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Community College Journal of Research and Practice
ISSN: 1066-8926 (Print) 1521-0413 (Online) Journal homepage: http://www.tandfonline.com/loi/ucjc20
Does High School Performance Predict College Math Placement?
Lynne E. Kowski
To cite this article: Lynne E. Kowski (2013) Does High School Performance Predict College Math Placement?, Community College Journal of Research and Practice, 37:7, 514-527, DOI: 10.1080/10668926.2012.754730
To link to this article: http://dx.doi.org/10.1080/10668926.2012.754730
Published online: 13 May 2013.
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Does High School Performance Predict College Math Placement?
Lynne E. Kowski
Mathematics Department, Raritan Valley Community College, Somerville, New Jersey, USA
Predicting student success has long been a question of interest for postsecondary admission counse-
lors throughout the United States. Past research has examined the validity of several methods
designed for predicting undergraduate success. High school record, standardized test scores,
extracurricular activities, and combinations of all three have historically been successful predictors.
However, in recent years, standardized test scores have become less effective for placing students in
lower level mathematics courses; placement exams such as Accuplacer 1
have taken their place,
especially in community colleges where no standardized test scores are necessary for admissions.
This paper comprises a literature review of past research devoted to predicting community college
success. Various state high school graduation requirements were examined as well as the issues
surrounding high school mathematics proficiency and its lack of connection to college readiness.
Academic aptitude factors—gleaned from high school transcripts analyzed to determine their influence on the need for remedial mathematics as determined by the mathematics portion of the
Accuplacer 1
placement exam—were also examined. Significant variables found to influence the probability of remedial mathematics for community college freshmen were overall high school
performance determined by the nonweighted high school grade point average (GPA), taking a math
class beyond the state-required sequence, and the socioeconomic status of the high school.
In the past 20 years, states have moved to institute high school level standards and assessments
required for graduation. At the time of this study, New Jersey had not yet developed a state-wide
exam with the intent of aligning specifically with postsecondary education. Since then,
New Jersey has become part of the national Common Core State Standards (CCSS) consortium,
which beginning with the 2014–2015 academic year will implement the Partnership for
Foremost, I would like to thank my advisor, Jimmy de la Torre, for all the helpful insights during this process, from
writing my Institutional Review Board protocol through the statistical analysis. Without Jimmy’s guidance, this study
would not have come to fruition; thus, I am grateful for his support. I would also like to thank Raritan Valley Community
College (RVCC), where I work, for supporting my research and allowing me access to all the data I required in order to
make this study a success. I would like to thank all my RVCC statistics service learning students, Stephanie Aguayo,
Megan Baloy, James Debicki, Julianne Giolli, Nicole Hoffman, Jeongsul Lee, Eric Longenecker, Mark Lysczczasz,
Robinson Miranda, Brett Orashen, Garrett Pineda, Thomas Stolp, Benjamin West, and Franciele Zipperer. Without their
20 plus hours each, combing through 659 transcripts, recalculating Grade Point Averages, identifying legitimate math
classes, and so much more, I would still be gathering raw data. Last, but not least, I would like to thank La Reina Bates
and Gary Parilis, both of whom spent many hours editing and guiding the flow of the paper.
Address correspondence to Lynne E. Kowski, Professor of Mathematics, Raritan Valley Community College, P.O.
Box 3300, Somerville, NJ 08876. E-mail: [email protected]
Community College Journal of Research and Practice, 37: 514–527, 2013
Copyright # Taylor & Francis Group, LLC
ISSN: 1066-8926 print=1521-0413 online
DOI: 10.1080/10668926.2012.754730
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Assessment of Readiness for College and Careers (PARCC), a high school assessment specifi-
cally aligned to assess the CCSS (Partnership for Assessment of Readiness for College and
Careers, 2012). It is important to understand the linkage between high school and college and
career readiness, as well as whether it exists, given the wide-ranging use of high school exams
across the country (Brown & Conley, 2007).
Performance in the first few courses of postsecondary education forms the basis for predicting
the probability of students’ future success in college (Armstrong, 2000). This is often compli-
cated by the significant disconnect found between high school performance and college readi-
ness (Berkner & Chavez, 1997; Moss & Bordelon, 2007). To assess the knowledge and skills
of first-year students—and in lieu of denying admission—secondary institutions use placement testing where, if needed, remedial course work can be assigned to ensure student preparation for
college-level work. As this might appear to be a wonderful fix to allow equity for all students to
attend college, it has some serious drawbacks.
More than one-third of first-year college students attending two- and four-year colleges and
universities enroll in reading, writing, or mathematics remedial courses, with almost a quarter of
incoming college freshman requiring remediation specifically in mathematics (Achieve, Inc.,
2012). Taking remedial courses can result in as much as up to two extra years towards
graduation. Two-year college retention rates over just over 50% (Achieve, Inc., 2012). In con- trast, nearly 65% of students who do not require remediation earn college degrees (Perkins, 2004).
