 1.27 courses of tasks; (b) special education teachers' familiarity
this nature. It is possible that the relatively small with course topics significantly and uniquely con-
numbers of methods courses taken by these teach- tribute to the prediction of the number of in-
ers influenced their general perceptions that they structional practices they provided to secondary
were not adequately prepared to teach math to students with LD and/or E/BD in math; and (c)
these students. These findings are consistent with the number of methods courses taken by general
previous research (Maccini & Gagnon, 2002). education teachers contributed to the prediction

SPECIFIC INSTRUCTIONAL of the number of instructional practices they made
for students with LD and/or E/BD in math.
PRACTICES AND FACTORS
A statistically significant difference existed
In the present study, it was determined that (a) between special educators and general educators
special educators used significantly more recom- on the average number of instructional practices
mended instructional practices than did general used with basic math facts, with special educators

TABLE 8
Nonhierarchical Regression Analysis for General Education and Special Education
Teachers'Assessment Accommodations

Construct Entered
Initial Entry of the Construct in Last Position
Variables Simple R R2 p-value R2 Increment p-value
General Education Teachers
Mean perceived knowledge .047 .002 .688 .002 .744
Total number of methods courses .368 .135 .006 .111 .016
Total years teaching LD and/or E/BD .063 .004 .583 .009 .493

Special Education Teachers
Mean perceived knowledge .080 .006 .465 .012 .345
Total number of methods courses .207 .043 .057 .028 .161
Total years teaching LD and/or E/BD .043 .002 .670 .007 .473


Exceptional Children







reporting using more instructional practices than
general educators. In fact, for each instructional
procedure, all but three instructional practices
(i.e., color coding, peer or cross-age tutoring, and
calculators) were statistically significantly differ-
ent, favoring special educators. No statistically


... both general and special education
teachers take few methods courses that
focus on teaching math to students with
LD and/or E/BD.

significant differences were noted between special
and general educators for the overall use of the 14
instructional procedures with problem-solving
tasks. However, for each instructional procedure,
special educators favored all but three (peer or
cross-age tutoring, calculators, and mnemonics).
Certain contextual information may help to
explain teacher differences. First, these two groups
of teachers differ greatly in terms of years of expe-
rience teaching students with LD and/or E/BD
(M= 12.36 years for special educators; M= 1.15
years for general educators). Also, general educa-
tion math teachers may have only a few students
with disabilities in their classes; whereas special
educators may be working almost entirely with
students with special needs.
Despite differences between general and
special educators in the number of recommended
instructional practices, there were several similari-
ties among the most frequent instructional prac-
tices reported. Specifically, during basic
skills/computational tasks, special and general ed-
ucation teachers both reported using the recom-
mended practices of individualized instruction by
teacher, extended time on assignments, and use of
calculators. The use of calculators was also a com-
mon response across teacher-type during prob-
lem-solving tasks. These results are encouraging
given the support from the literature for the criti-
cal need of providing enough time for students
with LD to learn information, establishing high
success rates, and developing strategies for helping
students to learn and retain information (Mercer,
1997). Although no studies currently exist that
examine the efficacy of standard and/or graphing
calculators on the math performance of secondary


students with LD, calculators hold great promise
for students with special needs. Maccini and
Gagnon (2005) noted the positive results of cal-
culator use with nondisabled students relative to
motivational factors, concept development, and
student achievement.
Although the fourth most frequent re-
sponse across teacher types differed, the variation
may be a function of resource availability. For in-
stance, special education teachers reported using
"problem read to students" as their fourth most
frequent instructional procedure, whereas general
education teachers noted the use of "peer or cross-
age tutoring" for helping students with special
needs on problem-solving and basic skills/compu-
tational tasks. This is not surprising given the het-
erogeneous nature of general classrooms with
varied skill levels and the need to cover the cur-
riculum. Use of peer tutoring has proven benefi-
cial during independent practice for secondary
students studying introductory algebra skills (All-
sopp, 1997).

SPECIFIC ASSESSMENT
ACCOMMODATIONS AND FACTORS
We found that special educators used more assess-
ment accommodations than did general educators
for both computational and problem-solving
tasks, and the total number of methods courses
taken predicted teacher use of assessment accom-
modations. More specifically, we found that spe-
cial educators were more likely than general



We found that special educators used
more assessment accommodations
than did general educators for both
computational and problem-solving
tasks...



educators to reduce the number of problems on
tests, use cue cards of strategy steps, and problems
read to students for both basic math skills and
problem-solving. They were also more likely to
use concrete objects as an accommodation for
problem-solving.


