The Effect of Ninth-Grade Physics in One Private School on Students’
Performance on the Mathematics Section of the PSAT
P.O. Box 141
Lincolndale, NY 10540
Germantown Friends School (GFS) in Philadelphia introduced ninth-grade physics
(replacing ninth-grade biology) in 1999. I have studied the effect of this change on the
mathematical performance of students on standardized tests taken late in the eighth grade
and early in the tenth grade. I examined data for six classes, three that did not have ninth-
grade physics and three that did have it, including in the survey only students who were
enrolled at GFS in the eighth, ninth, and tenth grades. There were no significant
differences in the performance of the six classes on the Quantitative Ability sub-test of
the CTP III test in the eighth grade. However, all three classes that had ninth-grade
physics performed significantly better on the mathematical section of the PSAT in the
tenth grade than did the three classes that did not have ninth-grade physics. This result is
not entirely surprising, since the ninth-grade physics course, despite its conceptual focus,
did make use of some algebra and a small amount of geometry.
INTRODUCTION AND METHODOLOGY
In the fall of 1999, Germantown Friends School (GFS) "inverted" its upper-school
science sequence from biology-chemistry-physics to physics-chemistry-biology, joining
about 150 other schools which, at that time, had opted for "physics first"1. Although the
arguments in favor of the inverted sequence1-8 are persuasive, they are based more on the
intellectual logic of the sequence than on measured outcomes. I do not know of any
quantitative studies that explore the effects of teaching physics in the ninth grade. I set
out to explore one small facet of the GFS change?how replacing biology by physics in
the ninth grade affects the math skills of the students.
The students attending this K-12, co-educational, private day school are from
Philadelphia and surrounding suburbs. Although many are from middle-class and upper-
middle class families, the school provides numerous scholarships and financial aid
opportunities to qualified students who exhibit financial need. The students in eighth
grade through twelfth grade are placed in distinct math courses based on ability grouping,
but the science curriculum maintains heterogeneous groupings. The total school
enrollment is approximately 900 students. There are about 80 to 88 students in each
eighth-grade class, and 88 to 98 in each ninth- and tenth-grade class. During eighth grade
through twelfth grade, the enrollment in each section of a course is typically 16 to 20.
The school is located in a lower-middle class urban community, and is academically
competitive. Graduates are often accepted into highly selective colleges and universities.
Faculty members do not need to be certified in order to teach at the school, but more than
two-thirds of them have an advanced degree.
The Physics Course
Since physics was introduced to the ninth grade, all of the ninth grade math and
physics teachers have met a number of times to discuss their respective courses.
Although no joint lessons have been presented to students, the teachers use these
conversations to learn what vocabulary is being introduced to the students. These
discussions also provide the teachers with information concerning what skills and tools
are being enhanced in each course and what background knowledge would most aid
students in each class. This collaboration has been quite informal, but it has improved
communication and coordination between the science and math departments.
Additionally, math teachers have made efforts to use the equations and concepts of
physics in their classrooms and they continue to occasionally borrow physics equipment
for demonstrations and classroom exercises.
This introductory physics course uses the third edition of Paul Hewitt’s
Conceptual Physics and the accompanying Concept-Development Practice Book. In the
three-year period 1999-2002, five different teachers taught this course but they followed
similar approaches and focused on many of the same topics. The course is hands-on and
is not a memorization intensive course. The students study motion in one and two
dimensions, Newton’s laws, momentum, energy, circular motion, center of gravity,
rotational mechanics, wave motion, sound, and light. In some years, the students have
also been able to explore areas of electricity, magnetism, and optics. The emphasis is on
conceptual comprehension of the material, but there is frequent quantitative work
performed in lecture and the laboratory that complements the information being studied.
The mathematics used is algebra and some topics from geometry. Students are not
expected to carry out derivations or solve multi-step problems of the kind that are
common in higher-level courses.
An annual event that takes place in this course is the Physics Olympics. For this
assignment, students spend at least three weeks in the spring applying their knowledge of
physics to one of a handful of construction assignments that aim to solve a problem under
certain constraints. Projects in the past have included a gravity powered car, an elastic
powered airplane, a light and strong tower made of index cards, a mousetrap powered
car, an egg drop, and a car that must travel forwards and backwards. Each group works
on one of the projects and ultimately competes against others who worked on the same
event. Projects are judged based on criteria supplied to students before they began
construction. Students must also write journals and reflection papers relating their design
to physical principles and concepts studied in the year or learned through independent
Methodology of This Study
Each student in the school completes a Comprehensive Testing Program III (CTP
III) Level F test during the spring of eighth grade. This standardized test is published and
distributed by the Educational Records Bureau and is composed of eight sections that
assess performance in verbal and quantitative areas. The Quantitative Ability section is
similar to, but not at the same depth as, the mathematics portion of the PSAT and SAT 1.
Scores are reported in percentiles relative to the national performance of eighth graders.
In the fall of tenth grade, many students choose to take the PSAT. These scores are
reported in percentiles relative to the national performance of college-bound juniors.