Despite multiple efforts to align high school preparation with college standards, recent studies
show that more students are entering college less prepared than ever (Crist, Jacquart, & Shupe,
2002). Many college-bound students’ high school curriculums are falling short in laying the
groundwork for success in a postsecondary education, especially in mathematics and English.
The result is many high school graduates spend their first year in college retaking courses passed
in high school such as arithmetic and algebra; these are courses that do not count towards
graduation credit (Pugh & Lowther, 2004).
Various reasons may explain this situation. Focusing on those students who immediately
continue on to a postsecondary education, the following are some of Brown’s (1999) reasons
remediation in mathematics is necessary:
1. Recent high school graduates enter with math grades that give a false impression of prior
knowledge. This is either because the grades tend to be inflated or because the actual content
covered differs from the official curriculum.
2. Competency in high school mathematics may not equate with remedial mathematics compe-
tency at the postsecondary level.
3. Students that fulfilled their mathematics requirements during their junior year of high school
fail to retain that knowledge a year and a half later when entering college; this makes high
school mathematics performance a poor predictor of college level mathematics success.
Students who fail to continue rigorous mathematics education through all four years of high
school may be vulnerable to inadequate performance in their first college math course and=or place below their true retained mathematical knowledge (Pugh & Lowther, 2004). Therefore,
the purpose of this study was to assess mathematics college-readiness as defined from various
aspects of the high school transcript such as overall grade point average (GPA) and highest level
of mathematics studied.
HIGH SCHOOL PERFORMANCE AND MATH PLACEMENT 515
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LITERATURE REVIEW
High School Mathematics Requirements and College Readiness
Many studies identifying influences of college achievement have found a link between high
school mathematics courses completed and postsecondary academic success (Adelman, 1999;
Keller, 2001; Kirst, 2001; Perkins, 2004). The U.S. Department of Education found students
who took a math course beyond algebra II in high school more than doubled their likelihood
of completing a bachelor’s degree (Adelman, 1999). Unfortunately, one out of every two high
school graduates do not take mathematics during their senior year, and only 18% of high school students go beyond algebra II (Adelman, 1999; Perkins, 2004). The senior year of high school is
the key to academic success throughout postsecondary education, and it should be spent
preparing for the rigorous coursework required in college.
Research examining student performance in first-year college core mathematics courses in
relation to time elapsed since the last high school mathematics course, suggests the further
away from past performance a student is the less accurate their perceived self-efficacy (Ban-
dura, 1997, 2001; Luzzo, Haper, Albert, Bibby, & Martinelli, 1999). College freshmen who
did not take a mathematics course during their senior year may approach a college math place-
ment test, and possibly even college mathematics courses, with perceptions of competence not
matched to actual capabilities. Therefore, past performance in high school mathematics may
not help predict college math performance for students who have taken mathematics their
senior year compared to those who have not (Schneider, Kirst, & Hess, 2003). Although most
states require high school students to take a certain number of courses in mathematics, very
few can ensure that the course content reflects the knowledge and skills required for college
readiness. In order to succeed, high school graduates need four years of mathematics with con-
tent equivalent to algebra I and II, geometry, and a fourth course such as statistics or precal-
culus. Those students who take advanced course sequences in mathematics are more likely to
be college ready, and they receive higher scores on college admissions tests (Schneider et al.,
2003).
Reviewing student transcripts as part of a longitudinal study on what high school indi-
cator best predicts college graduation, Adelman (1999) found that among all college stu-
dents, college completion rates increase when a rigorous college-prep curriculum is taken
in high school. ‘‘Of all components of curriculum intensity and quality, none has such
an obvious and powerful relationship to ultimate completion of degrees as the highest level
of mathematics one studies in high school’’ (Adelman, 1999, p. 16). Challenging high
school courses, regardless of the grade earned, prepare students for the college learning
environment and enhance their ability to succeed in upper-level classes (Adelman, 1999;
Bourquin, 1999).
Preparing for college requires taking the right courses. This is particularly true when it
comes to mathematics, where data show a strong correlation between taking higher-level
high school courses and achieving success in college, including the probability of
completion. The higher the levels of mathematics students take in high school, the more
likely high school graduates are to earn bachelor’s degrees (Achieve, 2004; Adelman,
1999; Adelman, 2006; Adelman, Daniel, & Berkovits, 2003; Bedsworth, Colby, & Doctor,
2006).
