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Title Page

ABSTRACT

Contents

1. Introduction 15

1.1. Background 15

1.2. Research significance 16

1.3. Ideas and methods 17

1.3.1. Software development model 18

1.3.2. Method of generating math questions 18

1.3.3. Intelligent solutions to the examination system 19

1.4. Thesis structure 19

2. Research Review 21

2.1. Software development models 21

2.1.1. Traditional software development models and their limitations 22

2.1.2. Agile development model and its limitations 23

2.1.3. RUP model and its limitations 25

2.2. Intelligent solutions to existing examination systems 30

2.2.1. Random selection method 30

2.2.2. Backtracking algorithm 32

2.2.3. Hybrid algorithm 33

2.2.4. Analysis and conclusion 33

2.3. Reinforcement learning 34

2.3.1. Definition 34

2.3.2. Q-Learning 37

2.3.3. Analysis and conclusion 39

3. Research Methods 41

3.1. Adapted RUP 41

3.1.1. Analysis of the characteristics of R&D projects 41

3.1.2. Selection of Software Development Model for R&D project 44

3.1.3. The adapting and tailoring of RUP 45

3.2. Mathematical models for generating questions 51

3.2.1. The ideas of mathematical models 52

3.2.2. Analysis and Modeling 53

3.2.3. Section Summary 57

3.3. Intelligent solutions 57

3.3.1. Traditional solution 58

3.3.2. Intelligent solution based on AI algorithms 66

4. R&D Process and Results 74

4.1. Inception phase 75

4.1.1. Business Modeling 77

4.1.2. Requirements 79

4.1.3. Analysis and Design 81

4.1.4. Implementation 84

4.1.5. Test 84

4.1.6. Project Management 87

4.2. Elaboration phase 87

4.2.1. Analysis and Design 88

4.2.2. Implementation 97

4.2.3. Project Management 97

4.3. Construction phase 99

4.3.1. First round of iterations 99

4.3.2. Second round of iterations 106

4.3.3. Third round of iterations 115

5. Conclusion 127

초록 129

References 131

Appendix 138

Table 1. Redefinition of each phase 46

Table 2. The necessity of workflows 47

Table 3. New definitions of core workflows 48

Table 4. Analysis of Matrix Addition and Subtraction 54

Table 5. Analysis of a question type for Calculating Un-... 56

Table 6. Difficulty levels and difficulty reference value 62

Table 7. The table of difficulty coefficients D(m, d) 67

Table 8. Three dimensions of requirements 80

Table 9. Function test 85

Table 10. Some test examples of the mathematical model:... 86

Table 11. The analysis of the constant-matrix multiplication 89

Table 12. The analysis of the matrix-matrix multiplication 90

Table 13. The analysis of the calculation of a simple deter-... 92

Table 14. The analysis of the solving linear equations using... 93

Table 15. The main functions of AHMES 94

Table 16. The basic interfaces of main functions 95

Table 17. The statistics of mathematical models designed in... 98

Table 18. The internal test results 105

Table 19. Feedback on the examination papers 112

Table 20. The difficulty adjustment results 113

Table 21. Statistics of currently implemented linear algebra... 114

Table 22. Data from one run 124

Table 23. The result of the adjustment in this test 125

Figure 1. Waterfall Model 23

Figure 2. Process diagram of Scrum 24

Figure 3. Rational Unified Process 28

Figure 4. A tailored simplified RUP 28

Figure 5. Reinforcement Learning 35

Figure 6. Adapted RUP 51

Figure 7. The flow chart of generating examination paper 61

Figure 8. The flow chart of difficulty adjustment 63

Figure 9. The flowchart of AL 71

Figure 10. The adapted RUP Cycle of AHMES 75

Figure 11. The use case diagram 79

Figure 12. The flowchart of a mathematical model: Matrix... 83

Figure 13. The structure of AHMES 94

Figure 14. The flow chart of AHMES 96

Figure 15. The Flow chart of solving linear equations using... 101

Figure 16. The flow chart of "AXB=C, calculate X" 102

Figure 17. A screenshot of the command line interface 104

Figure 18. Solving linear equations by Cramer's Rule 109

Figure 19. The modified structure 118

Figure 20. The modified flow chart of AHMES 119

Figure 21. The models' difficulty curves 122

Figure 22. The simulation test result 123