Winter 2006








Despite differences among general and spe-
cial educators in the number of assessment accom-
modations, there were several similarities among
the three most frequent assessment accommoda-
tions reported by both groups. These included (a)
extended time on tests, (b) calculators, and (c)
problems read to students. These results are posi-
tive given the documented research. Specifically,
Thompson et al. (2002) summarized and critically
evaluated empirical research studies from 1999 to
2001 that examined the effects of specific assess-
ment accommodations. The researchers catego-
rized the types of accommodations across
common formats (presentation, response, setting,
timing/scheduling, multiple accommodations,
other) and determined that the use of two formats
(extended time and oral presentation) had gener-
ally positive results on students' test scores. For ex-
ample, Calhoon et al. (2000) noted positive results
on a math performance assessment for secondary
students with LD with a teacher read aloud ac-
commodation, rather than standard paper/pencil
administration. Helwig et al. (1999) reported sim-
ilar results for students experiencing math difficul-
ties, regardless of their reading ability level. With
extended time, Fuchs, Fuchs, Eaton, Hamlett, and
Karns (2000) determined positive results for stu-
dents with LD in math on a curriculum-based
math measurement.
It should also be noted that there were
some inconsistencies between teachers' use of spe-
cific procedures for instruction and for assess-
ment. For example, the use of calculators was a
frequent response for special education teachers as
an assessment accommodation during problem-
solving tasks, but was not among the most fre-
quent responses as an instructional procedure. It
is important that students have training and expe-
rience with available assessment accommodations
during instruction (Thurlow, 2000).


LIMITATIONS AND FUTURE
RESEARCH
Five important limitations existed within the cur-
rent study. First, generalization of findings may be
at risk because of the small sample size and the
low response rate. The response rate remained low
despite multiple mailings and repeated reminders.


Also, comparisons between the respondents and
nonrespondents were not available. This was due
to the restrictions concerning participant confi-
dentiality from the survey company that managed
the mailings and returns. Future research needs to
include a larger sample and comparisons across
respondents and nonrespondents to increase the
validity of findings. Also, it is not known whether
the general educators sampled had some students
with special needs in their class or if they taught a
class completely comprised of students with spe-
cial needs. Variations in students within a class
may have an impact on instructional approaches
and assessment strategies and should be studied
further. Furthermore, it may be of concern that
the same choices existed for questions concerning
basic computational and problem-solving tasks.
Future research should include a more compre-
hensive list of instructional practices.
In the current study the number of meth-
ods courses uniquely and significantly con-
tributed to the prediction of the number of
assessment accommodations used by general edu-
cators. However, two issues remain unanswered:
(a) details concerning the methods courses taken
(e.g., focus of the courses, when courses were
taken, how course activities related to field experi-
ence); and (b) the extent to which the reported
assessment accommodations were appropriate in
type and number for students and whether they
were aligned with state policies (Pitoniak &
Royer, 2001). Future research should examine the
effects of types of methods courses to the number
of instructional practices and assessment accom-
modations used. Also, it is important to note that
the total amount of variance accounted for in the
regression analysis was relatively low. Future re-
search needs to expand the list of possible predic-
tors used to assess reported instructional practices
and accommodations.


INSTRUCTIONAL IMPLICATIONS
This study raises several questions about who
should teach math to secondary students with LD
and/or E/BD. On the one hand, general educa-
tion teachers appear to be more knowledgeable
about secondary math. On the other hand, spe-
cial education teachers have more formal course-


Exceptional Children


231








work on how to teach math to students with LD
and/or E/BD, and they are more likely to use the
recommended instructional practices and accom-
modations that were included in this study. In-
stead of worrying about who is best equipped to
teach these students, it may be more productive
to examine how general and special educators can
work together to facilitate these students' progress
in math (Thompson, Lazarus, & Thurlow, 2003).
As Kozleski, Mainzer, and Deshler (2000) stated,
"Special and general educators must work to-
gether to ensure that the highest possible number
of students with exceptionalities successfully ac-
cesses the important concepts and skills in the
general education curriculum" (p. 11).
The findings from this study indicate that
special education teachers need more preparation
in content of secondary mathematics, and general
educators would benefit from additional prepara-
tion in instructional practices and accommoda-
tions for learners with special needs. It is
unfortunate that some states do not have math re-
quirements for special education preparation pro-
grams (Graham & Fennell, 2001), as teacher
content knowledge and course completion have a
positive effect on student achievement (Good &
Grouws, 1987; Tooke, 1993).
One approach to increasing special educa-
tors' knowledge of secondary mathematics is to in-
tegrate such information into existing preservice
methods courses. Methods courses that addressed
both mathematics pedagogy and domain knowl-
edge had a significant impact on preservice teach-
ers' attitude toward math and significantly
increased their domain-specific knowledge of
math (Quinn, 1997). Jenkins, Pateman, and Black
(2002) also agreed that dual certification programs
can help secondary special education teachers ob-
tain content-specific knowledge and general edu-
cators sharpen their instructional practices.
Another approach for enhancing special ed-
ucators' knowledge and general educators' in-
structional practice is the use of ongoing,
comprehensive staff development opportunities
(Koency & Swanson, 2000; Whittington, 2002).
Whittington reported that 55% of all mathemat-
ics teachers surveyed in the 2000 National Survey
of Science and Mathematics Education indicated
a need for more professional development oppor-
tunities that focus on teaching students with spe-


cial needs. Obviously, such support can be offered
in conjunction with university coursework (Time
is Key, 2002 in Thompson et al., 2003).