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College Placement Testing and College Readiness
Underachievement in mathematics in the United States, and the possible factors contributing to
the decline of mathematics proficiency at the secondary and postsecondary levels, have been the
subject of much attention in recent years. The No Child Left Behind Act has increased pressure
on public school administrators to improve mathematics scores on standardized tests with little
regard to college readiness. The reform teaching methods of the past two decades have not given
students the knowledge or skills they need to succeed in college (Schwartz, 2007). High school
students need exposure to challenging mathematics courses to enhance their skills and develop a
deeper understanding of the content beyond the bells and whistles of reform teaching and new
technology (Bourquin, 1999).
A student’s performance in his or her first few college courses forms the basis for predicting
the probability of the student’s future achievements in college (Armstrong, 2000). However,
successful college performance is often complicated by the significant disconnect between high
school performance and college readiness (Berkner & Chavez, 1997; Moss & Bordelon, 2007).
For example, Hoyt and Sorensen (2001) found over half the students who successfully com-
pleted algebra II and geometry in high school had college placement test scores placing them
in remedial mathematics courses. Even though they earned a passing grade on their high school
transcript, these students failed to demonstrate the appropriate level of knowledge and skills on
their college placement exam.
One of the main criticisms of placement testing in the literature is the timing of the test. Place-
ment exams are generally administered to students by the postsecondary institution before the
academic year begins. Some high schools have moved toward administering placement exams
to their graduating seniors during the last month of school in an effort to better prepare their
students for college; other schools are working with the local college to administer the placement
test in 10th or 11th grade. Thus, those students who need math remediation to become
college-ready have an extra year or two to strengthen their mathematics skills while still in high
school (Frost, Coomes, & Lindeblad, 2009). Therefore, depending on the timing of the place-
ment test and whether the student took mathematics during their senior year of high school,
some students may end up taking the test almost one and a half years after completion of their
last mathematics class. Poor placement test performance due to being a little rusty can result in
placing perfectly capable students of higher-level mathematics instruction in remedial course-
work. Independent studies by Armstrong (1999), Jenkins (1991), and Isbell (1988) have all
determined that due to the timing of the placement test, a large portion of students actually
succeed in mathematics classes even though their test scores labeled them as unprepared.
Addressing the issue of developing better predictive placement techniques, Marwick (2002)
compared four mathematics placement methods at a midwestern university. All students who
took the Accuplacer 1
exam during summer 2001 were randomly assigned to one of four place-
ment methods: Accuplacer 1
exam score alone, high school preparation alone, a balance of the
two measures, or student choice constrained by the two measures. Accuplacer 1
is a computer
adaptive placement test that measures skills in math and English for placement in appropriate
college level courses. Marwick (2002) found that overall the students performed equally well
in their mathematics course regardless of which method was used for placement. When compar-
ing placement test scores with the student’s high school record, student placement would have
been approximately the same regardless of which technique was used. The results of this study
HIGH SCHOOL PERFORMANCE AND MATH PLACEMENT 517
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showed that placement by Accuplacer 1
score alone denied many students access to the
appropriate course in which they could have been successful. Marwick (2002) concluded that
placement techniques should involve a combination of high school record and placement test
score with students placed in the higher-level course recommendation.
Community college admission typically is open to all those with either a high school diploma
or General Educational Diploma (GED). Therefore, the majority of two-year colleges require
incoming students to pass remediation cutoffs on an assessment test before they are allowed
to enroll in college-level courses. In mathematics this requires placing beyond algebra II.
Currently, this is the most relevant benchmark for whether a person has successfully transitioned
into college-level mathematics (Golfin, Jordan, Hull, & Ruffin, 2005).
Common Core State Standards
The United States Department of Education recently announced an initiative to improve the
quality and college alignment of educational assessments by implementing high school
Common Core State Standards (Common Core State Standards Initiative, 2010). The CCSS
are designed to prepare students for college and the workplace, and they measure student knowl-
edge and skills across the full performance continuum. An additional objective of standards is to
support a culture of continuous improvement in education. This can be done by providing infor-
mation that can be used in a timely and meaningful manner to determine school and educator
effectiveness, as well as guide instruction (Common Core State Standards Initiative, 2012).
CONTEXT OF STUDY
The timing of this study was during a transition period. The High School Proficiency Assess-
ment (HSPA) was in a phase-out period while alternate assessments were being explored. At
the time of this writing (April 2011), this was to be the last year of HSPA; but at the New Jersey
Board of Education meeting in March 2011, the effectiveness of various assessment options was
still being determined along with whether a revised HSPA with better aligned outcomes should
be implemented or, rather, a national test—such as PARCC—specifically designed to align with the CCSS.
