# An Interval AHP Technique for Classroom Teaching Quality Evaluation

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Interval Number and Interval Judgment Matrix

**Definition**

**1.**

**Definition**

**2.**

#### 2.2. Analytic Hierarchy Process

#### 2.3. Hierarchical Evaluation Structure: Reformed Teaching Observation Protocol

## 3. Methodology

#### 3.1. Determining the Evaluation Criteria’ Weights with I-AHP

#### 3.1.1. Constructing Interval Judgment Matrices

#### 3.1.2. Calculating Criteria’ Basic Weights

#### 3.2. Determining the Assessor’ Weight

#### 3.2.1. Calculating the Similarity Coefficient of Assessors’ Evaluation

#### 3.2.2. Calculating the Difference of Assessors’ Evaluation

#### 3.2.3. Calculating the Weight of Evaluation Assessors

#### 3.2.4. Calculating the Criteria’ Final Weights

#### 3.3. Comprehensive Evaluation Model

## 4. Case Study

#### 4.1. Evaluation Object and Subject

#### 4.2. Constructing Interval Judgment Matrices

#### 4.3. Calculation the Weights of Factors ${F}_{1}$–${F}_{5}$

#### 4.3.1. Calculation the Basic Weights of Factors ${F}_{1}$–${F}_{5}$

#### 4.3.2. Calculating the Weights of Factors ${F}_{1}$–${F}_{5}$

#### 4.4. Assessors’ Weights

#### 4.4.1. Calculating the Similarity Coefficient of Assessors’ Evaluation

#### 4.4.2. Calculating the Degree of Difference of Assessors’ Evaluation and the Weight of Evaluation Assessors

#### 4.5. Final Weights for Factors ${F}_{1}$–${F}_{5}$

## 5. Comprehensive Evaluation with Interval Numbers

#### 5.1. Evaluation Standard and Data Collection

#### 5.2. Comprehensive Evaluation

## 6. Results and Analysis

#### 6.1. Results and Analysis of Interval Weights

#### 6.1.1. Ranking for Interval Weights

#### 6.1.2. Analysis for the Ranking Results

#### 6.2. Results and Analysis of Aggregated Scores

#### 6.2.1. Ranking for Aggregated Scores

#### 6.2.2. Analysis of Total Aggregated Scores

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Interval Reciprocal Judgment Matrices for Items

