Understanding California's Computer Science Transfer Pathways

This paper presents the first curricular landscape analysis of transfer pathways for computer science (CS) transfer students in the public higher education system in California, the largest and most complex higher education system in the United States. Drawing on data from 115 community colleges and 31 public universities in California, this study examines and compares computer science Bachelor's degree requirements, curriculum complexities, and both ideal and existing course articulation coverage between schools. We find considerable variation in the CS degree requirements across the system, particularly in the number of math courses required and the overall flexibility of the course requirements. Articulation agreements between community colleges and four-year schools have the potential to (and sometimes do) reduce the complexity of the degree for transfer students significantly, but articulation agreements are not consistently in place across the system. This research both suggests concrete action items and surfaces important areas of further exploration to create a more seamless process for transfer students to complete their CS Bachelor's degrees.


INTRODUCTION
Supporting transfer students has been identified as an important way to broaden participation in computer science (CS) [3].Community colleges tend to disproportionately enroll students from demographic groups that are underrepresented in computing [3,6].
Yet, despite this promise, current transfer student pathways are not nearly as diverse or as robust as they need to be.80% of community college students list an intent to transfer to a four-year university, but only 25% of them actually do [10].In CS specifically, women tend to be even more underrepresented in the transfer student population [2,3,12], and transfer students are not nearly as racially diverse as community college students [23].The idea that the transfer path is a smooth four-year journey is a myth for most students.One study found that transfer students took 1,213 distinct pathways to their resulting degree [9]!Moreover, students who transfer often do not achieve their goal within 6 years [9].
One factor affecting transfer students is that different universities routinely have vastly different requirements for their CS degrees and different agreements about which community college courses count towards this degree.However, the precise nature of the inconsistencies is not well understood.
This study looks at the transfer pathways in computer science between the 115 unique public community colleges in California, and 31 of the 32 public universities in California's system (one does not offer a CS degree).We characterized and compared each university's CS degree program to learn the variation between degree programs.We also gathered, compiled and examined each program's articulation agreements with each of the 115 public community colleges to learn how complete these agreements are and how well they are structurally serving the goal of offering students a seamless path through a CS Bachelor's degree program.This is the first study that we are aware of that takes such a broad and detailed look at the structure of the requirements for CS transfer students.Addressing structural issues with curricula and course articulations is a key part of the strategy to better meet the needs of transfer students and, in turn, to diversify computer science.This study both provides ideas for immediate actions, and surfaces a number of important areas of further investigation.
typically offer Bachelor's degrees and may also offer graduate degrees; and community colleges, which offer a much wider range of degrees including two-year associates degrees, certificates, and sometimes a limited number of Bachelor's degrees.Many fouryear universities use a selective admissions process, with varying degrees of selectivity.Community colleges typically have an openadmissions policy, and are typically less expensive.
To obtain a Bachelor's degree in CS, some students enter a fouryear university directly.However, a significant and growing number of students, referred to as "transfer students," first attend a community college where they complete their early Bachelor's degree requirements, and then they transfer to a four year university to complete their degree.Because the transfer pathway is so common, community colleges and four-year universities often coordinate their curriculum so that community college courses earn credit for equivalent courses at a four-year university.These agreements are called articulation agreements.The goal is to allow transfer students to complete their first two years of study at a community college and then transfer seamlessly to complete their upper division Bachelor's degree requirements at the four-year university.
Unfortunately, the reality is not nearly so simple, especially in CS.The remainder of this section explores the challenges that disrupt the CS transfer pathway.

