# Students’ Learning Behaviour in Programming Education Analysis: Insights from Entropy and Community Detection

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## Abstract

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## 1. Introduction

- RQ1: Can the concept of entropy be used to represent the individual learning behaviour of students?
- RQ2: From an entropy point of view, can we see a difference in the learning behaviour between the higher- and lower-performing communities of students?
- RQ3: Can entropy-based metrics be used as a dynamic index to monitor students’ learning progress during the studying time?

## 2. Related Works

#### 2.1. Analytics of Learning Behaviours

#### 2.2. The Concept of Entropy in Human Behaviour Studies

#### 2.3. The Effect of COVID-19 on Learning Behaviours

## 3. Data Collection

#### 3.1. Context of the Study

#### 3.2. Transition Frequency Features

## 4. Research Methodology

#### 4.1. Entropy of Learning Behaviour

#### 4.2. Coefficient of Variation of Entropy

#### 4.3. Random Matrix Theory

#### 4.4. Noise and Trend Effect Cleaning

#### 4.5. Distance of Learning Behaviours between Students

#### 4.6. Constructing the Graph of Students’ Learning Behaviours

#### 4.7. Community Detection on the MST Graph

## 5. Results

#### 5.1. Selecting Community Structure

#### 5.2. Representing Learning Progress Using Entropy

#### 5.3. Similarities and Differences in Learning Behaviours Represented in Entropy-Based Metrics

## 6. Discussion

#### 6.1. Research Question 1 Revisit: Representing the Students Learning Behaviours Using the Concept of Entropy

#### 6.2. Research Question 2 Revisit: Learning Behaviour Entropy between Higher- and Lower-Performance Student Communities

#### 6.3. Research Question 3 Revisit: Using Entropy-Based Metrics as Dynamic Indexes to Monitor the Students’ Level of Engagement during the Studying Time

- The choice of appropriate entropy measures and data sources for different learning contexts and objectives.
- The interpretation and communication of entropy-based metrics to teachers and students in a meaningful and actionable way.
- The ethical and privacy issues related to collecting and analysing behavioural data from students.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The heat maps show the entropy values for each student on each day in their programming courses. Warmer colours (more red) suggest higher entropy values and more active learning activities, while cooler colours (more blue) indicate lower entropy values and less active learning behaviours. In each figure, within every seven days, typically two days emerge as significantly more active than the rest, as evidenced by the majority of students exhibiting higher entropy values. This pattern aligns with the instructional schedule, wherein students typically dedicate one day to lecture sessions and another day to practical exercises in the lab. On non-scheduled learning days, a subset of students displays no activity, as evidenced by zero entropy values and the resultant plain blue hue on the heat maps.

**Figure 2.**The percentage of students having positive learning behavioural entropy values in three years of the course. Within each week, a substantial majority of students—typically exceeding 80%—in both higher- and lower-performing communities were observed to be actively engaged on lecture and practice days. The higher-performing communities (green lines) consistently display a higher percentage of active students, particularly on non-scheduled studying days, in comparison with that of the lower-performing communities (red lines).

**Figure 3.**The distribution of the coefficient of variation of entropy by higher- and lower-performing student communities across three courses. Learning dynamics present higher coefficients of variation in early stages, which decrease as courses progress. Lower-performing students (green bars) show higher entropy variation than higher-performing ones (red bars). Higher-performing communities stabilise earlier (red bars) than lower-performing communities (green bars). The vertical solid lines mark the “split-up day”—meaning that, in the following days, the statically significant differences between the two communities have been found.

**Figure 4.**The distribution of the coefficient of variation of entropy for the courses before and during the COVID-19-pandemic. Note that the End semester phase refers to the end point of the course, i.e., after week 12 with Module-2018 and Module-2019, and after week 10 with Module-2020.

Dataset | Number of Students | Number of Events | Average Events per Student |
---|---|---|---|

Module-2018 | 112 | 1,054,394 | 9414 |

Module-2019 | 151 | 1,484,297 | 9829 |

Module-2020 | 128 | 1,589,216 | 12,415 |

Transition | $\mathit{s}1$ | $\mathit{s}2$ | $\mathit{s}3$ | $\mathit{s}4$ | ⋯ |
---|---|---|---|---|---|

Lecture1-Lecture1 | 4 | 5 | 10 | 23 | ⋯ |

Lecture1-Labsheet1 | 0 | 14 | 9 | 12 | ⋯ |

Labsheet1-Practice1 | 12 | 6 | 0 | 21 | ⋯ |

⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ |

Dataset | Number of Students (Columns) | Number of Transitions (Rows) | Number of Higher-Performing Students | Number of Lower-Performing Students |
---|---|---|---|---|

Module-2018 | 112 | 825 | 54 | 58 |

Module-2019 | 151 | 878 | 87 | 64 |

Module-2020 | 128 | 602 | 69 | 59 |

**Table 4.**Community detection summary for Module. Groups are ordered in descending order based on the average grades in the terminal assessment of their members.

Module-2018 | Module-2019 | Module-2020 | ||||
---|---|---|---|---|---|---|

Number of Students | Average Grade | Number of Students | Average Grade | Number of Students | Average Grade | |

Group 1 | 18 | 0.79 | 12 | 0.89 | 19 | 0.71 |

Group 2 | 11 | 0.52 | 16 | 0.64 | 18 | 0.59 |

Group 3 | 15 | 0.5 | 21 | 0.61 | 19 | 0.56 |

Group 4 | 17 | 0.42 | 25 | 0.57 | 15 | 0.43 |

Group 5 | 11 | 0.25 | 17 | 0.32 | 19 | 0.42 |

Group 6 | 13 | 0.21 | 14 | 0.32 | 11 | 0.38 |

Group 7 | 13 | 0.17 | 20 | 0.31 | 15 | 0.36 |

Group 8 | 14 | 0.05 | 26 | 0.25 | 12 | 0.08 |

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**MDPI and ACS Style**

Mai, T.T.; Crane, M.; Bezbradica, M.
Students’ Learning Behaviour in Programming Education Analysis: Insights from Entropy and Community Detection. *Entropy* **2023**, *25*, 1225.
https://doi.org/10.3390/e25081225

**AMA Style**

Mai TT, Crane M, Bezbradica M.
Students’ Learning Behaviour in Programming Education Analysis: Insights from Entropy and Community Detection. *Entropy*. 2023; 25(8):1225.
https://doi.org/10.3390/e25081225

**Chicago/Turabian Style**

Mai, Tai Tan, Martin Crane, and Marija Bezbradica.
2023. "Students’ Learning Behaviour in Programming Education Analysis: Insights from Entropy and Community Detection" *Entropy* 25, no. 8: 1225.
https://doi.org/10.3390/e25081225