PURPOSE
The purpose of this study was to use a mathematics placement test as a means to assess
mathematics college readiness defined from various aspects of the high school transcript such
as overall GPA, math GPA, the number of math classes taken, the number-of-years of mathemat-
ics, the highest level of mathematics, and the last grade-level math was taken. Using these
indicators, does high school performance impact placement in college mathematics, specifically
eliminating placement into remedial coursework? College mathematics placement tests are
increasingly being used to determine at which level of college mathematics a student will start.
That is why researchers need to evaluate how effective these mathematics placement tests are at
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predicting the performance of students who do not take math during their senior year of high
school and for those who do not go beyond algebra II.
RESEARCH QUESTIONS
This research project focuses on the following central questions:
1. Is mathematics proficiency for high school graduation equivalent to college math placement?
2. Which predictor(s), if any, correlate and help predict a student’s college math placement?
METHODOLOGY
Overview of Guiding Questions
This study seeks to determine whether high school math performance can predict math placement
by the Accuplacer 1 placement exam. The College Board Accuplacer
1 Computerized Placement
Test is a computer adaptive test that chooses the difficulty of questions based on responses to pre-
vious items. There are 10 different tests available that measure reading, writing, English, and
mathematics ability. Within the mathematics category, three different tests are available to mea-
sure varying skill levels: the arithmetic test, the elementary algebra test, and the college-level
mathematics test. Each of these tests is multiple-choice with no enforced time limit.
Is what high schools consider college-ready in mathematics consistent with college standards
for readiness? Open-admission community colleges require all entering students to take
placement tests in math and English. As a result, many incoming freshman are placed in
remedial classes, classes with content that should have been mastered in high school. This
research evaluates where, in terms of math, incoming community college freshmen are being
placed.
Cohort Criteria
To eliminate some obvious confounding variables, the analysis consisted of a New Jersey
suburban community college single cohort of 659 first-time, full-time students. The students
graduated high school in June 2009 and took the Accuplacer 1
math placement test before the
start of the fall 2009 semester. Each student’s high school and county, Accuplacer 1
math place-
ment scores, and placement math class were obtained from the college records. The remaining
data—the overall high school grade point average, math GPA, number of single math classes (repeats counted as one math class), highest level of math taken, math beyond basic algebra
I-geometry-algebra II sequence, the highest grade the student took a math class, and the District
Factor Group (DFG) of the high school—were calculated from the students’ 659 high school transcripts. The DFG provides a systematic approach for classifying New Jersey school districts
based on the socioeconomic status (SES) observed within the communities served by the district
(State of New Jersey, Department of Education, 2004). Poor districts are assigned the classi-
fication of A and B, while middle districts are assigned a classification of CD, DE, FG, and
HIGH SCHOOL PERFORMANCE AND MATH PLACEMENT 519
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GH, and the wealthiest districts were defined to include districts with the DFG classification of
I and J.
Data Preparation
Because of differences in how schools report grades, data conversions were required to establish
a standard metric. Each high school GPA was converted to a 4.0 scale (see Table 1). All non-
pass=fail classes were included. Classes taken multiple times were counted each time in both the overall high school GPA and the separate math GPA. For the mathematics GPA, certain classes
were not considered authentic math classes and were not included in the GPA calculations.
These were Special Review Assessment (SRA) math (a math class taken by a senior who did
not pass the math portion of the HSPA during his or her junior year), study skills for math, busi-
ness math, consumer math, math for living, HSPA math, math essentials, math lab, math experi-
ence, accounting, and finance. Other data gleaned from the transcripts included the number of
different math classes a student took (repeats due to failing only counted once), the highest level
of math class taken, and the last year the student took a math class.
Since the passing of New Jersey’s Lampitt Bill in September 2007, testing out of elementary
algebra for nonmath intensive majors would equate to no mathematics remediation. Conse-
quently, whether the student placed beyond elementary algebra or not was used as the dependent
variable. Two other independent variables were added. Because various nonrequired math
courses are offered by high schools, these were simplified into a single binary variable: whether
a student took more than the minimum required algebra I-geometry-algebra II sequence. The last
variable was the DFG of the high school.
DATA ANALYSES
Descriptive Statistics
Descriptive statistics were used to understand the character of the sample, expose any anomalies,
and identify any additional areas for investigation. Various basic descriptive statistics, such as
measures of central tendency and spread about the middle, guided the relationship between what
TABLE 1
Conversion of Grades to a 4.0 Scale
4.0 scale Letter grade Percentages
4.0 A�, A, Aþ 91–100 3.5 Bþ 86–90 3.0 B�, B 81–85 2.5 Cþ 76–80 2.0 C�, C 70–75 1.0 D�, D, Dþ 61–69 0.0 U, F �60
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a high school considers proficient for graduation and what a college deems proficient for college
readiness and success.
