Title:	Exploring and Analyzing Academic Curricula
Version:	1.0.0
Description:	Provides an implementation of ‘Curricular Analytics’, a framework for analyzing and quantifying the complexity of academic curricula. Curricula are modelled as directed acyclic graphs and analytics are provided based on path lengths and edge density. This work directly comes from Heileman et al. (2018) <doi:10.48550/arXiv.1811.09676>.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.1
URL:	https://github.com/Danyulll/CurricularAnalytics
BugReports:	https://github.com/Danyulll/CurricularAnalytics/issues
Imports:	dplyr (≥ 1.1.4), igraph (≥ 2.0.3), stats (≥ 4.4.0), tools (≥ 4.4.0), utils (≥ 4.4.0), visNetwork (≥ 2.1.2)
Suggests:	knitr, rmarkdown
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2024-05-28 20:36:58 UTC; danie
Author:	Daniel Krasnov [aut, cre], Dr. Irene Vrbik [aut, cph]
Maintainer:	Daniel Krasnov <danielkrasnovdk@hotmail.com>
Depends:	R (≥ 3.5.0)
Repository:	CRAN
Date/Publication:	2024-05-29 10:40:08 UTC

Calculate blocking factor

Description

A helper function for calculating the blocking factor for each node and the total blocking factor of a curriculum graph.

Usage

blocking_factor(node_list, edge_list)

Arguments

Details

Blocking quantifies when a failing a course would result in being blocked from registering for future courses. More formally the blocking factor of a node v_i is defined as

b_c(v_i) = \sum_{v_j \in V} I(v_i,v_j)

where I is the indicator function:

=\begin{cases}1, & \text{if } v_i \to v_j \\ 0, & \text{if }v_i \not\to v_j\end{cases}

The blocking factor for an entire curriculum graph G_c is defined as

b(G_c)=\sum_{v_i \in V} b_c(v_i)

Value

A list that contains the following:

Author(s)

Daniel Krasnov

References

Heileman, Gregory L, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman. 2018. “Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations.” arXiv Preprint arXiv:1811.09676.

Examples

edge_list <- data.frame(from = c(1, 3), to = c(3, 4))
node_list <-
data.frame(
id = 1:4,
label = c("MATH 100", "DATA 101", "MATH 101", "MATH 221"),
term = c(1, 1, 2, 2)
)
bf_list <- blocking_factor(node_list,edge_list)
print(bf_list)
# Output:
# $bynode
# id bf
# 2  1  2
# 3  2  0
# 4  3  1
# 5  4  0
# $total
# [1] 3

Calculate centrality

Description

A helper function for calculating the centrality for each node.

Usage

centrality_factor(node_list, edge_list)

Arguments

Details

A course is considered central if it has many requisite edges flowing in and out of the node. More formally it is the number of long paths that include the node. That is, consider a curriculum graph G_c and a vertex v_i. A long path is a path that satisfies the following conditions:

• v_i,v_j,v_k are distinct

• v_j \to v_i \to v_k

• v_j is a source node (in-degree zero)

• v_k is a sink node (out-degree zero)

Let P_{v_i}=\{p_1,p_2,\dots\} denote the set of all paths defined as above. Then the centrality of a node v_i is given by

q(v_i)=\sum^{|P_{v_i}|}_{l=1}\#(p_l)

More plainly this is the number of paths containing v_i of at least length 3 where v_i is neither a source nor sink node.

Value

A dataframe containing the centrality of each node

Author(s)

Daniel Krasnov

References

Heileman, Gregory L, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman. 2018. “Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations.” arXiv Preprint arXiv:1811.09676.

Examples

edge_list <- data.frame(from = c(1, 3), to = c(3, 4))
node_list <-
data.frame(
 id = 1:4,
 label = c("MATH 100", "DATA 101", "MATH 101", "MATH 221"),
 term = c(1, 1, 2, 2)
)

cf_df <- centrality_factor(node_list,edge_list)
print(cf_df)
# Output:
#   id cf
#1  1  0
#2  2  0
#3  3  3
#4  4  0

Create Curriculum From CSV File

Description

Generates a curriculum graph from a csv file.

Usage

curriculum_graph_from_csv(filepath)

Arguments

Value

A list that contains the following:

Examples

# Have filepath point to a csv of the following form
#id	label	term	requisites
#1	MATH 100	1
#2	DATA 101	1
#3	MATH 101	2	1
#4	MATH 221	2	3
#5	STAT 230	3	3;2
filepath <-
system.file("extdata", "Example-Curriculum.csv", package = "CurricularAnalytics")
C <- curriculum_graph_from_csv(filepath)
plot_curriculum_graph(C)

Create Curriculum Graph Object

Description

Generates a curriculum graph from a node and edge list.

