# Toward Adaptability of E-Evaluation: Transformation from Tree-Based to Graph-Based Structure

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## Abstract

**:**

## 1. Introduction

- Find the appropriate structure to store a tasks dataset for usage in adaptive learning.
- Offer automatic test transformation/generation from the stored tasks dataset, dedicated for different purpose knowledge assessment tests.

## 2. Related Works

#### 2.1. Existing Models for Adaptive E-Learning

#### 2.2. Data Structures Used for E-Evaluation Tests and Its Tasks Storage

- It is convenient to check whether appropriate tasks of different complexity have been prepared to check all competencies.
- Once properly designed, it can be used to create tests for a variety of course topics, and it eliminates the need to recreate test tasks for each topic, as the instructor only needs to select the required tree branches or indicate the appropriate level of complexity of the tasks.
- The connections between tasks are presented.

#### 2.3. Existing Task Dataset Form Transformation Methods

## 3. Proposed Competence Tree Improvements for Increase of Tasks Dataset Flexibility

- All sub-competencies should be arranged based on their relative complexity. Therefore, in each branch of the competence tree, lower complexity tasks will be presented on the left and complexity will increase going to the right. This should be performed by the competence tree designer and might be based on personal opinion or historical data, which can be used to compare the complexity of competencies as well as tasks.
- Competence should define whether a child’s competencies are sequentially dependent or independent of each other. This is required to understand whether it is worth giving a sibling task of higher complexity if the student failed the lower complexity task.

## 4. Proposed Competence Tree Transformations to Graph-Based E-Evaluation Structure

#### 4.1. TBCG Transformation for Shortest Path E-Evaluation

Algorithm 1 Pseudocode of TBCG transformation. | |

1: | root = root competence of the competence tree |

2: | add task T of competence root to the test flow |

3: | TBCGstep(root) |

4: | TBCGstep(cComp) |

5: | if competence cComp has child competences then |

6: | connect T to new decision node D to indicate whether task T was solved correctly |

7: | add negative and positive paths for decision D, with merge in the end |

8: | for each child competence C of competence cComp (going from right to left) do |

9: | add task T of competence C to the negative path of the decision node D |

10: | TBCGstep(C) |

11: | end for |

12: | end if |

#### 4.2. BTCG Transformation for Incremental Knowledge E-Evaluation

Algorithm 2 Pseudocode of BTCG transformation. | |

1: | root = root element of the competence tree |

2: | cPath = None |

3: | cLast = None |

4: | BTCG(root, cPath, cLast) |

5: | BTCG(cComp, cPath, cLast): |

6: | if competence cComp has child competences then |

7: | for each child competence C of competence cComp (going from left to right) do |

8: | if competence C has no sequential dependency with sibling competences then |

9: | cPath = end of the test flow |

10: | end if |

11: | BTCG(C, cPath, cLast) |

12: | if cLast == None then |

13: | add task T of competence cComp to the test flow |

14: | cLast = C |

15: | cPath = path from task T |

16: | else |

17: | if competence C has sequential dependency with sibling competences then |

18: | connect cLast to new node D to indicate weather task T was solved correctly |

19: | add negative and positive paths for decision D |

20: | cPath = positive path of decision node D |

21: | add new task T of competence C to cPath |

22: | cLast = C |

23: | merge positive and negative flows of cPath |

24: | else |

25: | if cLast <> None then |

26: | connect cLast to new node D to indicate weather task T was solved correctly |

27: | add negative and positive paths for decision D |

28: | cPath = positive path of decision node D |

29: | add new task T of competence C to cPath |

30: | merge positive and negative flows of cPath |

31: | cPath = end of the test flow |

32: | cLast = None |

33: | else |

34: | add new task T of competence C to cPath |

35: | end if |

36: | end if |

37: | end if |

38: | end for |

39: | if competence C has no sequential dependency with sibling competences then |

40: | connect T to new node D to indicate whether all sibling tasks solved correctly |

41: | add negative and positive paths for decision D |

42: | cPath = positive path of decision node D |

43: | merge positive and negative flows of cPath |

44: | end if |

45: | end if |

46: | if cLast == None then |

47: | add new decision node D to indicate whether task all sibling tasks solved correctly |