## References

- Saaty, T.L. How to make a decision: The analytic hierarchy process. Eur. J. Oper. Res.
**1990**, 48, 9–26. [Google Scholar] [CrossRef] - Liang, L.; Sheng, Z.H.; Xu, N.R. An improved analytic hierarchy process. Syst. Eng.
**1989**, 5–7. [Google Scholar] - Ma, Y.D.; Hu, M.D. Improved AHP method and its application in multiobjective decision making. Syst.-Eng.-Theory Pract.
**1997**, 6, 40–44. [Google Scholar] - Jin, J.L.; Wei, Y.M.; Pan, J.F. Accelerating genetic algorithm for correcting the consistency of judgment matrix in AHP. Syst.-Eng.-Theory Pract.
**2004**, 24, 63–69. [Google Scholar] - Wang, X.J.; Guo, Y.J. Consistency analysis of judgment matrix based on G1 method. Chin. J. Manag. Sci.
**2006**, 316, 65–70. [Google Scholar] - Li, C.H.; Du, Y.W.; Sun, Y.H.; Tian, S. Multi-attribute implicit variable weight decision analysis method. Chin. J. Manag. Sci.
**2012**, 20, 163–172. [Google Scholar] - Wang, H.B.; Luo, H.; Yang, S.L. A ranking method of inconsistent judgment matrix based on manifold learning. Chin. J. Manag. Sci.
**2015**, 23, 147–155. [Google Scholar] - Wei, C.P.; Zhang, Z.M. An algorithm to improve the consistency of a comparison matrix. Syst.-Eng.-Theory Pract.
**2000**, 8, 62–66. [Google Scholar] - Zhu, J.J.; Liu, S.X.; Wang, M.G. A new method to improve the inconsistent judgment matrix. Syst.-Eng.-Theory Pract.
**2003**, 95–98. [Google Scholar] - Tian, Z.Y.; Wang, H.C.; Wu, R.M. Consistency test and improvement of possible satisfaction and judgment matrix. Syst.-Eng.-Theory Pract.
**2004**, 216, 94–99. [Google Scholar] - Sun, J.; Xu, W.S.; Wu, Q.D. A new algorithm for group decision-making based on compatibility modification and ranking of incomplete judgment matrix. Syst.-Eng.-Theory Pract.
**2006**, 7, 88–94. [Google Scholar] - Jiao, B.; Huang, Z.D.; Huang, F.; Li, W. An aggregation method of group AHP judgment matrices based on optimal possible-satisfaction degree. Control. Decis.
**2013**, 28, 1242–1246. [Google Scholar] - Liu, B.; Xu, S.B.; Zhao, H.C.; Huo, J.S. Analytic hierarchy process–a decision-making tool for planning. Syst. Eng.
**1984**, 108, 23–30. [Google Scholar] - Liu, B. Group judgment and analytic hierarchy process. J. Syst. Eng.
**1991**, 70–75. [Google Scholar] - He, K. The scale research of analytic hierarchy process. Syst.-Eng.-Theory Pract.
**1997**, 59–62. [Google Scholar] - Xu, Z.S. New scale method for analytic hierarchy process. Syst.-Eng.-Theory Pract.
**1998**, 75–78. [Google Scholar] - Wang, H.; Ma, D. Analytic hierarchy process scale evaluation and new scale method. Syst.-Eng.-Theory Pract.
**1993**, 24–26. [Google Scholar] - Hou, Y.H.; Shen, D.J. Index number scale and comparison with other scales. Syst.-Eng.-Theory Pract.
**1995**, 10, 43–46. [Google Scholar] - Luo, Z.Q.; Yang, S.L. Comparison of several scales in analytic hierarchy process. Syst.-Eng.-Theory Pract.
**2004**, 9, 51–60. [Google Scholar] - Lv, Y.J.; Chen, W.C.; Zhong, L. A Survey on the Scale of Analytic Hierarchy Process. J. Qiongzhou Univ.
**2013**, 20, 1–6. [Google Scholar] - Wu, Y.H.; Zhu, W.; Li, X.Q.; Gao, R. Interval analytic hierarchy process–IAHP. J. Tianjing Univ.
**1995**, 28, 700–705. [Google Scholar] - Deng, S.J.; Zhang, Y.; Ren, J.J.; Yang, K.X.; Liu, K.; Liu, M.M. Evaluation Index of CRTS III Prefabricated Slab Track Cracking Condition Based on Interval AHP. Int. J. Struct. Stab. Dyn.
**2021**, 21, 2140013. [Google Scholar] [CrossRef] - Milosevic, M.R.; Milosevic, D.M.; Stanojevic, A.D.; Stevic, D.M.; Simjanovic, D.J. Fuzzy and Interval AHP Approaches in Sustainable Management for the Architectural Heritage in Smart Cities. Mathematics
**2021**, 9, 304. [Google Scholar] [CrossRef] - Wang, S.X.; Ge, L.J.; Cai, S.X.; Zhang, D. An Improved Interval AHP Method for Assessment of Cloud Platform-based Electrical Safety Monitoring System. J. Electr. Eng. Technol.
