#
An AI-Application-Oriented In-Class Teaching Evaluation Model by Using Statistical Modeling and Ensemble Learning^{ †}

^{1}

^{2}

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. In-Class Evaluation Framework

## 3. Index System Design

## 4. The Module of Statistical Modeling

#### 4.1. Analytic Hierarchy Process and Entropy Weight Method

- Build an analytic hierarchy model module,
- Construct a judgment matrix,
- Hierarchical ordering and consistency check,
- Consistency test and get subjective weight.

#### 4.2. Analytic Hierarchy Process-Entropy Weight (AHP-EW) Statistical Modeling for In-Class Teaching Evaluation

- Step 1: Determine the type of indicators and find the corresponding feature sequence.

- Step 2: Calculate the subjective and objective weights of the features for the indicators.

- Step 3: Calculate comprehensive weights by the combination weighting optimization method.

- Step 4: Calculate each student sample’s final score of students’ concentration.

## 5. The Module of Ensemble Learning

#### 5.1. AdaBoost

#### 5.2. Adaboost-Ensemble Learning (Adaboost-EL) for In-Class Teaching Evaluation

- Step 1: Determine the type of the indicator and set the corresponding input data for ensemble learning module.

- Step 2: Construct the ensemble learning module and adjust its parameters.

## 6. Experiment and Performance Analysis

#### 6.1. Input Data

#### 6.2. Performance Analysis Indicators

- (1)
- Root mean square error (RMSE):

- (2)
- Accuracy (Accu.):

- (3)
- Confusion Matrix

- (4)
- Precision (P)

- (5)
- Recall (R)

- (6)
- F1_score (F1)

- (7)
- Macro_Precision (M_P)

- (8)
- Macro_Recall (M_R)

- (9)
- Macro_F-measure (M_F1)

#### 6.3. Model Construction and Parameter Selection

#### 6.3.1. The Example of Statistical Modeling Module

- Step 1: Determine the type of the indicator and find the corresponding feature sequence.

- Step 2: Calculate the subjective and objective weights of 11 features for students’ concentration

- Step 3: Calculate comprehensive weights by the combination weighting optimization method.

- Step 4: Calculate each student sample’s final score of students’ concentration.

#### 6.3.2. The Example of Ensemble Learning Module

- Step 1: Determine the type of the indicator and set the corresponding input data for the AdaBoost-EL method.

- Step 2: Construct the ensemble learning module and adjust its parameters.

#### 6.4. Performance Analysis

#### 6.4.1. Performance Analysis of Statistical Modeling Module

#### 6.4.2. Performance Analysis of Ensemble Learning Module

#### 6.4.3. Comparison between the Two Modules

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1.

Algorithms A1 Calculating objective weights by the entropy weight method | |

Input:For totally N samples and M corresponding features, the j-th feature value of the i-th sample ${x}_{ij}\left(i=1,2,\dots ,N;j=1,2,\dots M\right)$; | |

Process: | |

1. ${X}_{ij}=\frac{{x}_{ij}-\mathrm{min}\left\{{x}_{1j},\cdots ,{x}_{nj}\right\}}{\mathrm{max}\left\{{x}_{1j},\cdots {x}_{nj}\right\}-\mathrm{min}\left\{{x}_{1j},\cdots ,{x}_{nj}\right\}}\text{}$ | % Normalization of positive influence feature |

2. ${X}_{ij}=\frac{\mathrm{max}\left\{{x}_{1j},\cdots ,{x}_{nj}\right\}-{x}_{ij}}{\mathrm{max}\left\{{x}_{1j},\cdots {x}_{nj}\right\}-\mathrm{min}\left\{{x}_{1j},\cdots ,{x}_{nj}\right\}}\text{}$ | % Normalization of negative influence feature |

3. $k=\frac{1}{\mathrm{ln}\left(n\right)}>0$, ${e}_{j}=-k{\sum}_{i=1}^{n}{p}_{ij}\mathrm{ln}\left({p}_{ij}\right),j=1,2,\cdots ,m$ | |

% Entropy value of the j-th feature | |

4. ${d}_{j}=1-{e}_{j},j=1,2,\cdots ,m$ | % Information entropy redundancy of the j-th feature |

endOutput: Subjective weight of the j-th feature |

#### Appendix A.2.

Algorithms A2 Learning process of the AdaBoost algorithm | |

Input:Dataset${\mathit{D}}_{\mathbf{1}}\left(\mathit{i}\right)=\mathbf{1}/\mathit{m}$;$D=\{({x}_{1},{y}_{1}),({x}_{2},{y}_{2}),\dots ,({x}_{m},{y}_{m})\}$; Basic-learner$L$; Iteration$T$; | |