Odds Ratio
The primary focus of this investigation was whether the conditional odds ratio of testing out of
elementary algebra (remedial college math) is more or less likely for one group over another. For
example, controlling for GPA, does one DFG have better odds of testing out of elementary
algebra than another DFG? In addition, the Mantel-Haenszel test measures the strength of associ-
ation by estimating the common odds ratio, the results of which directed the logistic regression
analysis.
Logistic Regression
As mentioned above, this analysis focused on factors from high school that influenced math
placement, specifically testing beyond elementary algebra. Logistic regression analysis examines
the probability of success; specifically the probability a student will test out of elementary
algebra. Influential variables considered were the overall high school GPA; high school math
GPA; number of high school math classes; highest level of high school math; math beyond basic
algebra I-geometry-algebra II sequence (dummy coded 1 ¼ yes, 0 ¼ no); highest grade the student took math; and DFG of the high school—along with any possible interactions.
RESULTS AND DISCUSSION
Cohort Demographics
The community college for this study serves two of the more wealthy counties in New Jersey,
resulting in 52% of the cohort originating from a DFG I high school (the second wealthiest), with an additional 5% graduating from DFG J high school (the wealthiest). No students from this cohort graduated from a high school with DFG A, and only 6% were from high schools classified as DFG B.
Most students in this cohort took a math course their senior year, and yet still did not place
out of elementary algebra (algebra I). Some of those students, though, took algebra II in their
senior year, finishing the required sequence. For those who completed the required algebra
I-geometry-algebra II sequence and took an additional math class, the types of math classes var-
ied substantially. Because the rigor of the various classes could not be determined from the high
school transcripts, students were simply classified based on whether they took a math class
beyond the required sequence (53% of the sample).
Cohort Descriptive Statistics
The largest percentages of students were placed into elementary algebra (45%) and intermediate algebra (31%). Both algebra courses are math courses that should have been mastered at a high
HIGH SCHOOL PERFORMANCE AND MATH PLACEMENT 521
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school level, algebra I and algebra II respectively. To have a majority of students entering col-
lege placed into remedial mathematics courses shows that there is a gap between preparation for
college in high school and college expectations. Only 40.5% of the students tested out of elementary algebra, the highest level remediation needed in order to take a college level math
class for nonmath intensive majors: majors not requiring precalculus or statistics. Even more
discouraging is that only 9.7% of the students tested out of intermediate algebra, the highest level of remediation required to take precalculus or statistics: math courses required for almost
all associates of applied sciences transfer degrees.
Logistic Regression
In the logistic regression, each DFG was dummy coded zero through seven with DFG A as the
reference group zero. Only DFG classification B was found to be significant (p ¼ .0311) in the likelihood of placing out of elementary algebra (see Table 2). Thus, the data was recoded assign-
ing DFG B equal to one and all other DFGs equal to zero. Also significant (p ¼ .0021) was the number of unique math classes a student took in high school. In order to escape bias regarding
particular math course rigor, the data was recoded assigning a value of one to those who took
math beyond algebra II and a value of 0 to those who did not.
In contrast, the high school math GPA did not prove to be significant (p ¼ .8053). One poss- ible explanation may have to do with a misguided self-efficacy. Regardless of when they took
their last math class, students who did well in high school math may have skewed self-efficacy
and feel that prepping for the placement test is unnecessary; which may prove successful or not
depending how well the student retains the knowledge. If students took their last math class dur-
ing their junior year earning an A or B grade, they may feel overly confident in their mathemat-
ical abilities and not prep for the placement test, thus placing lower than what their math grades
would predict. In addition, poor math students may learn for the moment; that is, study for the
test and pass without retaining knowledge. There are too many confounding variables that affect
TABLE 2
Logistic Regression Output: All Variables
Variable DF Wald chi square p value
NUM CLAS 6 20.7011 .0021
HS GPA 1 16.6572 <.0001
SES 7 17.0147 .0173
SES 7 1 0.1667 .6831
SES 6 1 1.3452 .2461
SES 5 1 0.0052 .9426
SES 4 1 0.5655 .4520
SES 3 1 0.3623 .5473
SES 2 1 1.2247 .2684
SES 1 1 4.6459 .0311
MATH GPA 1 0.0376 .8463
BEYONDHS 1 24.8176 <.0001
Note. Only SES level 1 proved significant.
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the math GPA; this causes nonsignificance in terms of predictive value for placing out of
remedial math. Contrary to the insignificant math GPA variable, the overall high school GPA
was significant in predicting placement beyond elementary algebra (p < .0001). The overall high school GPA gives information about the student’s academic profile.