**2017**, 12, 959–968. [Google Scholar] [CrossRef] [Green Version] - Wang, S.X.; Ge, L.J.; Cai, S.X.; Wu, L. Hybrid interval AHP-entropy method for electricity user evaluation in smart electricity utilization. J. Mod. Power Syst. Clean Energy
**2018**, 6, 701–711. [Google Scholar] [CrossRef] [Green Version] - Ghorbanzadeh, O.; Moslem, S.; Blaschke, T.; Duleba, S. Sustainable Urban Transport Planning Considering Different Stakeholder Groups by an Interval-AHP Decision Support Model. Sustainability
**2019**, 11, 9. [Google Scholar] [CrossRef] [Green Version] - Moslem, S.; Ghorbanzadeh, O.; Blaschke, T.; Duleba, S. Analysing Stakeholder Consensus for a Sustainable Transport Development Decision by the Fuzzy AHP and Interval AHP. Sustainability
**2019**, 11, 3271. [Google Scholar] [CrossRef] [Green Version] - Xu, Z.S. Research on consistency of interval judgment matrices in group AHP. Oper. Res. Manag. Sci.
**2000**, 9, 8–11. [Google Scholar] - Saaty, T.L. The analytic network process. In Decision Making with the Analytic Network Process; Springer: Berlin, Germany, 2006; pp. 1–26. [Google Scholar]
- Saaty, T.L.; Vargas, L.G. Inconsistency and rank preservation. J. Math. Psychol.
**1984**, 28, 205–214. [Google Scholar] [CrossRef] - Saaty, T.L. Decision making with the analytic hierarchy process. Int. J. Serv. Sci.
**2008**, 1, 83–98. [Google Scholar] [CrossRef] [Green Version] - Adamson, S.L.; Banks, D.; Burtch, M.; Cox, F., III; Judson, E.; Turley, J.B.; Benford, R.; Lawson, A.E. Reformed undergraduate instruction and its subsequent impact on secondary school teaching practice and student achievement. J. Res. Sci. Teach.
**2003**, 40, 939–957. [Google Scholar] - Matosas-López, L.; Aguado-Franco, J.C.; Gómez-Galán, J. Constructing an Instrument with Behavioral Scales to Assess Teaching Quality in Blended Learning Modalities. J. New Approaches Educ. Res.
**2019**, 8, 142–165. [Google Scholar] [CrossRef] - Metsäpelto, R.; Poikkeus, A.; Heikkilä, M.; Heikkinen-Jokilahti, K.; Husu, J.; Laine, A.; Lappalainen, K.; Lähteenmäki, M.; Mikkilä-Erdmann, M.; Warinowski, A. Conceptual Framework of Teaching Quality: A Multidimensional Adapted Process Model of Teaching; OVET/DOORS working paper. PsyArXiv
**2020**. [Google Scholar] [CrossRef] - Budd, D.A.; Van der Hoeven Kraft, K.J.; McConnell, D.A.; Vislova, T. Characterizing Teaching in Introductory Geology Courses: Measuring Classroom Practices. J. Geosci.
**2013**, 61, 461–475. [Google Scholar] - Bok, D.C. Higher Learning; Harvard University Press: Cambridge, MA, USA, 1986. [Google Scholar]
- Goe, L.; Holdheide, L.; Miller, T. A Practical Guide to Designing Comprehensive Teacher Evaluation Systems; Center on Great Teachers & Leaders: Washington, DC, USA, 2011. [Google Scholar]
- Danielson, C.; McGreal, T.L. Teacher Evaluation to Enhance Professional Practice; Assn for Supervision & Curriculum: New York, NY, USA, 2000. [Google Scholar]
- Piburn, M.; Sawada, D.; Turley, J.; Falconer, K.; Benford, R.; Bloom, I.; Judson, E. Reformed Teaching Observation Protocol (RTOP) Reference Manual; ACEPT Technical Report No. IN00-3; Tempe: Arizona Board of Regents: Phoenix, AZ, USA, 2000. [Google Scholar]
- Macisaac, D.; Falconer, K. Reforming physics instruction via RTOP. Phys. Teach.
**2002**, 40, 479–485. [Google Scholar] [CrossRef] - Lawson, A.E. Using the RTOP to Evaluate Reformed Science and Mathematics Instruction: Improving Undergraduate Instruction in Science, Technology, Engineering, and Mathematics; National Academies Press/National Research Council: Washington, DC, USA, 2003. [Google Scholar]
- Teasdale, R.; Viskupic, K.; Bartley, J.K.; McConnell, D.; Manduca, C.; Bruckner, M.; Farthing, D.; Iverson, E. A multidimensional assessment of reformed teaching practice in geoscience classrooms. Geosphere