REFERENCES

Algozzine, B., O'Shea, D. J., Crews, W. B., & Stod-
dard, K. (1987). Analysis of mathematics competence
of learning disabled adolescents. Journal of Special Edu-
cation, 21, 97-107.
Allsopp, D. H. (1997). Using classwide peer tutoring
to teach beginning algebra problem-solving skills in
heterogeneous classrooms. Remedial and Special Educa-
tion, 18, 367-379.
Blank, R., & Dalkilic, M. (1992). State policies on sci-
ence and mathematics education. Washington, DC: State
Education Assessment Center, Council of Chief State
School Officers.
Bley, N. S., & Thornton, C. A. (2001). Teaching math-
ematics to students with learning disabilities (4th ed.).
Austin, TX: Pro-Ed.
Calhoon, M. B., Fuchs, L. S., & Hamlett, C. L.
(2000). Effects of computer-based test accommoda-
tions on mathematics performance assessments for sec-
ondary students with learning disabilities. Learning
Disability Quarterly, 23, 271-282.
Fuchs, L. S., Fuchs, D., Eaton, S. B., Hamlett, C. L.,
& Karns, K. M. (2000). Supplementing teacher judg-
ments of mathematics test accommodations with objec-
tive data sources. School Psychology Review, 29, 65-85.
Gagnon, J. C., & McLaughlin, M. J. (2004). Curricu-
lum, assessment, and accountability in day treatment
and residential schools. Exceptional Children, 70, 263-
283.
Good, T., & Grouws, D. (1987). Increasing teachers'
understanding of mathematical ideas through inservice
training. Phi Delta Kappan, 68(10), 778-783.
Graham, K. J., & Fennell, F. (2001). Principles and
standards for school mathematics and teacher educa-
tion: Preparing and empowering teachers. School Sci-
ence and Mathematics, 101, 319-327.
Graham, S., Harris, K. R., Fink, B., & MacArthur, C.
(2003). Primary grade teachers' institutional adapta-
tions for weaker writers: A national survey. Journal of
Educational Psychology 95, 279-293.
Helwig, R., Rozek-Tedesco, M. A., Tindal, G., Heath,
B., & Almond, P. (1999). Reading as an access to
mathematics problem-solving on multiple-choice tests
for sixth-grade students. Journal of Educational Re-
search, 93, 113-125.


Winter 2006








Individuals with Disabilities Education Act (IDEA) of
1997. Pub. L. No. 105-17. U.S. Department of Educa-
tion, Washington, DC. (ERIC Document Reproduc-
tion Service No. ED 430 325)
Jenkins, A. A., Pateman, B., & Black, R. S. (2002).
Partnerships for dual preparation in elementary, sec-
ondary, and special education programs. Remedial and
Special Education, 23, 359-371.
Koency, G., & Swanson, J. (2000, April). The special
case of mathematics: Insufficient content knowledge a
major obstacle to reform. Paper presented at the Annual
Meeting of the American Educational Research Associ-
ation, New Orleans, LA.
Kozleski, E., Mainzer, R., & Deshler, D. (2000). Bright
futures for exceptional learners: An agenda to achieve. Re-
ston, VA: Council for Exceptional Children. (ERIC
Document Reproduction Service No. ED451668)
Maccini, P., & Gagnon, J. C. (2000). Best practices for
teaching mathematics to secondary students with spe-
cial needs. Focus on Exceptional Children, 32, 1-22.
Maccini, P., & Gagnon, J. C. (2002). Perceptions and
application of NCTM standards by special and general
education teachers. Exceptional Children, 68, 325-344.
Maccini, P., & Gagnon, J. C. (2005). Mathematics and
technology-based interventions for secondary students
with learning disabilities. In D. Edyburn, K. Higgins,
& R. Boone (Eds.), The handbook of special education
technology research and practice (pp. 599-622). Winston-
Salem, NC: Knowledge By Design.
Maccini, E, McNaughton, D. B., & Ruhl, K. (1999).
Algebra instruction for students with learning disabili-
ties: Implications from a research review. Learning Dis-
ability Quarterly, 22, 113-126.
Menikoff, L. (2004). Using accommodations for stu-
dents with learning, cognitive, and behavioral disabili-
ties. In D. Goh (Ed.), Assessment accommodations for
diverse learners (pp. 97-117). Boston: Allyn & Bacon.
Mercer, C. D. (1997). Students with learning disabilities
(5th ed.). Upper Saddle River, NJ: Merrill.
Monk, D. H. (1994). Subject area preparation of sec-
ondary mathematics and science teachers and student
achievement. Economics of Education Review, 13, 125-
145.
National Council of Teachers of Mathematics
(NCTM). (2000). Principle and standards for school
mathematics. Reston, VA: Author.
No Child Left Behind Act. Reauthorization of the Ele-
mentary and Secondary Education Act. Pub. L. No.
107-110; 2102(4) (2001).
Pitoniak, M. J., & Royer, J. M. (2001). Testing accom-
modations for examinees with disabilities: A review of