Percentile scores on the Quantitative Ability subtest of the CTP III were collected
for the graduating classes of 2000 through 2005. The participants in this study were
enrolled at GFS during eighth, ninth, and tenth grades. Students who did not take both
the eighth grade CTP III test and tenth grade PSAT were omitted from the study. For the
classes of 1999-2002, biology was offered in the ninth grade; for the classes of 2003-
2005, physics was offered. For the latter three classes, the few students who did not take
ninth-grade physics were omitted from the study. The CTP III data served as a baseline
to see if all six classes had comparable quantitative skills at the end of eighth grade.
After statistical analyses established that the six classes’ scores were comparable, I
analyzed these same students’ scores on their tenth grade PSATs. For the three classes
that did not have physics, I used statistical tests to determine whether these three classes
had comparable grades on the math portion of the PSAT. I then compared these data
with the PSAT performance of those members of the next three classes who had studied
physics to see if statistically different results were observed.
Table 1 shows students’ performance on the Quantitative Ability subtest of the
eighth grade CTP III test, and the sample size, for the six graduating classes of 2000 to
A chi-square test for the mean scores listed in Table 1 gives the results ? 2=0.107,
df = 5, and p < 0.005. This means that there is a greater than 99.5% likelihood that the
deviations that occur among the six years can be attributed to chance€
. Therefore, the
chi-square statistical test implies that it is highly probable that the observed fluctuations
among the six graduating classes are not unexpected and all six classes have similar
quantitative abilities at the end of eighth grade.
Between the eighth-to-tenth-grade experiences of the first three classes
(graduating in 2000-2002) and the latter three classes (graduating in 2003-2005), the
change from biology to physics was the only significant change in the curriculum or
The average percentile performance of each class, during its sophomore year, on
the quantitative portion of the PSAT is listed in Table 2.
A chi-square test for the PSAT scores between 2000-2002 resulted in ? 2=0.203,
df = 2, and p = 0.90. This implies that there is a 90% chance that the variations in the
scores during this time period are explained by chance. Therefore, the graduating classes
of 2000, 2001, and 2002 can be viewed as having similar quantitative skills during the
fall of tenth grade.
The scores from the classes of 2000-2002 were combined together to establish a
larger data set of students’ performances on the PSATs prior to the placement of physics
in the freshmen year. These values were compared with the data collected for each year
after the change in the science curriculum. The aggregate percentile performance of the
pre-inversion classes and each post-inversion class is noted in Table 3. A two-sample t-
test related the pre-inversion and post-inversion sets, and the results are listed in Table 4.
Table 4 shows that for the class of 2003, the results are significant at the p < 0.1
level and the data for the classes of 2004 and 2005 are significant at the p < 0.005 level.
This means that there is a less than 10% chance that the increase observed for the class of
2003 relative to the pre-inversion classes occurred by chance. Similarly, there is less than
a 0.5% chance that the increase noted for the classes of 2004 and 2005 relative to the pre-
inversion years was a result of chance. This data indicates a strong association between
physics in the freshmen year and improved test scores on the mathematics’ portion of the
PSATs for students at Germantown Friends School.
SUMMARY AND DISCUSSION
For the six-year span of this study, all of the eighth-grade classes had comparable
quantitative abilities as measured on the standardized test. Before ninth-grade physics
was introduced, students’ scores on the math portion of the PSAT in tenth grade
remained relatively constant from year-to-year. Placing physics in the ninth grade
curriculum coincided with an observed improvement in the mean performance on the
math section of the PSAT. It is highly likely that chance does not account for this
improvement. The improvement was less marked for the first class to take physics (class
of 2003) than for the next two classes (classes of 2004 and 2005). This could be
associated with who taught the course and how, since the teachers were not the same for
all three of these years.
Although this paper discusses a circumscribed study consisting of a small sample
at a specific school, it is important because despite all the discussions and papers
regarding ‘physics first’ I have been unable to find any quantitative studies that analyze
the effects of teaching physics in the ninth grade. This paper does not definitively prove
that the physics course is solely responsible for raising students’ performance on
standardized assessments of quantitative ability, but this change in performance has a
strong correlation with the curricular changes made in our science sequence.
I would like to thank Ken Ford for his help, support and encouragement with this paper.
Additionally, I want to thank Suzanne Levin Weinberg, Chin-Tang Liu, Olga Livanis,
Leon M. Lederman and Denise Koehnke for their contributions to this paper and project.
I also want to thank Germantown Friends School and the many members of that
institution who enabled me to use its resources for this study.
Table 1: Performance of each grade on quantitative portion of the CTP III test
Year of Senior Graduation
Mean CTP III
Sample Size (n)
Table 2: Performance of each grade on mathematics’ portion of the PSAT
Year of Senior Graduation
Sample Size (n)
Table 3: PSAT performance of pre-inversion classes and each post-inversion class
Year of Senior Graduation
Sample Size (n)
Table 4: T-test results comparing post-inversion PSAT scores for each class with pre-
Year of Senior
Degrees of freedom