**2017**, 13, 608–627. [Google Scholar] [CrossRef] [Green Version] - Sawada, D.; Piburn, M.D.; Judson, E.; Turley, J.; Falconer, K.; Benford, R.; Bloom, I. Measuring Reform Practices in Science and Mathematics Classrooms: The Reformed Teaching Observation Protocol. Sch. Sci. Math.
**2002**, 102, 245–253. [Google Scholar] [CrossRef] - Lund, T.J.; Pilarz, M.; Velasco, J.B.; Chakraverty, D.; Rosploch, K.; Undersander, M.; Stains, M. The best of both worlds: Building on the COPUS and RTOP observation protocols to easily and reliably measure various levels of reformed instructional practices. CBE Life Sciences Education
**2015**, 14, 1–12. [Google Scholar] [CrossRef] [Green Version] - Addy, T.M.; Blanchard, M.R. The problem with reform from the bottom up: Instructional practices and teacher beliefs of graduate teaching assistants following a reform-minded university teacher certificate programme. Int. J. Sci. Educ.
**2010**, 32, 1045–1071. [Google Scholar] [CrossRef] - Amrein-Beardsley, A.; Popp, S.E.O. Peer observations among faculty in a college of education: Investigating the summative and formative uses of the Reformed Teaching Observation Protocol (RTOP). Educ. Assess. Eval. Account.
**2012**, 24, 5–24. [Google Scholar] [CrossRef] - Campbell, T.; Wolf, P.G.; Der, J.P.; Packenham, E.; AbdHamid, N. Scientific inquiry in the genetics laboratory: Biologists and university science teacher educators collaborating to increase engagements in science processes. J. Coll. Sci. Teach.
**2012**, 41, 82–89. [Google Scholar] - Ebert-May, D.; Derting, T.L.; Hodder, J.; Momsen, J.L.; Long, T.M.; Jardeleza, S.E. What we say is not what we do: Effective evaluation of faculty professional development programs. Bioscience
**2011**, 61, 550–558. [Google Scholar] [CrossRef] [Green Version] - Erdogan, I.; Campbell, T.; Abd-Hamid, N.H. The student actions coding sheet (SACS): An instrument for illuminating the shifts toward student-centered science classrooms. Int. J. Sci. Educ.
**2011**, 33, 1313–1336. [Google Scholar] [CrossRef] - Tong, D.Z.; Xing, H.J.; Zheng, C.G. Localization of Classroom Teaching Evaluation Tool RTOP—Taking the Evaluation of Physics Classroom Teaching as An Example. Educ. Sci. Res.
**2020**, 11, 31–36. [Google Scholar] - Tong, D.Z.; Xing, H.J. A Comparative Study of RTOP and Chinese Classical Classroom Teaching Evaluation Tools. Res. Educ. Assess. Learn.
**2021**, 6. [Google Scholar] [CrossRef] - Liu, F. Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Sets Syst.
**2009**, 160, 2686–2700. [Google Scholar] [CrossRef] - Ghorbanzadeh, O.; Feizizadeh, B.; Blaschke, T. An interval matrix method used to optimize the decision matrix in AHP technique for land subsidence susceptibility mapping. Environ. Earth Sci.
**2018**, 77, 584. [Google Scholar] [CrossRef] - Lyu, H.-M.; Sun, W.-J.; Shen, S.-L.; Arulrajah, A. Flood risk assessment in metro systems of mega-cities using a GIS-based modeling approach. Sci. Total Environ.
**2018**, 626, 1012–1025. [Google Scholar] [CrossRef] - Chen, J.F.; Hsieh, H.N.; Do, Q.H. Evaluating teaching performance based on fuzzy AHP and comprehensive evaluation approach. Appl. Soft Comput. J.
**2014**. [Google Scholar] [CrossRef] - Broumi, S.; Smarandache, F. Cosine similarity measure of interval valued neutrosophic sets. Neutrosophic. Sets Syst.
**2014**, 5, 15–20. [Google Scholar] - Chen, X.Z.; Zhang, X.J. The research on computation of researchers’ certainty factor of the indeterminate AHP. J. Zhengzhou Univ. Sci.
**2013**, 34, 85–89. [Google Scholar] - Suh, H.; Kim, S.; Hwang, S.; Han, S. Enhancing Preservice Teachers’ Key Competencies for Promoting Sustainability in a University Statistics Course. Sustainability
**2020**, 12, 9051. [Google Scholar] [CrossRef] - Guo, Z.M. The evaluation of mathematics self-study ability of college students based on uncertain AHP and whitening weight function. J. Chongqing Technol. Bus. Univ. Sci. Ed.
**2019**, 36, 65–72. [Google Scholar] - Jiang, J.; Tang, J.; Gan, Y.; Lan, Z.C.; Qin, T.Q. Safety evaluation of building structure based on combination weighting method. Sci. Technol. Eng.
**2021**, 21, 7278–7285. [Google Scholar] - Wang, Y.M.; Yang, J.B.; Xu, D.L. A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets Syst.
**2005**, 152, 475–498. [Google Scholar] [CrossRef] - Xu, Z.S.; Chen, J. Some models for deriving the priority weights from interval fuzzy preference relations. Eur. J. Oper. Res.
**2008**, 184, 266–280. [Google Scholar] [CrossRef] - Dick, W.; Carey, L. The Systematic Design of Instruction, 4th ed.; Harper Collins College Publishers: New York, NY, USA, 1996. [Google Scholar]