Process: | |

1. ${D}_{1}\left(i\right)=1/m$; | % Initialize training set weight |

2. for $t=1,\cdots ,T$: | |

3. ${h}_{t}=L\left(D,{D}_{t}\right);$ | % use D and D_{t} to train the learner h_{t} |

4. ${\mathrm{e}}_{\mathrm{t}}={\mathrm{Pr}}_{\mathrm{x}~{\mathrm{D}}_{\mathrm{t},\mathrm{y}}}\text{}\mathrm{I}\left[{\mathrm{h}}_{\mathrm{t}}\left(\mathrm{x}\right)\ne \mathrm{y}\right]$; | % Calculate the error of learner h_{t} |

5. if ${e}_{t}>0.5$ then break | |

6. ${\mathsf{\alpha}}_{\mathrm{t}}=\frac{1}{2}\mathrm{ln}(\frac{1-{\mathrm{e}}_{\mathrm{t}}}{{\mathrm{e}}_{\mathrm{t}}})$; | % Calculate the coefficient of learner h_{t} |

7. ${D}_{t+1}\left(i\right)=\frac{{D}_{t}\left(i\right)}{{Z}_{t}}\times \{\begin{array}{c}\mathrm{exp}\left(-{\alpha}_{t}\right),{h}_{t}\left({x}_{i}\right)={y}_{i}\\ \mathrm{exp}\left({\alpha}_{t}\right),{h}_{t}\left({x}_{i}\right)\ne {y}_{i}\end{array}=\frac{{D}_{t}\left(i\right)\mathrm{exp}\left(-{\alpha}_{t}{y}_{i}{h}_{t}\left({x}_{i}\right)\right)}{{Z}_{t}}$ | |

8. % Update the weight of training set, where Z_{t} is the normalization factor. | |

% ${Z}_{t}={\sum}_{i=1}^{m}{D}_{i}\xb7\mathrm{exp}\left(-\alpha \xb7{y}_{i}\xb7L\left({x}_{i}\right)\right)$ | |

9. end | |

Output:$H\left(x\right)=sign({\sum}_{t=1}^{T}{\alpha}_{t}{h}_{t}\left(x\right))$ |

## Appendix B

Device | Picture | Description |

Real Classroom | Overall layout of the smart classroom | |

Pickup DS-2FP2020-A | To obtain the voice data in the classroom | |

Camera for students iDS-ECD8012-H/T (8–32 mm) | In the front of the classroom. To record the voice for students, and obtain the data such as students’ movement, emotion… | |

Camera for teachers iDS-EGD0288-HFR (8–32 mm) (2.8 mm) | In the middle of the classroom. To record the voice for teachers, and obtain the data such as teachers’ movement, emotion… |

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Index | Input | Feature | Output |
---|---|---|---|

Students Concentration | Students’ Movement Students’ Emotion Concentration Judgment Matrix Concentration Labels | Frequency and Average Duration of 8 types of Students’ Movement; Frequency and Average Duration of 2 types of Students’ Emotion; | Score_Concentration |

Students’ Participation | Students’ Movement Students’ Emotion Participation Judgment Matrix Participation Labels | Frequency and Average Duration of 8 types of Students’ Movement; Frequency and Average Duration of 2 types of Students’ Emotion; | Score_Participation |

Teachers’ Type | Teachers’ Movement Teachers’ Emotion Teaching Type Labels | Frequency and Average Duration of 9 types of Teachers’ Movement; Frequency and Average Duration of 2 types of Teachers’ Emotion; | Score_ Indoctrination Score_ Natural Score_ Interactive |

Teachers’ Style | Teachers’ Movement Teachers’ Emotion Teachers’ Volume and Speed Teaching Style Labels | Frequency and Average Duration of 9 types of Teachers’ Movement; Frequency and Average Duration of 2 types of Teachers’ Emotion; Mean and Variance od Teachers’ Volume and Speed | Score_Passionate Score_Humorous Score_Solemn |

Teachers’ Media usage | Teachers’ Movement Media Usage Labels | Frequency and Average Duration of 9 types of Teachers’ Movement; | Score_ Multimedia Score_ Blackboard |

