Development and Application of Intelligent Assessment System for Metacognition in Learning Mathematics among Junior High School Students
Abstract
:1. Introduction
2. Literature Review
2.1. Metacognition
2.2. Relationships between Metacognition and Mathematics Performance
2.3. Assessment of Mathematical Metacognition
2.4. Research Questions
 How to construct a metacognitive intelligence assessment system for junior secondary school students in mathematics?
 How to apply the system in Hexi District, Tianjin City, China, and test the effectiveness of its application?
3. Method
3.1. Design and Participants
3.1.1. Designing the Research of the Intelligent Assessment and Strategy Implementation System for Students’ Metacognition in Junior High School Mathematics
 (1)
 A strategic framework was preliminarily constructed according to the existing metacognitionrelated research and theoretical foundations;
 (2)
 Greater details were added into the strategies via casebycase analysis, interviews, etc., after taking into account the aforementioned research on metacognitive characteristics of highly productive middle school students;
 (3)
 The improvement strategies were revised and perfected via expert consultation;
 (4)
 The experts were reconsulted to confirm the strategies;
 (5)
 These expertapproved strategies were embedded into the intelligent strategy implementation module;
 (6)
 The metacognitive improvement strategies were implemented; and lastly,
 (7)
 The strategies’ effectiveness was tested.
3.1.2. Designing the Application Effectiveness Testing and Research of the Intelligent Assessment and Strategy Implementation System
3.2. Instruments
3.2.1. Questionnaire on Metacognition in Learning Mathematics
3.2.2. Test of Academic Performance in Mathematics
3.2.3. Intelligent Assessment System
4. Results
4.1. Development of Intelligent Assessment System
4.1.1. Assessment Theoretical Framework and Assessment Scale
4.1.2. Regional Norms
4.1.3. Development of Improvement Strategy
Initial Construction of Improvement Strategy
 (1)
 Based on theoretical orientation construction of the strategic framework
 (2)
 Based on excellent case interviews enrichment of specific content of strategy
 Metacognitive knowledge dimension. Excellent students had a strong sense of reflection and would summarize the mastery of mathematical knowledge and the success or failure of problemsolving results and correctly attribute them. They were good at selfquestioning in the problemsolving process and able to extract and transform information in text, graphics and symbols.
 Metacognitive experience dimension. Excellent students had the habit of previewing knowledge in advance and summarizing the knowledge framework independently. They had a more positive emotional experience during mathematical learning and could overcome or transform negative experience.
 Metacognitive monitoring dimension. Excellent students would formulate reasonable learning, problemsolving or examination plans, timely adjust their learning mentality and regularly test and evaluate their mathematical learning results.
Revision of Improvement Strategy
 There were repeats in suggestions of each subdimension and problems in orientated dimensions. For example, experts pointed out that “both knowledge and regulation dimensions of the strategy paid attention to the application of metacognitive cues, and the strategic orientation dimensions needed to be further considered”, “the examinationoriented mentality did not belong to the learning mentality, so whether it should be considered in the dimension of regulation”, and “checking writing errors did not belong to the planning dimension”.
 The logicality between the recommendations still needed to be strengthened. For instance, the logicality of “first judge whether it conforms to their own situation, and then actively improve their own mathematical learning” should be strengthened. The logical relationship between “paying attention to group honor” and “comparing your past mathematical learning state and achievement with the present” is unclear.
 The language was not refined and accurate enough. Experts suggested that the language should be refined in many parts of the full text. For example, “Facing the praise of teachers and classmates or the progress in achievements” could be changed to “when making progress or being praised”. “Pay attention to problemsolving dexterity” is inaccurate and difficult for students to understand and implement. The overall modification suggestions for the mathematical metacognitive improvement strategy are displayed in Table 2.
Determination of Improvement Strategy
4.1.4. Intelligent Assessment Software
4.2. Intelligence Assessment Diagnosis and NormReferenced Analysis
4.2.1. Results of Mathematics Metacognitive Diagnosis of Junior High School Students of Hexi District and NormReferenced Analysis
 (1)
 Results of mathematics metacognitive diagnosis of junior high school students of Hexi District
 (2)
 Normreferenced analysis of the levels of students in Hexi District against the norm of Tianjin
4.2.2. Results of Mathematics Metacognitive Diagnosis of Students Participating in the Case Study and NormReference Analysis
4.3. Test of Applicative Efficacy of the Intelligence Assessment and Strategy Implementation System
4.3.1. Analysis of the Overall Applicative Efficacy in the Region
4.3.2. Analysis of Applicative Efficacy on Students Participating in the Case Study
 (1)
 Analysis of applicative efficacy on student A who had weak MMK
 (2)
 Analysis of applicative efficacy on student B who had weak MME
 (3)
 Analysis of applicative efficacy on student C who had weak MMM
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Questionnaire of Junior High School Students’ Mathematics Metacognition Level
1  Mathematical Metacognitive Knowledge  Score  

