This paper describes the creation of a mathematical model that represents the mapping of an undergraduate engineering degree program to the CDIO syllabus. A graph-based model of a curriculum formalizes the process of modeling curricular data in a structured form. It also formally models the connections among curricular entities. A graph-based model represents entities as nodes and relationships among entities as links between nodes. The CDIO curriculum graph model has two types of entities: (1) CDIO skills and (2) curricular entities (such as classes or modules). The graph model represents the relationships among curricular entities (e.g., prerequisites) as well as the mapping between curricular entities and CDIO skills. The result is a structured model on which we build educational analytics and data visualization tools.
In creating a model of a CDIO-based curriculum, we first model the structure of the curriculum itself. We choose the curricular unit to be modeled, for example, a class. Each class is modeled as a node. Information on each class is modeled as a property of the node – for example, the website URL of the class, the number of credits the class is worth, etc. A class is just one example of a modeling choice for the curricular entity; other more granular examples include learning units, modules, resources, etc.
Next we model the CDIO syllabus. Each CDIO skill is modeled as a node. CDIO skills within a category are assigned a common group. Next we model the relationships in the system. Relationships can be directed and undirected. We model the relationships among curricular entities, such as prerequisite and corequisite requirements. We model the mapping between curricular entities and CDIO skills. If Class A addresses CDIO skill 2.1.1, we create a directed relationship between Class A and CDIO skill 2.1.1. In the graph model, these relationships are drawn as edges. We do this mapping for all curricular entities over all the CDIO skills.
This graph-based modeling approach provides a powerful basis for visualization and analytics. For example, we can analyze outgoing edges to see a particular class’s coverage of the CDIO syllabus. Conversely, we can analyze incoming edges to reveal all the classes across a curriculum that address a particular CDIO skill. This analysis can reveal gaps and provide a data-driven basis for curricular innovations.
The full paper will discuss a case study of mapping the CDIO-based aerospace engineering undergraduate curriculum at the Massachusetts Institute of Technology. The paper will describe the modeling process and the resulting map in detail, and will present analytics.
Proceedings of the 13th International CDIO Conference in Calgary, Canada, June 18-22 2017