In summary, these were the only significant variables affecting the probability of whether or
not a student would test out of elementary algebra: how he or she performed in high school with
respect to high school transcript GPA (p < .0001), whether or not he or she was from DFG B (p ¼ .0148), and whether or not he or she took math in high school beyond the required algebra I-geometry-algebra II sequence (p < .0001). The Hosmer and Lemeshow Goodness-of-Fit Test examines whether or not the model is a good fit; that is, whether the model is good at predicting
if a student will place beyond elementary algebra in comparison to what was observed. The null
hypothesis is that the model is a good fit, thus the nonsignificance desired was also obtained
(p value ¼ .4159) (see Table 3).
Cohort Model
The final model for this cohort is
Logit½pðy ¼ 1Þ� ¼ �3:9390 þ 0:9985x1 þ 0:8802x2 þ 1:1978x3 where p(y ¼ 1) is the probability of testing out of elementary algebra, x1 is the overall high school GPA, x2 is the dummy variable classifying those students from DFG B, and x3 is the dummy-variable classifying those students who took a high school math class beyond the
minimum graduation requirements.
Discussion
With logistic regression, the maximum likelihood estimates are exponentials that convert to odds
ratios; thus, examining the regression model in terms of odds ratios leads to the following
interpretation: Controlling for the other variables, for every one-point increase in high school
GPA, a student is 2.7 times more likely to test out of elementary algebra. High school GPA gives
an overview of the student’s scholastic aptitude, attitude, and academic maturity. A student who
has performed well academically throughout high school might be more likely to prepare him or
herself before taking a placement test by reviewing any pertinent information. On the flip side, a
student who has coasted throughout high school by passing minimal requirements might feel no
TABLE 3
Logistic Regression Output: Significant Variables
Variable B p value Exp(B) Lower 95% CI Upper 95% CI
HS GPA 0.9985 <.0001 2.714 1.898 3.881
SES B 0.8802 0.0148 2.411 1.188 4.895
BEYONDHS 1.1978 <.0001 3.313 2.332 4.706
Note. Hosmer and Lemeshow Goodness-of-fit p value ¼ .4149. Model is a good fit.
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need to study before a placement test and, therefore, might more likely place into a remedial
math class.
Controlling for the other variables, students from DFG B high schools are 2.4 more times
likely to test out of elementary algebra than students from more wealthy districts. Because
attending college is a large financial investment, students from a poor district are less likely
to go to any college (including community college) if they exhibited poor academic performance
in high school—especially because low placement would require extra remedial classes. In contrast, students from wealthier districts whose academics are not up to par may still go to
an open enrollment community college.
Controlling for the other variables, students who take any high school math class beyond the
required algebra I-geometry-algebra II sequence are 3.3 times more likely to test out of elemen-
tary algebra. Students taking classes beyond the required sequence not only have an appreciation
for math, they are often taking math during their senior year. Even when not taking
algebra-based courses like precalculus, math beyond the basics keeps algebraic thinking skills
current, increasing the likelihood of testing out of elementary algebra.
IMPLICATIONS
As noted earlier, the timing of this study was during a transition period. In the past two years
New Jersey has joined the U.S. Department of Education initiative to improve the quality and
college alignment of educational assessments by implementing high school Common Core State
Standards (CCSS). As previously noted, the CCSS are designed to prepare students for college
and the workplace and measure student knowledge and skills across the full performance
continuum. In addition to the CCSS, the implementation of the PARCC assessment is set to
be administered for the first time in 2014–2015. At the time of this writing (April 2011), this
was to be the last year of HSPA, but at the New Jersey Board of Education meeting in March
2011, the effectiveness of various assessment options was still being determined along with
whether, instead, a revised HSPA with better aligned outcomes should be implemented. The
timing of this study is particularly relevant as a result.
This study was designed to investigate how the New Jersey high school assessment in math-
ematics aligned with college standards, and it uncovered that the state assessment system in
mathematics is only partially signaling preparedness for college. The results of this study pro-
vide valuable information about how the assessment system in mathematics can be changed
to better reflect effective instructional practices. A four-year mathematics requirement with at
least one year of mathematics beyond algebra II would better prepare college-bound students.
CONSIDERATIONS FOR FUTURE RESEARCH
Future studies should consider the following: (a) Given each student’s math placement on
Accuplacer 1 , how do students do in their first college math class? (b) Are differences in success
based on students’ math placement or whether students took math their first semester or delayed
one or more semesters? and (c) According to Accuplacer 1
placement and success or failure in
the math class as well as the current semester GPA, were students placed properly?
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Regardless of future high school assessments adopted, there needs to be a study to compare
individual high school math proficiency with college math placement. Does high school math
proficiency align with college placement, measuring the same learning outcomes? If an effective
alignment is accomplished, colleges may start honoring student achievement on high-school-
standards-based assessments by using high school performance data in their admissions and
placement decisions, solidifying the link between high schools and colleges.