CS Transfer Pathways: Challenges
Transfer students generally face many well-documented challenges, which are are summarized comprehensively in a recent report from the Community College Research Center [7].One of the biggest barriers is misalignment of courses between institutions.Lyon and Denner explored the pathways taken by CS transfer students and found that they are anything but linear [16], and rarely completed in 2+2 years [15].One of the central causes of what they identify as "pathways setbacks" is the refusal of four-year universities to accept transfer credit.A large-scale quantitative study by Jaggars et al. similarly identifies lacking or unclear credit agreements as a core issue for transfer students [14].Sometimes, even when courses exist that would transfer, students cannot enroll in courses as planned due to lack of course availability.This results in loss of time, money, and credits [20].Additionally, the need to maintain a high GPA make math and CS courses daunting for students [14].
Perhaps because of this complex landscape, another barrier transfer students face is the lack of clear advising.Studies have shown the importance of advising and support from faculty [21].However, Lyon and Denner found that many transfer students reported needing better informed advisors in their community colleges [14].Other work has reported similar results [19].Advisors may be available, but only some have experience or familiarity with the courses required for a CS major.This issue is exacerbated by the fact that students frequently attend multiple community colleges [15].
A related challenge is financial constraints.Obtaining a (CS) degree to earn a good living can be a primary motivator for transfer students [5], but financial constraints can lead to students dropping out of the transfer path [22].Unclear requirements and classes that do not articulate cause students to have to pay for unnecessary or duplicate courses, raising the cost of their degree.
In this work we focus on addressing the curricular barriers that in turn will help improve advising and affordability for transfer students.However, in addition to these structural barriers, transfer students-particularly women and students from groups that are underrepresented in CS-also face social barriers.Students who do not fit the dominant CS college student demographic (18-22 year old White or Asian male) are often excluded and have a hard time connecting with other students at a four-year university [1,4,8,17].Transfer students must also adjust to a new educational environment in very short period of time, which can lead to a phenomenon called "transfer shock," causing transfer students to under-perform [12,13].Separate work is required to address these social barriers along with the curricular barriers we address here.

MOTIVATION AND RESEARCH QUESTIONS
We chose to focus on California because it is the largest higher education system in the United States [11].It has a unique and complex structure, comprising 10 major research universities, 9 of which have undergraduate programs (the University of California (UC) system), 23 teaching-focused undergraduate+graduate universities (the California State University (CSU) system), and 115 public community colleges.Together these colleges and universities enroll around three million students [11].With such a large impact on the education of the United States, understanding the transfer pathways for computer science students in California is important not only because of the number of students impacted, but also to illustrate patterns that likely occur in other systems across the country, and potentially in other countries.
We posed the following research questions for our work: (1) What are the CS degree requirements at four year universities in California, and how much do they vary?(2) How complex are the intended transfer student curricular requirements at California four year universities, and how well do articulation agreements enable what is intended?
Understanding these curricular structures will provide us with a baseline for transfer students' experiences and a foundation on which to begin to improve transfer student pathways.

APPROACH 4.1 Data Collection
4.1.1Degree requirements.We gathered data about the CS program requirements from all 31 California public four year universities that have CS Bachelor's degree programs.We also gathered data about the articulation agreements between these schools and 1151 California community colleges.We gathered CS Bachelor's of Arts (BA) and Bachelor's of Science (BS) 2022-2023 graduation requirements by hand via schools' course catalogs and department websites.When we encountered particularly confusing requirements, we reached out to the university through email to get answers to our questions.We did not include any GE or campus-wide requirements, unless specifically required as a prerequisite to a needed course, in which case we recorded it and used it in only for calculating degree complexity, as described in Section 4.2.
Our analysis required us to have a single set of graduation requirements for each program.However, many degree programs include an aspect of choice, some of which can change the overall number of courses or units students take in the program.When we encountered a requirement that necessitated a choice among several classes that might affect the size of the program, we applied the "fastest path to graduation" principle: We chose classes with the fewest extra prerequisites/lowest credits/fewest overall classes.
When a program offered both a BS and a BA degree, we included both degrees in our data collection.We focused only on CS degree programs; we did not include other computing degrees such as Computer Engineering, Information Science, etc. 2  We verified the data by hand by having a second member of the research team check the sheet for obvious errors (such as acronym misspellings).We then summed the math and CS unit totals and matched them against the 2022-2023 catalog.Finally, we verified against the catalog that all requirements in the plan were met.