Indicator | Input | Base Learners | Classification Algorithm | Output |
---|---|---|---|---|

Students’ Concentration | Students’ Movement Students’ Emotion Concentration Labels | Regression Tree | Forecast Score of Concentration | |

Students’ Participation | Students’ Movement Students’ Emotion Participation Labels | Forecast Score of Participation | ||

Teachers’ Type | Teachers’ Movement Teachers’ Emotion Teaching Type Labels | Classification Tree | SAMME | Types: Indoctrination, Natural, Interactive |

Teachers’ Style | Teachers’ Movement Teachers’ Emotion Teachers’ Volume and Speed Teachers’ Style Labels | Types: Passionate, Humorous, Solemn | ||

Teachers’ Media-usage | Teachers’ Movement Media Usage Labels | Types: Multimedia, Blackboard |

Data Categories | Collection Methods | Data Content | |
---|---|---|---|

200 teacher samples | Movement | Collect teachers’ movements per 3 s | Movement number (1–9) and corresponding time |

Emotion | Collect teachers’ emotions per 3 s | Emotion numbers (1–2) and corresponding time | |

Volume and Speed | Collect teachers’ volume (dB) and speed (word per minute) per 3 s | Volume value, speed value and corresponding time | |

Speech Text | The content sequence of process speech text in the whole class | Every sentence and its start and end time | |

Labels | Three evaluation labels marked by experts to evaluate the teachers from the courses. | Teaching type (1–3), Teaching style (1–3), Media usage (1–2). | |

300 student samples | Movement | Collect students’ movements per 3 s | Movement numbers (1–8) and corresponding time |

Emotion | Collect students’ emotions per 3 s | Emotion numbers (1–2) and corresponding time | |

Labels | According to the test after class and the Concentration and Participation in the whole class | Scores of the tests, Concentration and Participation in class |

Predicted | Positive | Negative | |
---|---|---|---|

Actual | |||

Positive | TP | FN | |

Negative | FP | TN |

Subjective Weights and Orders | Objective Weights and Orders | Comprehensive Weights and Orders | |||||
---|---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) |

Feature | Weights | Orders | Weights | Orders | Reasonable Value Range | Weights | Orders |

X1 | 0.166 | 1 | 0.072 | 7 | [0.072–0.166] | 0.121 | 2 |

X2 | 0.142 | 3 | 0.109 | 4 | [0.109–0.142] | 0.125 | 1 |

X3 | 0.094 | 6 | 0.062 | 10 | [0.062–0.094] | 0.080 | 8 |

X4 | 0.031 | 10 | 0.071 | 8 | [0.031–0.071] | 0.053 | 11 |

X5 | 0.151 | 2 | 0.043 | 11 | [0.043–0.151] | 0.095 | 5 |

X6 | 0.140 | 4 | 0.102 | 5 | [0.102–0.140] | 0.120 | 3 |

X7 | 0.106 | 5 | 0.075 | 6 | [0.075–0.106] | 0.088 | 6 |

X8 | 0.041 | 8 | 0.069 | 9 | [0.041–0.069] | 0.056 | 10 |

X9 | 0.032 | 9 | 0.133 | 1 | [0.032–0.133] | 0.083 | 7 |

X10 | 0.023 | 11 | 0.132 | 3 | [0.023–0.132] | 0.073 | 9 |

X11 | 0.074 | 7 | 0.133 | 2 | [0.074–0.133] | 0.105 | 4 |

Loss Function | The Number of Base Learners | RMSE |
---|---|---|

Linear | 30 | 10.2316 |

50 | 9.6649 | |

70 | 9.3749 | |

100 | 10.0136 | |

Square | 30 | 9.9312 |

50 | 10.3445 | |

70 | 10.1863 | |

100 | 9.3807 | |

Exponential | 30 | 10.2625 |

50 | 9.7782 | |

70 | 10.0313 | |

100 | 9.8675 |

Statistical Modelling | Score Indicator | RMSE |

Concentration | 11.167 | |

Participation | 13.409 |

Statistical Modelling | Category Indicators | Precision | Recall | F1 | Accuracy | M_P | M_R | M_F1 | |

Teachers’ Type | Indoctrination | 0.987 | 0.938 | 0.962 | 0.815 | 0.789 | 0.791 | 0.790 | |