48: | add negative and positive paths for decision D |

49: | cPath = positive path of decision node D |

50: | add new task T of competence C to cPath |

51: | merge positive and negative flows of cPath |

52: | else |

53: | add task T of competence cComp to the cPath |

54: | end if |

## 5. Analysis of Transformation Results and Comparison to Contextual Graph to Practice Tree Transformation

## 6. Conclusions and Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Results of Graph-to-Tree Transformations

**Figure A1.**Result of original contextual graph transformation to Practice tree for graph, presented in Figure 9.

**Figure A2.**Result of original contextual graph transformation to Practice tree for graph, presented in Figure 10.

**Figure A3.**Result of modified contextual graph transformation to a tree structure for graph, presented in Figure 9.

**Figure A4.**Result of modified contextual graph transformation to a tree structure for graph, presented in Figure 10.

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**Figure 4.**Result of TBCG transformation for competence tree, presented in Figure 3.

**Figure 5.**A transformation process: (

**a**) TBCG where all a student’s answers are incorrect (tasks sequence is 1, 3, 7, 10, 9, 8, 6, 2, 5, 4); (

**b**) BTCG where all a student’s answers are correct (tasks sequence is 4, 5, 2, 6, 8, 9, 10, 7, 3, 1).

**Figure 6.**Result of BTCG transformation for the competence tree, presented in Figure 3 when all competencies are sequentially dependent.

**Figure 7.**Result of BTCG transformation for the competence tree, presented in Figure 3 when all competencies except 2nd level competencies 2, 3, and 4 are sequentially dependent.

**Figure 9.**Result of TBCG transformation for competence tree, presented in Figure 8.

**Figure 10.**Result of BTCG transformation for competence tree, presented in Figure 8, when all competencies except 2nd level competencies 2 and 3 are sequentially dependent.

Analyzed Competence Tree | Number of Task Nodes in Competence Tree | Transformation Method | Transformation Case | Number of Task Nodes in a Graph | Number of Decision Nodes in a Graph | Does the Graph Meet a Graph-Based Testing Structure? |
---|---|---|---|---|---|---|

Example1 ^{1} | 21 | TBCG | - | 21 | 9 | Yes |

BTCG | Full sequential dependency | 21 | 20 | Yes | ||

2nd level sequential independency | 21 | 20 | Yes | |||

Example2 ^{2} | 10 | TBCG | - | 10 | 4 | Yes |

BTCG | 2nd level sequential independency | 10 | 9 | Yes |

Analyzed Graph | Number of Task Nodes in a Graph | Number of Decision Nodes in a Graph | Number of Task Nodes in a Tree | Number of Decision Nodes in a Tree | Does the Graph Meet a Tree-Based Testing Structure? | |||
---|---|---|---|---|---|---|---|---|

Original | Modified | Original | Modified | Original | Modified | |||

Example1 ^{1} | 21 | 9 | 799 | 177 | 63 | 63 | No | Partly ^{5} |

Example2 ^{2} | 21 | 20 | 5190 | 360 | 400 | 400 | No | Partly ^{5} |

Example3 ^{3} | 10 | 4 | 41 | 16 | 6 | 6 | No | Partly ^{5} |

Example4 ^{4} | 10 | 9 | 183 | 30 | 29 | 29 | No | Partly ^{5} |

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**MDPI and ACS Style**

Margienė, A.; Ramanauskaitė, S.
Toward Adaptability of E-Evaluation: Transformation from Tree-Based to Graph-Based Structure. *Appl. Sci.* **2021**, *11*, 4082.
https://doi.org/10.3390/app11094082

**AMA Style**

Margienė A, Ramanauskaitė S.
Toward Adaptability of E-Evaluation: Transformation from Tree-Based to Graph-Based Structure. *Applied Sciences*. 2021; 11(9):4082.
https://doi.org/10.3390/app11094082

**Chicago/Turabian Style**

Margienė, Asta, and Simona Ramanauskaitė.
2021. "Toward Adaptability of E-Evaluation: Transformation from Tree-Based to Graph-Based Structure" *Applied Sciences* 11, no. 9: 4082.
https://doi.org/10.3390/app11094082