An Interval AHP Technique for Classroom Teaching Quality Evaluation
Abstract
:1. Introduction
2. Preliminaries
2.1. Interval Number and Interval Judgment Matrix
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 –
4.3.1. Calculation the Basic Weights of Factors –
4.3.2. Calculating the Weights of Factors –
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 –
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
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Value of Importance | Comparative Judgment |
---|---|
1 | is as important as |
3 | is slightly more important than |
5 | is strongly more important than |
7 | is very strongly more important than |
9 | is extremely more important than |
2,4,6,8 | Represents the median value of the above adjacent judgment |
Reciprocal | If the ratio of the importance of and is , |
then ratio of and is |
Target Level | Factor Level (F) | Item Level (I) |
---|---|---|
Teaching quality evaluation | . Lesson Design and Implementation | . Respect student preconceptions and knowledge of mathematics |
. Form a math learning group | ||
. Explore before formal presentation | ||
. Seek alternative approaches different in textbooks | ||
. Adopt student ideas in teaching | ||
. Content: Propositional Knowledge | . Involve fundamental concepts of mathematics | |
. Promote coherent understanding of mathematical concepts | ||
. Teacher have a solid grasp of the contents (especially for unrelated questions) | ||
. Encourage abstraction (mathematics models or formulas) | ||
. Emphasize the connection between mathematics and other disciplines or social life | ||
. Content: Procedural Knowledge | . Students use models, formulas, graphics to express their understanding | |
. Students make predictions, assumptions or estimates | ||
. Make critical inferences or estimates of results | ||
. Students reflect on their learning in mathematics class | ||
. Students infer or question corresponding conclusions, concepts and formulas | ||
. Classroom culture: Communicative Interactions | . Students communicate their understanding and ideas with various ways | |
. Teachers’ questions lead to students’ thinking differently about mathematics | ||
. Students actively discuss mathematics problems | ||
. The direction of the class is determined by the discussion of students | ||
. Students actively express their views without being ridiculed | ||
. Classroom culture: Student/ Teacher Relationships | . Encourage students to actively participate in discussion | |
. Encourage students to solve mathematical problems in many ways | ||
. Teacher is patient when students think about problems or complete assignments | ||
. When students investigate or study, the teacher acts as a resource | ||
. 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 | |||||
---|---|---|---|---|---|
No.1 | 5.2669 | 0.9779 | 0.0596 | =(0.3033, 0.1160, 0.0706, 0.4004, 0.1056) | |
5.0958 | 0.9958 | 0.0214 | = (0.4482, 0.1484, 0.0757, 0.2365, 0.0690) | ||
No.2 | 5.2148 | 0.9896 | 0.0479 | =(0.1424, 0.3161, 0.2915, 0.1143, 0.1170) | |
5.3465 | 0.9813 | 0.0773 | = (0.2607, 0.3275, 0.2450, 0.0890, 0.0674) | ||
No.3 | 5.3339 | 0.9733 | 0.0745 | = (0.1674, 0.0814, 0.0993, 0.3766, 0.2527) | |
5.2508 | 0.9775 | 0.0560 | = (0.2856, 0.1094, 0.1224, 0.3050, 0.1509) | ||
No.4 | 5.2592 | 0.9804 | 0.0579 | = (0.0655, 0.1221, 0.3655, 0.2712, 0.1370) | |
5.4217 | 0.9615 | 0.0941 | = (0.1151, 0.1457, 0.3793, 0.2202, 0.1201) | ||
No.5 | 5.3621 | 0.9582 | 0.0808 | = (0.2589, 0.2254, 0.0958, 0.1962, 0.1767) | |
5.4353 | 0.9532 | 0.0972 | = (0.3487, 0.2395, 0.0895, 0.1629, 0.1177) |