1.1  I am aware of my mathematical learning ability and confident that I can solve various mathematical questions on my own.  5  4  3  2  1 
1.2  I have a relatively clear understanding of common solving or demonstration approaches to mathematical problems.  5  4  3  2  1 
1.3  I am aware of the goals or tasks of my mathematical learning.  5  4  3  2  1 
1.4  I know what knowledge is examined in mathematical homework assigned by my teacher.  5  4  3  2  1 
1.5  I am able to grasp mathematical knowledge (e.g., concept, equation and theorem) taught in classroom.  5  4  3  2  1 
1.6  I am able to discern the level of my understanding about some issues.  5  4  3  2  1 
1.7  I know whether I have understood the mathematical content I learned.  5  4  3  2  1 
1.8  I have a clear understanding of the types of mathematical learning tasks (e.g., autonomous learning and group discussion).  5  4  3  2  1 
1.9  I often adopt a variety of methods to solve mathematical problems.  5  4  3  2  1 
1.10  I find that I have actively used effective learning strategies.  5  4  3  2  1 
1.11  I adopt different learning approaches for different mathematical content.  5  4  3  2  1 
2  Mathematical Metacognitive Experience  Score  
2.1 *  I cannot connect newly learned mathematical concepts or theorems with similar knowledge (e.g., cannot connect linear equations in one unknown with linear inequalities in one unknown). *  5  4  3  2  1 
2.2  I try to find out central ideas behind mathematical problems (e.g., overall substitution).  5  4  3  2  1 
2.3  In mathematical learning, the times I make mistakes will be fewer if I noticed such mistakes many times.  5  4  3  2  1 
2.4  I realize that I have to plan the goals of my mathematical learning.  5  4  3  2  1 
2.5  Successfully solving mathematical problems makes me happy.  5  4  3  2  1 
2.6  I have a sense of accomplishment after completing mathematical homework.  5  4  3  2  1 
2.7 *  I am always confident about myself before learning new mathematical knowledge. *  5  4  3  2  1 
3  Mathematical Metacognitive Monitoring  Score  
3.1  After solving a problem, I would carefully summarize the inherent connections between different knowledge points to deepen my understanding.  5  4  3  2  1 
3.2  Before taking a mathematics test, I would review relevant content in a planned manner (e.g., knowledge points where errors can easily occur or content that has not been adequately acquired).  5  4  3  2  1 
3.3  When a mathematical problem cannot be solved by one method, I would timely turn to other problemsolving strategies.  5  4  3  2  1 
3.4  When solving problems, I frequently remind myself of the necessity to pay attention to the given conditions or conclusions.  5  4  3  2  1 
3.5  When I meet difficulties, I would try to refind the solutions.  5  4  3  2  1 
3.6  If I do not understand a mathematical concept, I would analyze an actual example related to the concept.  5  4  3  2  1 
3.7  In mathematical learning, I would reflect over areas I have not fully grasped.  5  4  3  2  1 
3.8  After a certain period of mathematical learning, I would evaluate the effectiveness of my learning in various ways.  5  4  3  2  1 
3.9  After solving a problem, I would check whether my method is correct.  5  4  3  2  1 
3.10  When solving a mathematical problem, I would think of whether I have solved its key questions.  5  4  3  2  1 
3.11  When I have finished my mathematical homework, I would repeat some of the key parts to ensure that I have fully understood them.  5  4  3  2  1 
3.12  I would memorize some problemsolving techniques (e.g., when doing an operation, start with involution, followed by multiplication and division and finally addition and subtraction).  5  4  3  2  1 
3.13  I can better understand a problem when I take notes of its knowledge points.  5  4  3  2  1 
4  Lie Detection Questions  Score  
4.1  In mathematical learning, I would reflect over areas I have not fully grasped.  5  4  3  2  1 
4.2  I am aware of the goals or tasks of my mathematical learning.  5  4  3  2  1 
4.3  When solving a mathematical problem, I would think of whether I have solved its key questions.  5  4  3  2  1 
4.4  Successfully solving mathematical problems makes me happy.  5  4  3  2  1 
4.5  I never erroneously solve a mathematical problem.  5  4  3  2  1 
Appendix B
Performance  Improvement Strategy 

