1. Data Requirements
To get started, we need to discuss what kind of data is needed to run the basic analyses in the package. The main premise of Curricular Analytics, and similar complementary methods, is to treat a program or curriculum as a graph (or network). In this model, we treat each course as a vertex (or node) in the network. The edges, or connections among the vertices, are the prerequisites and corequisites defining the sequence in which courses must be completed. For example, the data would be entered like so.
courses <- c("A","B","C","D","E","F","G","H","I")
prerequisites <- c(" "," "," ","A","C"," ","D","F","D")
corequisites <- c(" ","A"," "," "," "," "," "," ","H")Note that the entry for “A,” or the first index of the vector, is intended to be associated with the corresponding first index of the two other vectors: prerequisites and corequisites. Typically, this would be entered in a spreadsheet where each row corresponds to a course and its relevant information.
Believe it or not, these data are sufficient to perform the standard analyses in Curricular Analytics. However, it is useful to include some additional information to the network to make it correspond to actual curricula. Specifically, we want to specify the term in which each of these courses are taken. So, we can introduce a vector that gives each course a term.
To run the analyses in the package, we need to create an object that works with the functionality of the igraph package - which enables much of the analysis. Now, we’ll load our package to get access to the functions we need.
The function that will create what we call the plan of study object is called create_plan_of_study. It will take four inputs at minimum, the courses, the prerequisites, the corequisites, and the terms. There are several optional arguments we will attend to later.
example_plan_of_study <- create_plan_of_study(Course = courses,
Prereq = prerequisites,
Coreq = corequisites,
Term = terms)To plot this plan of study, we use the plot_plan_of_study function. The only input is the object we just created.
When we model curricula as networks in this way, we should always get what is called a “directed acyclic graph.”
Directed: Meaning that the order in which you move from vertex to vertex matters Acyclic: Meaning that you CANNOT revisit a vertex; there are no “cycles” or loops
These properties naturally emerge from our understanding of how academic programs work. Prerequisites define the order in which courses can be completed, which suggests that movement from one vertex to another has a direction. Moreover, because the program defines the sequencing of courses, students are not expected to go back and retake courses (though this does happen, we are not handling student data, only the program information). Therefore, there should be no loops - satisfying the acyclic criterion.
There are occasional exceptions that have appeared during our analyses of engineering programs in the US, particularly how laboratory courses are connected to their lecture counterparts. In these cases, the program author will sometimes list the lecture course as a corequisite for the laboratory course AND the laboratory course as a corequisite for the lecture course. This issue is referred to as courses being mutually coreqed. This configuration creates a cycle and thereby violatesthe acyclic criterion. This situation may not seem like a pertinent issue, but the presence of a cycle renders some functions usuable.
Whenever you have courses that are mutually coreqed you must select one direction to define the corequisite relationship. In the case of laboratory courses, we recommend that the corequisite relationship be defined in the row of the laboratory course. If you are running several programs, be consistent in the chosen direction.
To check whether your data is ready for analysis, you can use the following function called admissibility test. This function checks for cases where there are illogical arrangements of courses (e.g., a course and its prereq occurring in the same semester) and cycles present. The only input is the plan of study object we created. If there are issues, the function will point you to which courses are causing the problem(s).
## $DAGErrors
## NULL
##
## $PrereqErrors
## NULL
##
## $CoreqErrors
## NULLWhat if there are issues? Let’s mess up the plan of study data. We’ll introduce three common errors. First, we’ll make A and B corequisites with one another - which introduces a cycle, a problematic feature of these graphs we’ll discuss later when we’re calculating different quantities. We’ll make E a prerequisite for F and have I and H be corequisites, both of which are illogical combinations. The admissibility test will flash us messages of any relevant errors and give a vector of the problematic courses.
courses <- c("A","B","C","D","E","F","G","H","I")
prerequisites <- c(" "," "," ","A","C","E","D","F","D")
corequisites <- c("B","A"," "," "," ","I"," "," ","H")
#E is a prereq for F in same semester
#A and B are mutually coreqed, F has coreq I in diff semesters
error_plan_of_study <- create_plan_of_study(Course = courses,
Prereq = prerequisites,
Coreq = corequisites,
Term = terms)
admissibility_test(error_plan_of_study)## (Not Directed Acyclic Graph): Your plan of study did not pass an admissibility test. One or more of your prerequisites/corequisites form a cycle. Check if courses are mutually coreqed. If so, check the original plan of study for the correct direction.## (Illogical Prereqs): One or more courses have a prereq in the same semester as themselves.## (Illogical Coreqs): One or more courses that serve as coreqs are in different semesters.## $DAGErrors
## [1] "A" "B"
##
## $PrereqErrors
## [1] "E" "F"
##
## $CoreqErrors
## [1] "I" "F"Note that the plotting functionality depends on the graph being a DAG, so if that test is failed, you will be given a warning message to fix it. However, the plan of study will still be plotted.
## Warning in plot_plan_of_study(error_plan_of_study): Your data fails the
## Directed Acyclic Graph admissibility test. Crucialities cannot be added to the
## plot. Please use *admissibility_test* to diagnose and fix the error.
1.1 Representing more complex prerequisite relationships
In the original conceptualization of Curricular Analytics, data entry can only handle AND type relationships with pre and corequisites. For those that want to incorporate more detailed prerequisite relationships, we offer the following notation to make data entry more straightforward. Moreover, future metrics could take advantage of this additional information.
AND-type relationships
For AND type relationships, meaning the student must pass both A, B, and C. We use commas to separate them: A, B, C.
OR-type relationships
For OR type relationships, meaning the student must pass both A, B, or C. We use plus signs to separate them: A + B + C.
