Physics describe the students who take physics courses,

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Education Research frequently investigates what students studying physics do on
small time scales

single courses, observations within single courses), or post-education time
scales (e.g., what jobs do physics  majors
 get?) but  there is little research into how students get
from the beginning to the end of a physics degree. Our work attempts to
visualize students paths through the physics major, and quantitatively describe
the students who take physics courses, receive physics degrees, and change
degree paths into and out of the physics program at Michigan State University.



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and retaining students in the physics major is an important challenge that
departments across the country are facing 1, 2. Understanding the kinds of
programs and practices that can support and sustain students intending to major
or those currently majoring in physics is critical to grow a diverse population
of physics graduates. The research that looks at specific student experiences
to develop rich descriptions of how those experiences influence students’
perceptions and choices provides some understanding 3, 4.As does the work
that uses prior student experiences to model eventual outcomes 5. Equally
important is working to understand what might be learned using data from
institutions themselves. For this project, we have collected student
registration data at Michigan State University (MSU) in order to develop
analytic methods that help unpack the pathways into and out of the major.


has collected a wide body of data on students for the last 10+ years. This data
set contains information on over 100,000 students who have taken math and
physics courses at MSU. Two percent of these students have declared a physics
major at some point in their academic career and 0.5% of students have earned a
bachelor’s degree in physics. This data includes time stamped course and degree
major choices, grades and demographics such as gender, ethnicity, and family
educational history.


this methods paper, we are interested in (1) understanding the means of
analysis that provide information on students’ paths into and out of the
physics major, (2) developing visual representations of these analyses that
communicate what paths students take through the major, and (3) describing

possible mechanism (inferred from the available data) that can explain what
differentiates students who receive a degree in physics and those that do not.
In doing this work, our aim is not to dismiss the rich work around retention
and recruitment, e.g., Refs. 3–5, but rather to provide additional context on
that this (and other work) might draw. In this paper, we have not conducted an
analysis using demographics.







is a large, land grant university with approximately 39,000 undergraduate
students currently enrolled. MSU has both a college of arts and sciences and a
college of engineering and enrolls > 2000 students in introductory physics courses
annually. The student population is predominately white (65.7%) with a sizable
minority population (34.3%).MSU has slightly more women enrolled than men (48%
men, 52% women).The physics major enrolls a greater proportion white students
(73.8%) in comparison to the general population and graduates a greater
proportion as well (83.1%). MSU physics graduate gender contrasts to the
general population (83% men, 17% women) – a proportion that is typical of
physics departments across the country 6.







have begun to describe student pathways at two levels. One level looks at the
starting major that students declare and the final major for which the student
receives a degree. We visually represent the movement from start to finish
using an alluvial diagram (FIG. 1) 7. This diagram helps visualize

student initial conditions affect graduation outcomes (e.g., what proportion of
students graduate with their initially intended degree). A second level
describes the order in which students complete each course required for the
major. We represent this visually using a bubble diagram (FIG. 2).This level
highlights the track that students take through the physics program and how
completion of those courses relates to recommended, “on-track” schedule.
Approximately half (44.1%) of students who declare a

major at MSU do so when they first arrive at MSU. The remaining students switch
into the physics major from a different degree programs or have not declared a
major. Graduating students who declare a physics major are likely to remain in
a STEM degree program even if they move away from physics (FIG. 1).
Approximately one-third (33.7%) of students who attempt to get a degree in
physics at MSU do so. An additional one-third (33.7%) complete a degree in an








1. Color online  Approximately one
third of students declaring a physics major go on to receive a degree in physics.
Most students (87%) who declare a physics major eventually receive a degree in
STEM if they graduate. Groups on the left are the initial major declared by the
student. Groups on the right are the graduating major. The students receive a
degree in.



program. The remaining students are likely to pursue other STEM offerings
(e.g., chemistry or mathematics).

frequently complete physics courses outside of the recommended schedule by the
physics department (FIG. 2). For example, students who declare a physics major but
ultimately receive a different degree are most likely to take their
introductory mechanics course (PHY 183) in their third semester and
introductory electricity and magnetism course (PHY 184) in their fourth
semester. Students who receive degrees in physics are more likely to take this
introductory sequence prior to their third semester. Additionally, many
students who eventually earn degrees in physics take Senior – level E
(PHY 481) up to 1 year before the recommended schedule. While we acknowledge
there could be many reasons for students taking courses at different times, we
are (currently) interested in finding useful representations that describe for
a single institution what pathways students take through the major.









this initial study, we found that grades earned in math and physics courses
differentiate students that eventually earn physics degrees from other
graduates. Because course grades are not normalized measurements, we cannot
compare raw grades between different courses, different course instructors,

different semesters. Thus, we have used the standard score or “Z-score” 9 to
normalize students’ grades in a single course offering.







I. Numbers of students and their corresponding normalized
scores for the groups represented in FIG. 3a. Students are labeled by their
graduating major and whether or not they ever declared a physics major.