Value of Importance | Comparative Judgment |
---|---|

1 | ${F}_{i}$ is as important as ${F}_{j}$ |

3 | ${F}_{i}$ is slightly more important than ${F}_{j}$ |

5 | ${F}_{i}$ is strongly more important than ${F}_{j}$ |

7 | ${F}_{i}$ is very strongly more important than ${F}_{j}$ |

9 | ${F}_{i}$ is extremely more important than ${F}_{j}$ |

2,4,6,8 | Represents the median value of the above adjacent judgment |

Reciprocal | If the ratio of the importance of ${F}_{i}$ and ${F}_{j}$ is ${f}_{ij}$, |

then ratio of ${F}_{j}$ and ${F}_{i}$ is ${f}_{ji}=1/\phantom{1{f}_{ij}}\phantom{\rule{0.0pt}{0ex}}{f}_{ij}$ |

Target Level | Factor Level (F) | Item Level (I) |
---|---|---|

Teaching quality evaluation | ${F}_{1}$. Lesson Design and Implementation | ${I}_{1}$. Respect student preconceptions and knowledge of mathematics |

${I}_{2}$. Form a math learning group | ||

${I}_{3}$. Explore before formal presentation | ||

${I}_{4}$. Seek alternative approaches different in textbooks | ||

${I}_{5}$. Adopt student ideas in teaching | ||

${F}_{2}$. Content: Propositional Knowledge | ${I}_{6}$. Involve fundamental concepts of mathematics | |

${I}_{7}$. Promote coherent understanding of mathematical concepts | ||

${I}_{8}$. Teacher have a solid grasp of the contents (especially for unrelated questions) | ||

${I}_{9}$. Encourage abstraction (mathematics models or formulas) | ||

${I}_{10}$. Emphasize the connection between mathematics and other disciplines or social life | ||

${F}_{3}$. Content: Procedural Knowledge | ${I}_{11}$. Students use models, formulas, graphics to express their understanding | |

${I}_{12}$. Students make predictions, assumptions or estimates | ||

${I}_{13}$. Make critical inferences or estimates of results | ||

${I}_{14}$. Students reflect on their learning in mathematics class | ||

${I}_{15}$. Students infer or question corresponding conclusions, concepts and formulas | ||

${F}_{4}$. Classroom culture: Communicative Interactions | ${I}_{16}$. Students communicate their understanding and ideas with various ways | |

${I}_{17}$. Teachers’ questions lead to students’ thinking differently about mathematics | ||

${I}_{18}$. Students actively discuss mathematics problems | ||

${I}_{19}$. The direction of the class is determined by the discussion of students | ||

${I}_{20}$. Students actively express their views without being ridiculed | ||

${F}_{5}$. Classroom culture: Student/ Teacher Relationships | ${I}_{21}$. Encourage students to actively participate in discussion | |

${I}_{22}$. Encourage students to solve mathematical problems in many ways | ||

${I}_{23}$. Teacher is patient when students think about problems or complete assignments | ||

${I}_{24}$. When students investigate or study, the teacher acts as a resource | ||

${I}_{25}$. Teacher listens carefully when students discuss and express their views |

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

RI | 0.00 | 0.00 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 | 1.51 | 1.48 |

Assessor | $\mathit{\Lambda}$ | ${\mathit{\lambda}}_{{}_{max}}$ | $\mathit{\alpha}/\mathit{\beta}$ | $\mathbf{CR}$ | ${\mathit{w}}_{1\mathit{L}}/{\mathit{w}}_{1\mathit{R}}$ |
---|---|---|---|---|---|

No.1 | ${\mathsf{\Lambda}}_{1}^{-}$ | 5.2669 | 0.9779 | 0.0596 | ${w}_{1L}$=(0.3033, 0.1160, 0.0706, 0.4004, 0.1056) |