Subset of courses
When students are provided a list of courses from which they are required to pass some subset of them, we can use the FROM keyword in the following fashion. So, for example, if the list of courses is A, B, C, D, E and students must complete two of them, then we would write: FROM(A,B,C,D,E)[2]. In general, for X courses that must be completed, the notation is FROM(A,B,C,D,…,Z)[X].
Minimum grade
If a course must be completed with a minimum grade before enrolling in a later course, we use the keyword MINGRADE. For example, if A must be completed with at least a C-, then we would write: MINGRADE(A)[C-]. In general, if A must be completed with grade X, we notation is MINGRADE(A)[X].
Combining different types of requirements
Sometimes you might need to combine the various requirements discussed so far. For example, AND and OR requirements could be mixed: the student must pass both A and either B or C. In this case, we will group them using parentheses: A, (B + C). Use parentheses to group any ORs, otherwise commas can be used to combine requirements. Here are a few possible arrangements:
(A,B) + C: Either A and B or C
A, (MINGRADE(B)[C-] + MINGRADE(C)[C-]): A and B with at least a C- or C with at least a C-
(A + B + MINGRADE(C)[D]) + MINGRADE(E)[C-]: Either A or B or C with at least a D OR E with at least a C-.
“Junior” standing, admission to major, and similar requirements
Some authors might elect to include specific curricular blockades into their analyses, such as requirements to be a specific level (e.g., junior standing) or gain admission to a specific major. These can be representing by adding a new course that only serves as a medium to embed the requirements in the plan of study.
For example, suppose courses G and I in our example plan of study require the student to be a senior. We can add the course SenStand to the list of courses and prerequisites. Note that when we add SenStand, we need to add its prerequisites, corequisites, and term.
When adding these kinds of requirements into the plan of study, it’s most convenient to add them in the term prior to wherever they are called as prerequisites. For example, if the course requiring “senior standing” is in term 7, it is best to put it in term 6.
courses <- c("A","B","C","D","E","F","SenStand","G","H", "I")
prerequisites <- c(" "," "," ","A","C"," "," ", "D","F,SenStand","D,SenStand")
corequisites <- c(" ","A"," "," "," "," "," ", " "," ", "H")
terms <- c(1, 1, 1, 2, 2, 2, 2, 3, 3, 3)
example_plan_of_study_sen_standing <- create_plan_of_study(Course = courses,
Prereq = prerequisites,
Coreq = corequisites,
Term = terms)
plot_plan_of_study(example_plan_of_study_sen_standing)
Other requirements
If there are requirements beyond what is described here, such as passing a placement exam or having a specific ACT/SAT score, these can be put in a notes column on your spreadsheet.
1.2 Converting the notation to all ANDs
In order to plot the networks properly, we need to go back to all AND relationships for the sake of aligning with the expected inputs for the igraph functions. To do so, we can use the simplify_requisites function. Example usage is below:
example_requisites <- c("(A+B),(C+D)",
"MINGRADE(A)[C-]+(MINGRADE(B)[D],MINGRADE(C)[D])",
"FROM(A,B,C)[2]"
)
simplify_requisites(example_requisites)## [1] "A,B,C,D" "A,B,C" "A,B,C"When the networks are plotted using the create_plan_of_study function, only courses listed in the plan of study will be used in the construction of the network. In general, this will work without issue. However, be cautious of cases such as when course C requires either A or B, but A and B both appear in the plan of study. In this case, the cruciality of C will be overestimated.
1.3 Representing electives
There are several ways to represent electives in the plan of study. Here we will review a selection of methods that we are aware of.
1.3.1 Electives as generic, standalone courses
The standard advice for dealing with electives when extracting data is to represent them as standalone courses with no connections. Note that when you add courses with the same name, the create_plan_of_study function will automatically rename them. For example, we can add to courses called Elec to the last term like so:
courses <- c("A","B","C","D","E","F","G","H","I","Elec","Elec")
prerequisites <- c(" "," "," ","A","C"," ","D","F","D"," ", " ")
corequisites <- c(" ","A"," "," "," "," ",","," ","H"," ", " ")
terms <- c(1, 1, 1, 2, 2, 2, 3, 3, 3, 3 , 3)
example_plan_of_study_elec <- create_plan_of_study(Course = courses,
Prereq = prerequisites,
Coreq = corequisites,
Term = terms)
plot_plan_of_study(example_plan_of_study_elec)
1.3.2 Electives as generic, but connected courses
There are, of course, other ways to include electives in the plan of study that can more faithfully represent the curricular complexity students face. For instance, if there are specific courses that are common prerequisites for the electives, then we can incorporate those directly as we would for any other course. Consider that E and F are prerequisites for one of the electives and C is a prerequisite for the other elective. In this case, we need to differentiate the electives from one another by labeling them as Elec 1 and Elec 2. We would represent this like so:
courses <- c("A","B","C","D","E","F","G","H","I","Elec 1","Elec 2")
prerequisites <- c(" "," "," ","A","C"," ","D","F","D","E,F", "C")
corequisites <- c(" ","A"," "," "," "," ",","," ","H"," ", " ")
terms <- c(1, 1, 1, 2, 2, 2, 3, 3, 3, 3 , 3)
example_plan_of_study_elec <- create_plan_of_study(Course = courses,
Prereq = prerequisites,
Coreq = corequisites,
Term = terms)
plot_plan_of_study(example_plan_of_study_elec)
1.3.3 Customizing pathways with frequently taken electives
Instead of making the electives generic courses, you can customize the plan of study by incorporating the actual courses student frequently take (such as by reviewing student course-taking data or speaking with advisors). This is most easily accomplished by developing a base plan of study, like what is described in the previous examples of handling electives, then specific pathways can be constructed by replacing the elective placeholders with the common elective courses. From there, you can calculate the average of the different pathways for an overall score, if desired.