Articulation agreements.
We used an automated tool to gather all 2022-2023 CS articulation agreements via the website assist.org, the official articulation website for California.In total there were 2,878 agreements.For each agreement, we separated out the university's requirements as they appeared on the agreement and the community college courses that mapped to these requirements.For each requirement, if there were multiple options for articulating courses, all options were collected.
Articulation agreements were verified by going through each agreement by hand and checking that the mapping of community college courses and university courses in the data matched the agreement.Additionally, a program went through the data looking for formatting issues so that options and requirements were correctly separated.As a final verification step, we sent our collected degree requirements and articulation agreements to CS department chairs and student affairs managers for each four-year university.Of the schools we had emailed, 9 of them responded and assisted us in validating our findings.This process resulted in only a few very minor corrections that did not affect our overall results.
When collecting data from the articulation agreements, we focused on CS and math requirements only because long sequences of math and/or CS courses are most likely to impact CS transfer student degree completion.Additionally, to compare schools on their CS transfer pathways specifically, general education requirements were withheld.

Data Analysis and Visualization
We used a combination of descriptive statistics, visualizations and graph algorithmic metrics to examine the composition and complexity of each degree program.The straightforward visualization and descriptive data will be described in the results section.In this section we describe our use of the Curricular Analytics (CA) tool 3  to measure the complexity of a computing degree.
CA represents a set of degree requirements as a directed graph, with a node to represent each course and edges to represent prerequisite dependencies between courses.CA has many features, 2 UC Berkeley has a CS BA and a EECS BS.Because they do not have a straight CS BS degree, we included their EECS BS degree. 3https://curricularanalytics.org/but we used its complexity metric, which quantifies how complex a curriculum is based on its number of required courses and course interdependencies.Complexity is defined as the sum of all of the blocking and delay factors of the included classes.The blocking factor is determined by how many classes are directly blocked by a student failing to pass a particular class.The delay factor is calculated by taking the longest string of classes in a given vector and assigning that number as the delay factor for each of those classes.
In addition to the overall complexity of each four year degree program, we were also interested in the complexity of the degree requirements for transfer students, who come in with some portion of the degree requirements satisfied.We refer to this complexity as the residual complexity, and it is calculated by removing the nodes (and the associated edges) representing the courses for which transfer students would have already received credit, and calculating the complexity of the remaining graph.
Articulation agreements for a single four-year university vary widely across community colleges, so in our analysis we focused on two types of residual complexity: ideal and existing.The ideal residual complexity (IRC) for a four year university measures the complexity of the remaining degree requirements if all required CS courses listed in a university's articulation agreement are satisfied.This is the lowest possible residual complexity for that university.However, in practice only some four-year universities have requirements listed in their articulation agreement that are fully met by even a single community college, so this ideal complexity may only sometimes be possible.We complement the IRC with the measure of existing residual complexity (ERC).ERC finds the community college with the most complete set of articulated courses for the given university, and measures the complexity of the remaining degree when the courses that are actually articulated are removed.