${\mathsf{\Lambda}}_{1}^{+}$ | 5.0958 | 0.9958 | 0.0214 | ${w}_{1R}$= (0.4482, 0.1484, 0.0757, 0.2365, 0.0690) | |

No.2 | ${\mathsf{\Lambda}}_{2}^{-}$ | 5.2148 | 0.9896 | 0.0479 | ${w}_{2L}$=(0.1424, 0.3161, 0.2915, 0.1143, 0.1170) |

${\mathsf{\Lambda}}_{2}^{+}$ | 5.3465 | 0.9813 | 0.0773 | ${w}_{2R}$= (0.2607, 0.3275, 0.2450, 0.0890, 0.0674) | |

No.3 | ${\mathsf{\Lambda}}_{3}^{-}$ | 5.3339 | 0.9733 | 0.0745 | ${w}_{3L}$= (0.1674, 0.0814, 0.0993, 0.3766, 0.2527) |

${\mathsf{\Lambda}}_{3}^{+}$ | 5.2508 | 0.9775 | 0.0560 | ${w}_{3R}$= (0.2856, 0.1094, 0.1224, 0.3050, 0.1509) | |

No.4 | ${\mathsf{\Lambda}}_{4}^{-}$ | 5.2592 | 0.9804 | 0.0579 | ${w}_{4L}$= (0.0655, 0.1221, 0.3655, 0.2712, 0.1370) |

${\mathsf{\Lambda}}_{4}+$ | 5.4217 | 0.9615 | 0.0941 | ${w}_{4R}$= (0.1151, 0.1457, 0.3793, 0.2202, 0.1201) | |

No.5 | ${\mathsf{\Lambda}}_{5}^{-}$ | 5.3621 | 0.9582 | 0.0808 | ${w}_{5L}$= (0.2589, 0.2254, 0.0958, 0.1962, 0.1767) |

${\mathsf{\Lambda}}_{5}^{+}$ | 5.4353 | 0.9532 | 0.0972 | ${w}_{5R}$= (0.3487, 0.2395, 0.0895, 0.1629, 0.1177) |

Factor | Lower Weight | Upper Weight |
---|---|---|

${F}_{1}$ | 0.1936 | 0.3030 |

${F}_{2}$ | 0.1747 | 0.1940 |

${F}_{3}$ | 0.1777 | 0.1679 |

${F}_{4}$ | 0.2695 | 0.2043 |

${F}_{5}$ | 0.1577 | 0.1057 |

Factor | Lower Weight | Upper Weight |
---|---|---|

${F}_{1}$ | 0.1990 | 0.3108 |

${F}_{2}$ | 0.1795 | 0.199 |

${F}_{3}$ | 0.1826 | 0.1722 |

${F}_{4}$ | 0.2769 | 0.2095 |

${F}_{5}$ | 0.162 | 0.1085 |

Factor | Lower Weight (${\mathit{w}}_{{\mathit{F}}_{\mathit{i}}}^{-}$) | Upper Weight (${\mathit{w}}_{{\mathit{F}}_{\mathit{i}}}^{+}$) | Items | Lower Weight (${\mathit{w}}_{{\mathit{I}}_{\mathit{i}}}^{-}$) | Upper Weight (${\mathit{w}}_{{\mathit{I}}_{\mathit{i}}}^{+}$) |
---|---|---|---|---|---|

