Physics

Education Research frequently investigates what students studying physics do on

small time scales

(e.g.

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.

I. INTRODUCTION

Recruiting

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.

MSU

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.

In

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

a

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.

II. MICHIGAN STATE PHYSICS

MSU

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.

III. STUDENT PATHWAYS

We

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

How

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

Physics

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

FIG.

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.

engineering

program. The remaining students are likely to pursue other STEM offerings

(e.g., chemistry or mathematics).

Students

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.

IV. EARNED GRADES DIFFERENTIATE

PHYSICS

GRADUATES FROM OTHERS

In

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,

and

different semesters. Thus, we have used the standard score or “Z-score” 9 to

normalize students’ grades in a single course offering.

TABLE

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.

The

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.

To

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.

We

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).

We

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.

FIG.

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

obtained.

FIG.

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.

V. DISCUSSION & CONCLUSIONS

In

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.

In

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).

Through

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.

2).

The

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

interact).

While

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.

Finally,

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.