Exceptional Children


psychometric, legal, and social policy issues. Review of
Educational Research, 71, 53-104.
Quality Education Data (QED) School Personnel Data
Base. (2000/2001). Denver, CO: Scholastic.
Quinn, R. J. (1997). Effects of mathematics methods
courses on the mathematical attitudes and content
knowledge of preservice teachers. The Journal of Educa-
tional Research, 91, 108-113.
Schumm, J. S., Vaughn, S., Haager, D., McDowell, J.,
Rothlein, L., & Saumell, L. (1995). General education
teacher planning: What can students with learning dis-
abilities expect? Exceptional Children, 61, 335-352.
Thompson, S., Blount, A., & Thurlow, M. L. (2002).
A summary of research on the effects of test accommoda-
tions: 1999 through 2001. (Minnesota Rep. No. 34).
Minneapolis: University of Minnesota, National Center
on Educational Outcomes.
Thompson, S., Lazarus, S., & Thurlow, M. (2003).
Preparing educators to teach students with disabilities in
an era ofstandards-based reform and accountability (Top-
ical Rep. No. 5). College Park: University of Maryland,
The Institute for the Study of Exceptional Children
and Youth.
Thurlow M., Albus, D., Spicuzza, R., & Thompson, S.
(1998). Participation and performance of students with
disabilities: Minnesota's 1996 Basic Standards Tests in
reading and math (Minnesota Rep. No. 16). Minneapo-
lis: University of Minnesota, National Center on Edu-
cational Outcomes.
Thurlow, M. L. (2000). Standards-based reform and
students with disabilities: Reflections on a decade of
change. Focus on Exceptional Children, 33, 1-13.
Thurlow, M. L., Elliott, J., & Ysseldyke, J. (1998). Test-
ing students with disabilities: Practical strategies for com-
plying with district and state requirements. Thousand
Oaks, CA: Corwin Press.
Time is Key to Teacher Training, (2002, January 30).
Education Daily, pp. 1-2.
Tooke, D. J. (1993). Student teachers' mathematical
backgrounds and attainment of their secondary stu-
dents. The Clearing House, 66, 273-277.
Wang, A., Coleman, A. B., Coley, R. J., & Phelps, R. P.
(2003). Preparing teachers around the world (Policy In-
formation Rep.). Princeton, NJ: Educational Testing
Service.
Weisberg, H. E, Krosnick, J. A., & Bowen, B. D.
(1989). An introduction to survey research and data anal-
ysis (2nd ed.). Glenview, IL: Scott, Foresman.
Whittington, D. (2002). 2000 national survey of science
and mathematics education: Status of high school mathe-
matics teaching. Chapel Hill, NC: Horizon Research.


233







Wilson, R., Majsterek, D., & Jones, E. D. (2001).
Mathematics instruction. In P. J. Schloss, M. A. Smith,
& C. N. Schloss (Eds.), Instructional methods for sec-
ondary students with learning and behavior problems (3rd
ed., pp. 281-306) Boston: Allyn & Bacon.


ABOUT THE AUTHORS

PAULA MACCINI (CEC MD Federation), Associ-
ate Professor, Department of Special Education,
University of Maryland, College Park. JOSEPH
CALVIN GAGNON (CEC VA Federation), Assis-
tant Professor, Graduate School of Education,
George Mason University, Fairfax, Virginia.


Correspondence concerning this article may be
sent to Paula Maccini, University of Maryland,
Special Education, 1308 Benjamin Building, Col-
lege Park, MD 20742. (e-mail: maccini@
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 USDE.

Manuscript received November 2003; accepted July
2005.


Winter 2006







Copyright of Exceptional Children is the property of Council for Exceptional Children and its
content may not be copied or mailed to multiple sites or posted to a listserv without the copyright
holder's express written permission. However, users may print, download, or email articles for
individual use.




University of Florida Home Page
© 2004 - 2011 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated May 24, 2011 - Version 3.0.0 - mvs