${F}_{1}$ | 0.1990 | 0.3108 | ${I}_{1}$ | 0.1243 | 0.1717 |

${I}_{2}$ | 0.2183 | 0.2497 | |||

${I}_{3}$ | 0.2604 | 0.2516 | |||

${I}_{4}$ | 0.2487 | 0.2128 | |||

${I}_{5}$ | 0.1482 | 0.1142 | |||

${F}_{2}$ | 0.1795 | 0.1990 | ${I}_{6}$ | 0.1282 | 0.1914 |

${I}_{7}$ | 0.1439 | 0.1768 | |||

${I}_{8}$ | 0.3149 | 0.3012 | |||

${I}_{9}$ | 0.2101 | 0.1684 | |||

${I}_{10}$ | 0.2029 | 0.1623 | |||

${F}_{3}$ | 0.1826 | 0.1722 | ${I}_{11}$ | 0.0878 | 0.1460 |

${I}_{12}$ | 0.2063 | 0.2454 | |||

${I}_{13}$ | 0.2499 | 0.2462 | |||

${I}_{14}$ | 0.3182 | 0.2549 | |||

${I}_{15}$ | 0.1378 | 0.1075 | |||

${F}_{4}$ | 0.2769 | 0.2095 | ${I}_{16}$ | 0.2008 | 0.2646 |

${I}_{17}$ | 0.1628 | 0.1938 | |||

${I}_{18}$ | 0.1574 | 0.1475 | |||

${I}_{19}$ | 0.2054 | 0.1758 | |||

${I}_{20}$ | 0.2737 | 0.2183 | |||

${F}_{5}$ | 0.1620 | 0.1085 | ${I}_{21}$ | 0.2002 | 0.2694 |

${I}_{22}$ | 0.2300 | 0.2444 | |||

${I}_{23}$ | 0.1802 | 0.1816 | |||

${I}_{24}$ | 0.2209 | 0.1892 | |||

${I}_{25}$ | 0.1687 | 0.1155 |

Factors | Items | Evaluation Value (${\mathit{x}}_{\mathbf{ij}},\mathit{i}=1,2,\cdots ,25,\mathit{j}=1,2,\cdots ,5$) | ||||
---|---|---|---|---|---|---|