Usage

curriculum_graph_from_list(node_list, edge_list)

Arguments

Value

A list that contains the following:

Author(s)

Daniel Krasnov

References

Heileman, Gregory L, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman. 2018. “Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations.” arXiv Preprint arXiv:1811.09676.

Examples

edge_list <- data.frame(from = c(1, 3), to = c(3, 4))
# courses in node list must be placed sequentially in term order to be properly displayed
node_list <-
data.frame(
 id = 1:4,
 label = c("MATH 100", "DATA 101", "MATH 101", "MATH 221"),
 term = c(1, 1, 2, 2)
)
C <- curriculum_graph_from_list(node_list,edge_list)
plot_curriculum_graph(C)

Calculate delay factor

Description

A helper function for calculating the delay factor for each node and the total delay factor of a curriculum graph.

Usage

delay_factor(node_list, edge_list)

Arguments

Details

The delay factor of a course is the longest path the nodes finds itself on. More formally the delay factor of a node v_k is given by

d_c(v_k)=\underset{i,j,l,m}{max}\left\{\#\left(v_i \overset{p_l}{\to} v_k \overset{p_m}{\to} v_j \right)\right\}

The delay factor of an entire curriculum graph G_c is defined as

d(G_c)=\sum_{v_k \in V}d_c(v_k)

Value

A list that contains the following:

Author(s)

Daniel Krasnov

References

Heileman, Gregory L, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman. 2018. “Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations.” arXiv Preprint arXiv:1811.09676.

Examples

edge_list <- data.frame(from = c(1, 3), to = c(3, 4))
node_list <-
data.frame(
 id = 1:4,
 label = c("MATH 100", "DATA 101", "MATH 101", "MATH 221"),
 term = c(1, 1, 2, 2)
)

df_list <- delay_factor(node_list,edge_list)
print(df_list)
# Output:
# $bynode
#   id df
# 2  1  3
# 3  2  1
# 4  3  3
# 5  4  3
# $total
# [1] 10

Plot a curriculum graph

Description

Plots an interactable vizNetwork visualization of the Igraph network object representing the curriculum graph.

Usage

plot_curriculum_graph(curriculum_graph, width = "100%", height = 500)

Arguments

Value

No object is returned. Rather the graph is plotted according to the specified term order in node_list. Clicking on a node will reveal its label, structural complexity (sc), centrality (cf), blocking factor (bf), and delay factor (df)

Author(s)

Daniel Krasnov

References

Heileman, Gregory L, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman. 2018. “Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations.” arXiv Preprint arXiv:1811.09676.

Examples

edge_list <- data.frame(from = c(1, 3), to = c(3, 4))
node_list <-
data.frame(
 id = 1:4,
 label = c("MATH 100", "DATA 101", "MATH 101", "MATH 221"),
 term = c(1, 1, 2, 2)
)
C <- curriculum_graph_from_list(node_list,edge_list)
plot_curriculum_graph(C)

Calculate structural complexity

Description

A helper function for calculating the structural complexity for each node and the total structural complexity of a curriculum graph.

Usage

structural_complexity(node_list, edge_list)

Arguments

Details

The structural complexity of a node v_k is defined as a linear combination of the node's delay and blocking factors. More formally

h(v_k) = d(v_k) + b(v_k)

. The structural complexity of an entire curriculum graph G_c is defined as

h(G_c)=d(G_c)+b(G_c)=\sum_{v_k \in V} \left(d_c(v_k) + b_c(v_k)\right)

Value

A list that contains the following:

Author(s)

Daniel Krasnov

References

Heileman, Gregory L, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman. 2018. “Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations.” arXiv Preprint arXiv:1811.09676.

Examples

edge_list <- data.frame(from = c(1, 3), to = c(3, 4))
node_list <-
data.frame(
 id = 1:4,
 label = c("MATH 100", "DATA 101", "MATH 101", "MATH 221"),
 term = c(1, 1, 2, 2)
)
sc_list <- structural_complexity(node_list,edge_list)
print(sc_list)
# Output:
# $bynode
#   id sc
# 1  1  5
# 2  2  1
# 3  3  4
# 4  4  3
# $total
# [1] 13