Z-score provides a measure of what fraction of a standard deviation (_)
that a particular value (x) deviates from the mean (_) of a distribution of scores. By
using the Z-score, we do assume that students’ scores within a given course
offering are drawn from a normal distribution.




compare groups of students, we first calculated the Z-score for each student in
a particular course offering for every course from a restricted list of courses
(described below). We grouped students by the degree they eventually earned (physics,
engineering, STEM, and non-STEM) as well as by the condition of declaring
physics as major any time in their academic career (yes, no) – leading to 7
total groups. We then calculated the mean Z-score and standard error for
physics courses and math courses separately for the population of students in
each of the seven groups of students. These mean Z-scores along with their
standard errors are shown in both in TAB. I and FIG. 3.




have restricted the courses from which we draw our data to only introductory
courses (100 & 200 level) required to earn a bachelor’s degree in physics.
Many different degree programs require these math and physics courses, thus
they provide a large basis to compare students (TAB. I). These courses include
introductory mechanics (PHY 183), introductory electricity and magnetism (PHY
184), introductory lab courses (PHY 191, PHY 192), a third semester course
covering thermodynamics and modern physics (PHY 215), and the calculus sequence
from Calculus I to a first course in ordinary differential equations (MTH 132,
MTH 133, MTH 234, MTH 235).



find that students who receive a degree in physics perform above average in
introductory math and physics (FIG. 3a; TAB. I). we refer to these plots as
“normalized comparisons.” Based on these normalized comparisons, students who
declare a physics major but then move to other STEM programs/Engineering
programs perform below average. Further, students who never declare a physics major
and receive a degree in STEM/Engineering programs perform above average. We
also find that students whose first declared major is an engineering program
but ultimate degree in physics perform below average in physics and mathematics
introductory courses.





2. Color online A time line of enrollment of students declaring a physics
major separated by their eventual graduating degree. Non physics graduates who
have declared a physics major typically take physics after the recommended
semester. Bubble size indicates the relative proportion of students taking the
course in comparison to the entire group (i.e., physics, engineering, other
STEM, non-STEM). Colored bubbles indicate courses taken during the recommended
semester, gray bubbles indicate courses taken outside of the recommended
semester, semester index is represented by the gray/white horizontal bars
(first semester courses are at the bottom, senior level courses are at the top).
Colors differentiate between exit  degree




3 Color online Physics students receiving BS/BA degrees in physics/astronomy
are above average in introductory course performance in comparison to students
who move to different programs before graduating. (Fig 3b) Students receiving
physics degrees who initially declared engineering majors earn below average
grades in introductory physics and math courses. The error bars represent the
standard error of the mean for each axis. (Fig 3a) data labels indicate degree
category students received, (Fig 3b) labels indicate initial major declared.








this paper, we have analyzed data collected by the registrar at MSU over the
last 10+ years. This data can begin to provide information about the pathways
that students take into and out of the physics major (for a given institutional
context). In this methods paper, we have presented 3 representations (FIGS.
1-3) that offer some shape to the story at MSU.




particular, we have found that students earning physics degrees who have
initially declared physics come from all areas of the university in roughly
equal measure (FIG. 1); contrary to departmental anecdotes. Students who leave
the major also earn degrees in different areas in roughly equal measures, which
is also is counter to the prevailing narrative in the department. Second, we
find that students who earn physics degrees tend to follow the departmentally recommended
path up to the last year of their studies. We also find that students who eventually
earn engineering degrees leave physics during or after the first E&M course
(PHY 184; Green circles in FIG. 2) while students who eventually earn other
STEM degrees leave much later (Pink circles in FIG. 2). Finally we  find that students who are physics degree
earners perform better in math and physics than students who declare physics and
eventually earn some other degree, but perform not as well on course work than
their engineering colleagues who never declared physics as a major (FIG. 3).



this work, we are not claiming that we have uncovered the full story from our
current analysis or that all possible representations have been generated to
explain our claims. Rather, we are suggesting that we have developed some
methods and representations (SEC. III) that provide some context for the paths
that students take through the physics major at MSU as well as a possible
mechanism for the observations of related to student attrition (SEC. IV). While
our results that show that students earning lower scores in math and physics
courses are more likely to not earn degrees in physics (FIG. 3) are fairly
obvious, we have also provided data that demonstrates that pathways of those
degree earners are different from students earning degrees in other areas (FIG.



insight gained into the pathways that students take as gleaned from this data
and our representations suggests there is a deeper and more interesting story
that might exist in our data. For example, how do these pathways differ for
different populations of students (e.g., based on incoming GPA, race, and
ethnicity)? Furthermore, there are some analyses to be done that might provide
additional context (e.g., how math and physics course enrollment and performance

our analyses and representations provide some context and detail about student
pathways through the major, we recognize that by assuming a particular pathway
for students to earn a degree (FIG. 2) that we are deemphasizing alternative pathways
and, likely, marginalizing non-traditional students. Moreover, that we assume a
particular course trajectory for students to earn a physics degree might paint
an unreasonably narrow picture of how students earn physics degrees. We are in
the process of developing additional analyses that are not predicated on the
student taking courses in a particular order. What we suspect is that a more
comprehensive diagram that demonstrates the relationship between math and
physics courses taken (i.e., in what order) will support our analysis and
provide new and interesting information on student progression through the
course work.



our present analysis neglects demographic information that might be important
for understanding how different groups of students might be affected
differently. As we construct new analyses and produce different representations
of our data, we might find that asking similar questions of the data from this
perspective will offer new insights into the pathways that women and
under-represented students take through the major. Such an analysis is
necessary if we are meant to foster and grow a diverse population of physics graduates.

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