CS Degree Requirements
To compare CS degree requirements across the different California public universities (RQ1), we visualized the total unit counts in different categories for each program (see Figures 1 and 2) 4 .Units from semester-based schools have been converted to quarter units.
We can see from these charts that the unit requirements for CS programs vary widely, ranging from a low of 78 quarter units to a high of 145 quarter units.Much of this variation comes from the courses required in math and science, and not CS.In the UC schools (Figure 1), Berkeley, Santa Cruz and Davis have notably fewer CS requirements, but the remainder of the schools require a fairly similar number of CS units.The patterns in the CSUs (Figure 2) are a bit less clear, but the number of CS requirements does not obviously grow as the number of required units grows.
Generally each school requires substantially the same lower division CS courses.However, the same course can be worth more units at some schools than others, sometimes because of a laboratory component.For example, UC San Diego's "Computer Organization and Systems Programming" is a four-unit course which appears to cover similar material to UC Santa Cruz's "Computer Systems and Assembly Language and Lab," which is worth seven units.Some At the upper division, we divided courses into "required" and "elective" to give a sense of how much choice students have in the program.Required courses are core courses that are mandatory and must be taken for graduation.Elective courses include any courses where students have a choice of what to take to satisfy a major requirement, including open electives.We see significant variation in the relative proportion of required vs. elective courses, with programs specifying only one or two courses that all students must take, while others have more prescriptive degree requirements.
The mathematics courses that each university offers are typically chosen from the following: Calculus I, II, III, linear algebra, differential equations, and statistics.Some schools require all of these, while others only require a few of them, and they again vary in their unit counts.
In terms of science, most UCs and CSUs require some physics courses.The others may either give the option of choosing physics, chemistry, biology, or another science course offered with a lab.Only four programs (UC Berkeley's BA, UC Santa Cruz, Cal Poly Humboldt, and CSU Monterrey Bay) do not require a science course for the CS major.
A few schools had requirements outside of CS, math and science.Nearly all of these are philosophy and ethics courses that fulfill an ethics requirement for the CS major.

Articulation Coverage
Our second research question investigated the intended degree experience is for transfer students.Figure 3 compares the ideal and existing residual complexities against the original degree complexities.Figure 3 demonstrates that while there is significant variation in the complexities of the four-year degree programs, both the average complexity and variance are significantly reduced for the intended remaining degree requirements for transfer students.The lower complexity scores are expected and perhaps not terribly informative because we have decoupled the lower and upper divisions and removed the courses on which most of the upper division courses depend.What is interesting is that a few schools still have fairly complex coursework remaining (e.g.UC Los Angeles, UC Riverside and CSU Northridge).The other point to note is that the IRC and ERC bars are very close, indicating that for most four-year schools there is at least one community college that offers all or almost all of the required courses in the articulation agreement.
This complexity analysis shows only what the curriculum looks like for a (near) ideal articulation, where students have the option to complete all lower division requirements at community college.However, this ideal is uncommon.More often, either an agreement does not exist or not all lower division requirements are articulated.
Figure 4 displays the articulation coverage between four-year universities and community colleges as a proportion (from 0 to 1) of required lower division math and CS units that are covered by the agreement, with darker colors indicating closer to full coverage.The first issue to note is that many agreements are missing entirely.Of the 3,472 possible articulation agreements, only 2,878 2022-2023 agreements exist on assist.org.Additionally, most agreements are incomplete.Only 306 agreements articulated all the lower division math and CS units from a given school, while 888 (31%) had over 75 percent of the these units articulated.
We see three patterns of articulation from the institutions in Figure 4: (1) broad high coverage, represented by consistently dark rows or columns; (2) selective high coverage, represented by rows and columns with dark and light spots; and (3) broad weak or missing coverage, represented by light rows or columns.
Schools with broad, high coverage have strong articulation agreements with a wide range of schools.We see this pattern for both four-year universities (rows) and community colleges (columns).CSU Monterey Bay (CSUMB), which has agreements with all community colleges, has the highest median percentage of lower division math and CS courses, with 93 of its 115 agreements having 100% coverage.Only 14% of its agreements cover less than 50% of the lower division math and CS courses.
Schools with selective high coverage partner well with a limited number of universities or community colleges.Most community colleges fall into this category, but some four-year universities, such as UC Merced (UCM) also do, perhaps because of Merced's relatively remote location in the state.UCM has particularly strong agreement with Merced College.The agreement between these schools had the most lower division math and CS courses mapped of any pair.Additionally, within this agreement, the ratio of transferable units from Merced College's courses to UC Merced's required units is also quite close to 1, meaning that transfer students complete a similar amount of work as non transfer students to meet these requirements.Other agreements sometimes require more than one course at a community college to earn credit for a single course at the four-year university.
Finally, several of the schools in the broad weak category are fouryear universities, including several UCs.This pattern also occurs for some community colleges, showing clear areas of curricular structural improvement needed for transfer students in CS.

