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Predicting Eighth-Grade Algebra Placement for Students with Individualized Education Programs
This study investigated student performance and teacher perception of student performance
affect placement in eighth-grade mathematics classes for students with disabilities. Authors used the
Early Childhood Longitudinal Study-Kindergarten dataset to investigate how each of the following
factors predicted placement in eighth-grade algebra or above:



fifth-grade cognitive math performance
fifth-grade teacher rating of student ability
student enrollment in special education services
Students who received special education services had reduced odds of being placed in algebra by the
time they entered eighth grade. Teacher evaluations of student performance played a greater role for
special education students particularly those with individualized education programs who had
inconsistently demonstrated high performance than for their typically developing peers. The purpose of
this study was to investigate whether the interplay of teacher perception of student mathematical
performance, actual student math performance, and eventual eighth-grade placement in Algebra I
demonstrate patterns different for students with individualized education programs (IEPs) than for
students without IEPs. Because the level of mathematics placement in middle school is often the
primary determinant of how a student will be tracked in high school. (Burns, Heubert, & Levin, 2004,
2006; Catsambis, 1994; Dauber, Alexander, & Entwistle, 1996; Gamoran & Mare, 1989; Geiser &
Santelices, 2006; Hallinan, 2003; Oakes, 1990)
Issues regarding special education deal with the dynamics of academic placements for two primary
reasons:


minority students continue to be identified for special education at a higher rate than majority
students (Artiles & Trent, 1994; President's Commission on Excellence in Special Education,
2002)
Special education students regularly served in a setting separate from their peers (Lipsky &
Gartner, 1987)
Although there is limited research on the relationship between special education
and mathematics placement there is even less research on elementary teacher insight
and its impact on the middle school mathematics placement of students with identified
disabilities. Severe studies in mathematics education often do not include special
education students. Students with disabilities, in general, have demonstrated long
history of poor performance in mathematics. Approximately 5% to 8% of students are
estimated as having a specific mathematics disability, the current study is concerned
with the 12% to 15% of students who have IEPs and, therefore, may be identified with a
broader set of disabilities. (Cawley, Parmar, Foley, Salmon, & Roy, 2001). The current
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study focused on students with IEPs, in general, but also on students with IEPs who had performed well
in mathematics through elementary school.
In the most recent analysis, Hughes and Smith (1990) synthesized 2 decades of literature on the
cognitive and academic performance of college students with disabilities. The authors located 106
articles on the topic of college students and learning disabilities and found 26 that pertained specifically
to cognitive and academic characteristics of the population. Hughes and Smith cited several studies that
found students with LD had measured levels of intellectual functioning comparable to their peers
without disabilities (Hughes & Smith, 1990). The study looked at these three hypotheses:
1. For students with disabilities, fifth-grade teacher rating of student ability will be a stronger
predictor of placement in eighth-grade mathematics classes than student
performance.
2. Students with an IEP will have significantly lower odds of being placed in
algebra or above in eighth grade than students not identified and without an IEP.
3. High-performing fifth-grade students with an IEP will have significantly
lower odds of being placed in algebra or above in eighth grade than highperforming students not identified with a disability.