VALIDITY AND LIMITATIONS
Results of this study validate previous studies showing that a more rigorous high school math
curriculum, beyond the algebra=geometry sequence, provides college-bound students a strong foundation for academic success (Achieve, 2006; Adelman, 1999; Adelman et al., 2003;
Adelman, 2006; Bedsworth et al., 2006). However, there are some limitations. Regarding the
high school transcripts, decisions were made about what classes to include as legitimate math
classes, interpretations of unfamiliar-named math classes, and whether to weight the GPA grade
for half-year and full-year classes equally. Furthermore, cut-off percentages and grades were
transposed to a particular four-point GPA scale. Because different high schools have different
cut-scores, this study may have inaccurately interpreted a GPA for that particular school.
CONCLUSION
With this small study, it appears that some New Jersey high school performance standards may be
out of touch with minimum college standards. This study demonstrates statistical evidence that there
is a gap between what is required to graduate high school and what is required to enter college. This
raises many questions, not the least of which is Should high schools teach college preparation course-
work to all students? Further, is it the school’s fault that their students struggle as freshmen in col-
lege? It seems on the surface that high schools should mandate a fourth year of math classes beyond
the algebra II level. This exposure to higher-level math in the senior year has obvious good conse-
quences on student performance in placement tests. Based on the results of this study, this would
greatly increase the percentage of students placing into credit math classes.
From the perspective of colleges, the results of this study determined that certain portions of the
high school transcript should be considered when determining mathematics remedial placement and
college-readiness. If a student places within the upper portion of the algebra placement domain (the
decision zone), and the student has taken a math class beyond the required algebra I-geometry-
algebra II state mandated requirements, and has graduated with an overall GPA of B grade or better,
then perhaps this student is college-ready and remedial mathematics is not necessary.
REFERENCES
Achieve, Inc. (2004). American Diploma Project: Creating a high school diploma that counts. Retrieved January 23,
2009, from http://www.achieve.org
Achieve, Inc. (2006). American Diploma Project: A preview. Urban Mathematics Leadership Network Meeting.
Retrieved January 29, 2009, from http://www.achieve.org
HIGH SCHOOL PERFORMANCE AND MATH PLACEMENT 525
D ow
nl oa
de d
by [
A ri
zo na
S ta
te U
ni ve
rs it
y L
ib ra
ri es
] at
0 7:
41 2
2 Ja
nu ar
y 20
16
Achieve, Inc. (2012). How well is New Jersey preparing all students for college, careers and life. Retrieved from http:// www.achieve.org/new-jersey
Adelman, C. (1999). Answers in the toolbox: Academic intensity, attendance patterns, and bachelor’s degree attainment
(Report No. PLLI-1999–8021). Jessup, MD: U.S. Department of Education. (ERIC Document Reproduction Service
No. ED431363).
Adelman, C. (2006). The toolbox revisited: Paths to degree completion from high school through college. Washington,
DC: U.S. Department of Education. Retrieved from http://www2.ed.gov/rschstat/research/pubs/toolboxrevisit/
toolbox.pdf
Adelman, C., Daniel, B., & Berkovits, I. (2003, September). Postsecondary attainment, attendance, curriculum, and per-
formance: Selected results from the NELS:88=2000 postsecondary education transcript study (PETS), 2000.
Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of
Education. (ERIC Document Reproduction Service No. ED480959).
Armstrong, W. B. (1999). Explaining community college outcomes by analyzing student data and instructor effects
(Unpublished Doctoral Dissertation). University of California, Los Angeles, Los Angeles, CA.
Armstrong, W. B. (2000). The association among student success in courses, placement test scores, student background
data, and instructor grading practices. Community College Journal of Research and Practice, 24(8), 681–695. Bandura, A. (1997). Self-efficacy: The exercise of control. New York, NY: W. H. Freeman.
Bandura, A. (2001). Social cognitive theory: An agentic perspective. Annual Review Psychology, 52(2001), 1–26.
Bedsworth, W., Colby, S., & Doctor, J. (October 2006). Reclaiming the American dream. Boston, MA: The Bridgespan Group. Retrieved from http://www.ezsozcj.givewell.net/files/Cause4/Sponsors%20for%20Educational%20O
pportunity%20(SEO)/13-2578670%20Cause%204%20ReclaimingtheAmericanDreamWhitePaper.pdf
Berkner, L., & Chavez, L. (1997). Access to postsecondary education for the 1992 high school graduates (Report
No. NCES-98–105). Washington, DC: Government Printing Office. (ERIC Document Reproduction Service
No. ED413854).
Bourquin, S. D. (1999). The relationship among math anxiety, math self-efficacy, gender, and math achievement among
college students at an open admissions commuter institution. Dissertation Abstracts International, Section A.