DISCUSSION
In this section, we tie together the results presented in the previous section to discuss how CS programs can use these results to better support their transfer students.We then describe the key areas for researchers to explore in order to further our efforts to improve the curricular paths for transfer students in CS.

Implications for CS Programs
Increase articulation agreement coverage.We found that there is significant variation among graduation requirements and articulation agreements.This variety in requirements can be confusing for students trying to plan out transfer pathways.Additionally, the community college a student starts their journey from will have a large impact on how well a student is set up for success at the receiving college.It is critical that four year colleges and community colleges work together to close gaps in articulation agreements, and this is especially important for several UC's that have weak articulation agreement coverage.
Reduce overall degree size and complexity.CS requirements at four-year universities vary significantly.Many schools successfully graduate CS majors with a minimal set of requirements, including few math and science requirements.Programs with more complex requirements should work to reduce their curriculum complexity in order to simplify and shorten transfer pathways.
Consider the expectations for transfer students.Although in general ideal residual complexities were low, at some schools the residual complexity remained fairly high, indicating that transfer students might still struggle even when they enter with all possible articulated courses.Universities can work to ensure that the intended experience for transfer students is reasonable.
Advertise strong partnerships.We found some partnerships that were quite strong.One example is the CSin3 program between Cal State Monterrey Bay and Hartnell College [18].In these cases both schools must work together to promote this pathway so that students see a viable path to a Bachelor's degree.

Open Questions and Next Steps
The findings have given rise to several follow up questions for further exploration.These questions include • What are the characteristics of community colleges and universities with low articulation rates?• What role does proximity play in articulation coverage?
• Is it realistic to complete articulated courses at different community colleges in two years?• How different are the courses required by different universities?I.e., How early does a student have to commit to their specific transfer university?We primarily studied the ideal transfer pathways, meaning that we did not take into account the nuance of how students actually traverse these pathways.It is imperative to address the divergence between ideal and reality.Practically, students might be unable to take specific courses due to scheduling conflicts, limited available seats, or their school not offering courses they need.Additionally, different articulation courses and requirements for different universities can force students to take more classes to apply for transfer to several universities, increasing the chances of acceptance at one.Extra waiting time and increased course load from maximizing transfer opportunity can result in unexpected delays and extend the duration of their community college enrollment.

Threats to Validity
The data presented is only valid for 2022-2023, so this study is of a snapshot in time.University requirements change often and some universities will have new changes for the next academic year.Also, despite our verification steps, it is likely that small errors still exist in the research data.

CONCLUSION
This study shows that most California CS transfer pathways are far from ideal, though there are examples that show what can be achieved.Articulation agreements vary widely in how many of the university's graduation requirements they cover as seen in the percentage of articulated units covered and the residual complexity.
Additionally, there is variability in how many units a university's CS program encompasses.Though certain schools may have a clear CS program with a low number of graduation requirements, their agreements may not have good coverage.This means that a transfer student can be left to complete a large number of requirements after transfer which could deter them from completing the degree.It is important to note that having a good agreement or CS program does not always mean that a transfer student will have a smooth transfer experience since students may struggle to get into needed classes and face delays if they do not pass a class on the first try.It is no wonder that many do not acquire their degree in the expected time frame, or do not complete it at all.The need for clear and more uniform transfer pathways from community colleges to public universities in California is important since transfer students face challenges beyond coursework.Simplifying the transfer pathways is a key to increasing CS transfer student success.We hope this will be addressed so that future cohorts of transfer students have a better chance of successfully completing their degrees.

Figure 3 :
Figure 3: Program Complexities and Residual Complexities.UCs are labeled in green.

Figure 4 :
Figure 4: Heat map showing the proportion of required lower division math and CS requirement articulation agreement coverage.Community college labels are not shown due to space restrictions.