The dependent variable in this study is student placement in algebra or above by eighth grade. They
recorded placement decisions as placed in algebra or not placed in algebra. Placed in algebra shows that
students were placed in algebra or a course above algebra in eighth grade; not placed in algebra means
that students were placed in a course below algebra in eighth grade. Logistic regression was used for
analysis; logistic regression yields the coefficient variable of the regression equation and a comparative
odds ratio.1
Logistic regression also yields a comparative statistic (i.e., the odds ratio) that provides an effect
size. The odds ratio for a binary variable is a comparison of the odds of placement of a subgroup to
those students not in that subgroup. The odds ratio answers the question "What is the size of the effect
that a given variable has on the outcome?" An odds ratio of 1 would indicate that when controlling for
other background variables the students of interest (i.e., students with IEPs) are placed into algebra or
above exactly as students without IEPs are placed: They experienced the same odds of placement as
their peers. An odds ratio less than 1 would indicate that students in that subgroup have smaller odds of
being placed than students without IEPs. Finally, an odds ratio greater than 1 would indicate that
students with IEPs have greater odds of being placed into algebra than students without an IEP. For
continuous variables, the odds ratio is interpreted similarly. With continuous variables, the odds ratio
indicates how much the odds change given a standard unit change in the continuous variable. For
example, if the odds ratio is 2 for math performance, this means that the odds of placement are doubled
for every standard deviation (SD) increase in math performance. (Hughes & Smith, 1990)
1 (Hughes & Smith, Predicting Eighth-Grade Algebra Placement for Students With Individualized Education Programs, 1990)
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SEDU 183
Hypothesis 1:Teacher Perception vs. Math Performance as Predictor of Math Placement
All Students
Variable
B
OR
CI
Teacher perception 0.34[**] 1.41 1.26-1.57
Math performance 1.09[**] 2.96 2.61-3.36
Interaction
0.16[**] 1.18 1.05-1.32
Note: OR = odds ratio; CI = confidence interval. *p < .05 **p .01
Hypothesis 2 Discussion
When controlling for math performance, teacher perception, socioeconomic status, gender, and
race, the odds of placement in algebra by the eighth grade were considerably diminished for students
with IEPs. This finding was strong and highly significant (B = .60, p < .01). The results (see Table 7) show
that students with IEPs were placed in algebra or higher by eighth grade at an overall lower raw rate
than their peers they had, after all, been identified with a disability that affected their learning in some
way it is important to note that these odds included controls for performance, socioeconomic status,
gender, and race. It could be argued that, controlling for these factors, students with IEPs should have
an equal, or even higher, rate of placement. (Table 7) : EBSCOhost: Predicting Eighth-Grade Algebra
Placement for Students With Individualized ...
Hypothesis 3 Discussion
For the group of inconsistently high performers, the trends for all students were amplified. Both
the significance level and the effect size increased dramatically for these students who present an
ambiguous, high-performing profile. For this subgroup and when controlling for background variables
including math performance the odds of placement in algebra by eighth grade were approximately one
fifth of their peers' (B = .18, p < .001). Placement in algebra class in middle school creates more
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opportunity for higher mathematics classes at the high school level, and these advanced classes in high
school in turn have a large influence on student educational outcomes (Burns et al., 2004, 2006;
Catsambis, 1994; Dauber et al., 1996; Gamoran & Mare, 1989; Geiser & Santelices, 2006; Hallinan, 2003;
Oakes, 1990).
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SEDU 183
Citations
Faulkner, V., Crossland, C., & Stiff, L. (2011, November). Predicting eight grade algebra
placement for students with individualized education programs. Retrieved from
http://web.ebscohost.com/ehost/detail?vid=5&sid=6c0b39e8-2df3-41ec-a7670c1079f93d9b@sessionmgr11&hid=21&bdata=JmxvZ2luLmFzcCZzaXRlPWVob3N0LWxpdmU= db=pbh&AN=85685755&anchor=toc
Dauber. , Alexander, , & Entwistle (1996). Predicting eight grade algebra placement for students
with individualized education programs. Retrieved from
http://web.ebscohost.com/ehost/detail?vid=5&sid=6c0b39e8-2df3-41ec-a7670c1079f93d9b@sessionmgr11&hid=21&bdata=JmxvZ2luLmFzcCZzaXRlPWVob3N0LWxpdmU= db=pbh&AN=85685755&anchor=toc
Cawley. , Parmar, , Foley, , Salmon, , & Roy (2001). Predicting eighth grade algebra placement
for students with individualized education programs. Retrieved from
http://web.ebscohost.com/ehost/detail?vid=5&sid=6c0b39e8-2df3-41ec-a7670c1079f93d9b@sessionmgr11&hid=21&bdata=JmxvZ2luLmFzcCZzaXRlPWVob3N0LWxpdmU= db=pbh&AN=85685755&anchor=toc
Lipsky. , & Gartner (1987). Predicting eighth grade algebra placement for students with
individualized education programs. Retrieved from
http://web.ebscohost.com/ehost/detail?vid=5&sid=6c0b39e8-2df3-41ec-a7670c1079f93d9b@sessionmgr11&hid=21&bdata=JmxvZ2luLmFzcCZzaXRlPWVob3N0LWxpdmU= db=pbh&AN=85685755&anchor=toc
Hughes. , & Smith (1990). Predicting eighth grade algebra placement for students with
individualized education programs. Retrieved from
http://web.ebscohost.com/ehost/detail?vid=5&sid=6c0b39e8-2df3-41ec-a7670c1079f93d9b@sessionmgr11&hid=21&bdata=JmxvZ2luLmFzcCZzaXRlPWVob3N0LWxpdmU= db=pbh&AN=85685755&anchor=toc