Natural | 0.776 | 0.776 | 0.776 | ||||||

Interactive | 0.604 | 0.659 | 0.630 | ||||||

Teachers’ Style | Passionate | 0.982 | 0.918 | 0.949 | 0.695 | 0.703 | 0.687 | 0.695 | |

Humorous | 0.511 | 0.414 | 0.457 | ||||||

Solemn | 0.615 | 0.728 | 0.667 | ||||||

Teachers’ Media Usage | Multimedia | 0.891 | 0.905 | 0.918 | 0.448 | 0.602 | |||

Blackboard | 0.919 |

Ensemble Learning | Score Indicator | RMSE |

Concentration | 8.318 | |

Participation | 9.375 |

Ensemble Learning | Category Indicators | Precision | Recall | F1 | Accuracy | M_P | M_R | M_F1 | |

Teachers’ Type | Indoctrination | 0.947 | 0.935 | 0.941 | 0.785 | 0.755 | 0.761 | 0.758 | |

Natural | 0.776 | 0.728 | 0.752 | ||||||

Interactive | 0.542 | 0.619 | 0.619 | ||||||

Teachers’ Style | Passionate | 0.951 | 0.935 | 0.943 | 0.73 | 0.729 | 0.719 | 0.724 | |

Humorous | 0.578 | 0.464 | 0.515 | ||||||

Solemn | 0.66 | 0.756 | 0.705 | ||||||

Teachers’ Media Usage | Multimedia | 0.881 | 0.89 | 0.897 | 0.433 | 0.584 | |||

Blackboard | 0.899 |

Statistical Modelling | RMSE | Overall Module Parameters | |||||||

Concentration | 11.167 | ||||||||

Participation | 13.409 | Precision | Recall | F1 | Accuracy | M_P | M_R | M_F1 | |

Teachers’ Type | Indoctrination | 0.987 | 0.938 | 0.962 | 0.815 | 0.789 | 0.791 | 0.790 | |

Natural | 0.776 | 0.776 | 0.776 | ||||||

Interactive | 0.604 | 0.659 | 0.630 | ||||||

Teachers’ Style | Passionate | 0.982 | 0.918 | 0.949 | 0.695 | 0.703 | 0.687 | 0.695 | |

Humorous | 0.511 | 0.414 | 0.457 | ||||||

Solemn | 0.615 | 0.728 | 0.667 | ||||||

Teachers’ Media Usage | Multimedia | 0.891 | 0.905 | 0.918 | 0.448 | 0.602 | |||

Blackboard | 0.919 | ||||||||

Ensemble Learning | RMSE | Overall Module Parameters | |||||||

Concentration | 8.318 | ||||||||

Participation | 9.375 | Precision | Recall | F1 | Accuracy | M_P | M_R | M_F1 | |

Teachers’ Type | Indoctrination | 0.947 | 0.935 | 0.941 | 0.785 | 0.755 | 0.761 | 0.758 | |

Natural | 0.776 | 0.728 | 0.752 | ||||||

Interactive | 0.542 | 0.619 | 0.619 | ||||||

Teachers’ Style | Passionate | 0.951 | 0.935 | 0.943 | 0.73 | 0.729 | 0.719 | 0.724 | |

Humorous | 0.578 | 0.464 | 0.515 | ||||||

Solemn | 0.66 | 0.756 | 0.705 | ||||||

Teachers’ Media Usage | Multimedia | 0.881 | 0.89 | 0.897 | 0.433 | 0.584 | |||

Blackboard | 0.899 |

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## Share and Cite

**MDPI and ACS Style**

Guo, J.; Bai, L.; Yu, Z.; Zhao, Z.; Wan, B.
An AI-Application-Oriented In-Class Teaching Evaluation Model by Using Statistical Modeling and Ensemble Learning. *Sensors* **2021**, *21*, 241.
https://doi.org/10.3390/s21010241

**AMA Style**

Guo J, Bai L, Yu Z, Zhao Z, Wan B.
An AI-Application-Oriented In-Class Teaching Evaluation Model by Using Statistical Modeling and Ensemble Learning. *Sensors*. 2021; 21(1):241.
https://doi.org/10.3390/s21010241

**Chicago/Turabian Style**

Guo, Junqi, Ludi Bai, Zehui Yu, Ziyun Zhao, and Boxin Wan.
2021. "An AI-Application-Oriented In-Class Teaching Evaluation Model by Using Statistical Modeling and Ensemble Learning" *Sensors* 21, no. 1: 241.
https://doi.org/10.3390/s21010241