Assessor-1 | Assessor-2 | Assessor-3 | Assessor-4 | Assessor-5 | ||

${F}_{1}$ | ${I}_{1}$ | [0.6,0.7] | [0.65,0.75] | [0.6,0.8] | [0.7,0.8] | [0.8,0.9] |

${I}_{2}$ | [0.7,0.8] | [0.8,0.85] | [0.75,0.85] | [0.7,0.8] | [0.85,0.9] | |

${I}_{3}$ | [0.65,0.75] | [0.7,0.8] | [0.55,0.6] | [0.5,0.6] | [0.6,0.8] | |

${I}_{4}$ | [0.65,0.75] | [0.7,0.8] | [0.55,0.6] | [0.5,0.6] | [0.6,0.8] | |

${I}_{5}$ | [0.4,0.5] | [0.5,0.55] | [0.5,0.6] | [0.6,0.7] | [0.6,0.65] | |

${F}_{2}$ | ${I}_{6}$ | [0.8,0.9] | [0.75,0.8] | [0.8,0.85] | [0.75,0.85] | [0.8,0.9] |

${I}_{7}$ | [0.6,0.8] | [0.7,0.8] | [0.8,0.85] | [0.8,0.9] | [0.75,0.8] | |

${I}_{8}$ | [0.8,0.9] | [0.8,0.85] | [0.8,0.9] | [0.9,0.9] | [0.75,0.85] | |

${I}_{9}$ | [0.5,0.6] | [0.75,0.8] | [0.6,0.7] | [0.65,0.7] | [0.785,0.85] | |

${I}_{10}$ | [0.8.0.9] | [0.8,0.85] | [0.8,0.9] | [0.75,0.8] | [0.75,0.85] | |

${F}_{3}$ | ${I}_{11}$ | [0.6,0.6] | [0.55,0.7] | [0.6,0.65] | [0.5,0.6] | [0.7,0.75] |

${I}_{12}$ | [0.65,0.7] | [0.65,0.75] | [0.7,0.75] | [0.8,0.9] | [0.75,0.8] | |

${I}_{13}$ | [0.75,0.8] | [0.7,0.75] | [0.7,0.8] | [0.6,0.8] | [0.75,0.85] | |

${I}_{14}$ | [0.5,0.6] | [0.4,0.5] | [0.6,0.65] | [0.5,0.55] | [0.6,0.7] | |

${I}_{15}$ | [0.7,0.8] | [0.6,0.65] | [0.6,0.7] | [0.7,0.8] | [0.75,0.85] | |

${F}_{4}$ | ${I}_{16}$ | [0.75,0.9] | [0.7,0.8] | [0.7,0.8] | [0.6,0.8] | [0.7,0.75] |

${I}_{17}$ | [0.75,0.8] | [0.7,0.8] | [0.75,0.85] | [0.65,0.8] | [0.8,0.85] | |

${I}_{18}$ | [0.5,0.6] | [0.55,0.6] | [0.45,0.5] | [0.6,0.7] | [0.6,0.7] | |

${I}_{19}$ | [0.35,0.4] | [0.5,0.6] | [0.55,0.6] | [0.5,0.6] | [0.5,0.6] | |

${I}_{20}$ | [0.75,0.8] | [0.7,0.8] | [0.65,0.7] | [0.6,0.7] | [0.75,0.8] | |

${F}_{5}$ | ${I}_{21}$ | [0.8,0.9] | [0.75,0.8] | [0.75,0.85] | [0.8,0.85] | [0.75,0.85] |

${I}_{22}$ | [0.6,0.7] | [0.7,0.75] | [0.6,0.65] | [0.7,0.8] | [0.7,0.8] | |

${I}_{23}$ | [0.8,0.9] | [0.85,0.9] | [0.75,0.8] | [0.8,0.9] | [0.7,0.8] | |

${I}_{24}$ | [0.6,0.8] | [0.6,0.7] | [0.65,0.7] | [0.75,0.8] | [0.7,0.8] | |

${I}_{25}$ | [0.6,0.7] | [0.5,0.6] | [0.45,0.5] | [0.5,0.6] | [0.6,0.7] |

Factor | Weight (${\mathit{w}}_{{\mathit{F}}_{\mathit{i}}}$) | Average Evaluation Value (${\mathit{y}}_{\mathit{i}}$) | Aggregated Score (${\mathit{S}}_{{\mathit{F}}_{\mathit{i}}}={\mathit{w}}_{{\mathit{F}}_{\mathit{i}}}{\mathit{y}}_{\mathit{i}}$) | Total Aggregated Score (y) |
---|---|---|---|---|

${F}_{1}$ | [0.1990,0.3108] | [0.6135,0.721] | [0.122,0.2241] | |

${F}_{2}$ | [0.1795,0.1990] | [0.7549,0.8372] | [0.1355,0.1666] | [0.6565,0.7510] |

${F}_{3}$ | [0.1826,0.1722] | [0.6310,0.7193] | [0.1152,0.1239] | |

${F}_{4}$ | [0.2769,0.2095] | [0.6257,0.7238] | [0.1733,0.1517] | |

${F}_{5}$ | [0.1620,0.1085] | [0.6817,0.7816] | [0.1104,0.0847] |

Interval Scale | Evaluation Level | Description |
---|---|---|

(0,0.2] | Very poor | The behavior never occurred, the performance is very poor |

(0.2,0.4] | Poor | The behavior occurred at least once, the performance is poor to describe the lesson |

(0.4,0.6] | Medium | The behavior occurred more than once, the performance very loosely describes the lesson |

(0.6,0.8] | Good | The behavior occurred more than two times, the performance fairly descriptive of the lesson |

(0.8,1] | Very good | The performance extremely descriptive of the lesson |

Factor | Weight | Ranking | Items of Minimum/Maximum Weight |
---|---|---|---|

${F}_{1}$ | [0.1990,0.3108] | 1 | ${I}_{5}/{I}_{3}$ |

${F}_{2}$ | [0.1795,0.1990] | 3 | ${I}_{6}/{I}_{8}$ |

${F}_{3}$ | [0.1826,0.1722] | 4 | ${I}_{11}/{I}_{14}$ |

${F}_{4}$ | [0.2769,0.2095] | 2 | ${I}_{18}/{I}_{20}$ |

${F}_{5}$ | [0.1620,0.1085] | 5 | ${I}_{25}/{I}_{22}$ |

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## Share and Cite

**MDPI and ACS Style**

Qin, Y.; Hashim, S.R.M.; Sulaiman, J.
An Interval AHP Technique for Classroom Teaching Quality Evaluation. *Educ. Sci.* **2022**, *12*, 736.
https://doi.org/10.3390/educsci12110736

**AMA Style**

Qin Y, Hashim SRM, Sulaiman J.
An Interval AHP Technique for Classroom Teaching Quality Evaluation. *Education Sciences*. 2022; 12(11):736.
https://doi.org/10.3390/educsci12110736

**Chicago/Turabian Style**

Qin, Ya, Siti Rahayu Mohd. Hashim, and Jumat Sulaiman.
2022. "An Interval AHP Technique for Classroom Teaching Quality Evaluation" *Education Sciences* 12, no. 11: 736.
https://doi.org/10.3390/educsci12110736