Humanities and Social Sciences, 60(3-A), 0679. Brown, C. (1999, winter). Placement testing a remedial mathematics for post-secondary students: Prescription for
success? St. John’s, NL, Canada: Memorial University of Newfoundland. Retrieved from http://www.mun.ca/
educ/faculty/mwatch/vol1/cbrown.html
Brown, R. S., & Conley, D. T. (2007). Comparing state high school assessments to standards for success in entry level
university courses. Educational Assessment, 12(2), 137–160.
Common Core State Standards Initiative. (2010). Draft. New Jersey Department of Education meeting, March 19, 2010.
Common Core State Standards Initiative. (2012). Common standards. Retrieved from http://www.corestandards.org/ Crist, C., Jacquart, M., & Shupe, D. A. (2002). Improving the performance of high school students: Focusing on con-
nections and transitions taking place in Minnesota. Washington, DC: Office of Vocational and Adult Education, U.S.
Department of Education. (ERIC Document Reproduction Service No. ED466943).
Frost, J. H., Coomes, J., & Lindeblad, K. K. (2009). Collaborating to improve students’ transitions from high school
mathematics to college: Characteristics and outcomes of a cross-sector professional development project. NASSP
Bulletin, 93(4), 227–240.
Golfin, P., Jordan, W., Hull, D., & Ruffin, M. (2005, September). Strengthening mathematics skills at the postsecondary
level: Literature review and analysis. Washington, DC: Office of Vocational and Adult Education, Division of Adult Education and Literacy, U.S. Department of Education with The CNA Corporation.
Hoyt, J. E., & Sorensen, C. T. (2001). High school preparation, placement testing, and college remediation. Journal of
Developmental Education, 25(2), 26–34. Isbell, V. K. (1988). Student placement in entry level courses of reading, writing, and mathematics in community
colleges. Dissertation Abstracts International, Section A. Humanities and Social Sciences, 50(07), A1871.
Jenkins, B. G. (1991, November). Meeting the diverse needs of two-year college students through appropriate course
placement. Paper presented at the Fall Conference of the North Texas Community=Junior College Consortium, Dallas, TX. (ERIC Document Reproduction Service No. ED341444).
Keller, M. (2001). College performance of new Maryland high school graduates: Student outcome and achievement
report (Report No. MHEC-2001-RES-15). Annapolis, MD: Maryland State Higher Education Commission. (ERIC
Document Reproduction Service No. ED458857).
526 L. E. KOWSKI
D ow
nl oa
de d
by [
A ri
zo na
S ta
te U
ni ve
rs it
y L
ib ra
ri es
] at
0 7:
41 2
2 Ja
nu ar
y 20
16
Kirst, M. W. (2001). Overcoming the high school senior slump: New education policies (Report No. K-16-R-01–01). Washington, DC: Institute for Educational Leadership & National Center for Public Policy and Higher Education.
(ERIC Document Reproduction Service No. ED455720).
Luzzo, D. A., Haper, P., Albert, K. A., Bibby, J. A., & Martinelli, E. A. (1999). Effects of self-efficacy enhancing
interventions on the math=science self-efficacy and career interests, goals, and actions of career undecided college
students. Journal of Counseling Psychology, 46(2), 233–243.
Marwick, J. (2002). Alternative methods of mathematics placement. The Community College Enterprise, 8(2), 41–50.
Moss, B., & Bordelon, S. (2007). Preparing students for college level reading and writing: Implementing a rhetoric and
writing class in the senior year. Reading Research and Instruction, 46(3), 197–221.
Partnership for Assessment of Readiness for College & Careers. (2012). About PARCC. Retrieved from http://www.
parcconline.org/about-parcc
Perkins, R. (Ed.). (2004, March). The high school transcript study: A decade of change in curricula and achievement, 1999–2000. Washington, DC: National Center for Educational Statistics, U.S. Department of Education.
Pugh, C. M., & Lowther, S. (2004, October). College math performance and last high school math course. Paper
presented at the Meeting of the Southern Association for Institutional Research, Biloxi, MS. Retrieved from
https:==oira.auburn.edu=about=publications=SAIRPaper2004.pdf
Schneider, B. L., Kirst, M., & Hess, F. M. (2003). Strategies for success: High school and beyond. Brookings Papers on
Education Policy, 6(2003), 55–93.
Schwartz, A. E. (2007). New standards for improving two-year mathematics instruction. Education Digest: Essential Readings Condensed for Quick Review, 73(2), 39–42.
State of New Jersey, Department of Education. (2004). NJ Department of Education District Factor Groups (DFG) for
school districts. Retrieved from http://www.state.nj.us/education/finance/sf/dfg.shtml
HIGH SCHOOL PERFORMANCE AND MATH PLACEMENT 527
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