Factor | Lower Weight | Upper Weight |
---|---|---|
0.1936 | 0.3030 | |
0.1747 | 0.1940 | |
0.1777 | 0.1679 | |
0.2695 | 0.2043 | |
0.1577 | 0.1057 |
Factor | Lower Weight | Upper Weight |
---|---|---|
0.1990 | 0.3108 | |
0.1795 | 0.199 | |
0.1826 | 0.1722 | |
0.2769 | 0.2095 | |
0.162 | 0.1085 |
Factor | Lower Weight () | Upper Weight () | Items | Lower Weight () | Upper Weight () |
---|---|---|---|---|---|
0.1990 | 0.3108 | 0.1243 | 0.1717 | ||
0.2183 | 0.2497 | ||||
0.2604 | 0.2516 | ||||
0.2487 | 0.2128 | ||||
0.1482 | 0.1142 | ||||
0.1795 | 0.1990 | 0.1282 | 0.1914 | ||
0.1439 | 0.1768 | ||||
0.3149 | 0.3012 | ||||
0.2101 | 0.1684 | ||||
0.2029 | 0.1623 | ||||
0.1826 | 0.1722 | 0.0878 | 0.1460 | ||
0.2063 | 0.2454 | ||||
0.2499 | 0.2462 | ||||
0.3182 | 0.2549 | ||||
0.1378 | 0.1075 | ||||
0.2769 | 0.2095 | 0.2008 | 0.2646 | ||
0.1628 | 0.1938 | ||||
0.1574 | 0.1475 | ||||
0.2054 | 0.1758 | ||||
0.2737 | 0.2183 | ||||
0.1620 | 0.1085 | 0.2002 | 0.2694 | ||
0.2300 | 0.2444 | ||||
0.1802 | 0.1816 | ||||
0.2209 | 0.1892 | ||||
0.1687 | 0.1155 |
Factors | Items | Evaluation Value () | ||||
---|---|---|---|---|---|---|
Assessor-1 | Assessor-2 | Assessor-3 | Assessor-4 | Assessor-5 | ||
[0.6,0.7] | [0.65,0.75] | [0.6,0.8] | [0.7,0.8] | [0.8,0.9] | ||
[0.7,0.8] | [0.8,0.85] | [0.75,0.85] | [0.7,0.8] | [0.85,0.9] | ||
[0.65,0.75] | [0.7,0.8] | [0.55,0.6] | [0.5,0.6] | [0.6,0.8] | ||
[0.65,0.75] | [0.7,0.8] | [0.55,0.6] | [0.5,0.6] | [0.6,0.8] | ||
[0.4,0.5] | [0.5,0.55] | [0.5,0.6] | [0.6,0.7] | [0.6,0.65] | ||
[0.8,0.9] | [0.75,0.8] | [0.8,0.85] | [0.75,0.85] | [0.8,0.9] | ||
[0.6,0.8] | [0.7,0.8] | [0.8,0.85] | [0.8,0.9] | [0.75,0.8] | ||
[0.8,0.9] | [0.8,0.85] | [0.8,0.9] | [0.9,0.9] | [0.75,0.85] | ||
[0.5,0.6] | [0.75,0.8] | [0.6,0.7] | [0.65,0.7] | [0.785,0.85] | ||
[0.8.0.9] | [0.8,0.85] | [0.8,0.9] | [0.75,0.8] | [0.75,0.85] | ||
[0.6,0.6] | [0.55,0.7] | [0.6,0.65] | [0.5,0.6] | [0.7,0.75] | ||
[0.65,0.7] | [0.65,0.75] | [0.7,0.75] | [0.8,0.9] | [0.75,0.8] | ||
[0.75,0.8] | [0.7,0.75] | [0.7,0.8] | [0.6,0.8] | [0.75,0.85] | ||
[0.5,0.6] | [0.4,0.5] | [0.6,0.65] | [0.5,0.55] | [0.6,0.7] | ||
[0.7,0.8] | [0.6,0.65] | [0.6,0.7] | [0.7,0.8] | [0.75,0.85] | ||
[0.75,0.9] | [0.7,0.8] | [0.7,0.8] | [0.6,0.8] | [0.7,0.75] | ||
[0.75,0.8] | [0.7,0.8] | [0.75,0.85] | [0.65,0.8] | [0.8,0.85] | ||
[0.5,0.6] | [0.55,0.6] | [0.45,0.5] | [0.6,0.7] | [0.6,0.7] | ||
[0.35,0.4] | [0.5,0.6] | [0.55,0.6] | [0.5,0.6] | [0.5,0.6] | ||
[0.75,0.8] | [0.7,0.8] | [0.65,0.7] | [0.6,0.7] | [0.75,0.8] | ||
[0.8,0.9] | [0.75,0.8] | [0.75,0.85] | [0.8,0.85] | [0.75,0.85] | ||
[0.6,0.7] | [0.7,0.75] | [0.6,0.65] | [0.7,0.8] | [0.7,0.8] | ||
[0.8,0.9] | [0.85,0.9] | [0.75,0.8] | [0.8,0.9] | [0.7,0.8] | ||
[0.6,0.8] | [0.6,0.7] | [0.65,0.7] | [0.75,0.8] | [0.7,0.8] | ||
[0.6,0.7] | [0.5,0.6] | [0.45,0.5] | [0.5,0.6] | [0.6,0.7] |
Factor | Weight () | Average Evaluation Value () | Aggregated Score () | Total Aggregated Score (y) |
---|---|---|---|---|
[0.1990,0.3108] | [0.6135,0.721] | [0.122,0.2241] | ||
[0.1795,0.1990] | [0.7549,0.8372] | [0.1355,0.1666] | [0.6565,0.7510] | |
[0.1826,0.1722] | [0.6310,0.7193] | [0.1152,0.1239] | ||
[0.2769,0.2095] | [0.6257,0.7238] | [0.1733,0.1517] | ||
[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 |
---|---|---|---|
[0.1990,0.3108] | 1 | ||
[0.1795,0.1990] | 3 | ||
[0.1826,0.1722] | 4 | ||
[0.2769,0.2095] | 2 | ||
[0.1620,0.1085] | 5 |
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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
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 StyleQin, 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