Dimension: Mathematical metacognitive knowledge (55 points)  
Subdimension: Knowledge about individuals (25 points)  
Middlelevel students (13 ≤ X < 17):


Subdimension: Knowledge about tasks (15 points)  
Middlelevel students (8 ≤ X < 10):


Subdimension: Knowledge about strategies (15 points)  
Middlelevel students (8 ≤ X < 10):


Dimension: Mathematical metacognitive experience (35 points)  
Subdimension: Cognitive experience (20 points)  
Middlelevel students (11 ≤ X < 14):


Subdimension: Affective experience (15 points)  
Middlelevel students (8 ≤ X < 10):


Dimension: Mathematical metacognitive monitoring (65 points)  
Subdimension: Planning (10 points)  
Middlelevel students (5 ≤ X < 7): There is room for improvement in working out mathematical learning plans. Lowlevel students (X < 5): Are weak in working out mathematical learning plans. 

Subdimension: Regulation (20 points)  
Middlelevel students (11 ≤ X < 14):


Subdimension: Evaluation (10 points)  
Middlelevel students (5 ≤ X < 7):


Subdimension: Inspection (15 points)  
Middlelevel students (8 ≤ X < 11):


Subdimension: Management (10 points)  
Middlelevel students (5 ≤ X < 7):


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Level  TScore  Raw Score (X)  Percentage Rating (PR)  

Mathematical metacognition  Top  T ≥ 68  X ≤ 120  PR ≤ 96.58 
Above Average  56 ≤ T < 68  102 ≤ X < 120  73.88 ≤ PR < 96.58  
Average  44 ≤ T < 56  83 ≤ X < 102  29.08 ≤ PR < 73.88  
Below Average  32 ≤ T < 44  61 ≤ X < 83  3.80 ≤ PR < 29.08  
Low  T < 32  X < 61  PR < 3.80  
MMK  Top  T ≥ 68  X ≥ 45  PR ≥ 96.43 
Above Average  56 ≤ T < 68  38 ≤ X < 45  75.25 ≤ PR < 96.43  
Average  44 ≤ T < 56  29 ≤ X <38  31.97 ≤ PR < 75.25  
Below Average  32 ≤ T < 44  19 ≤ X < 29  4.02 ≤ PR < 31.97  
Low  T < 32  X < 19  PR < 4.02  
MME  Top  T ≥ 68  X ≥ 31  PR ≥ 97.04 
Above Average  56 ≤ T < 68  24 ≤ X < 31  71.83 ≤ PR < 97.04  
Average  44 ≤ T < 56  19 ≤ X < 24  32.05 ≤ PR < 71.83  
Below Average  32 ≤ T < 44  14 ≤ X < 19  5.85 ≤ PR < 32.50  
Low  T < 32  X < 14  PR < 5.85  
MMM  Top  T ≥ 68  X ≥ 54  PR ≥ 96.51 
Above Average  56 ≤ T < 68  44 ≤ X < 54  76.16 ≤ PR < 96.51  
Average  44 ≤ T < 56  34 ≤ X < 44  28.63 ≤ PR < 76.16  
Below Average  32 ≤ T < 44  24 ≤ X < 34  3.64 ≤ PR < 28.63  
Low  T < 32  X < 24  PR < 3.64 
Dimension  SubDimension  Modification Suggestion 

MMK  KI  No change is needed 
KT  Strengthen logicality and check for typos  
KS  Give some examples to help students understand  
MME  CE  The preview part should focus on the study of algebraic knowledge rather than the solution of algebraic problems 
AE  Consider the overall logical structure and adjust the language to highlight the positive function of homework  
MMM  Planning  Some recommendations do not fall into this category, and refine language 
Regulation  When giving advice to students, do not use words that are not easy to understand, such as “dexterity”  
Inspection  Deleting part is not a recommendation for test dimension  
Evaluation  Do not focus too much on solving problems. Solving problems is not the totality of mathematics  
Management  Carefully study the definition of this dimension in scale papers and highlight “management” 
Performance  Improvement Strategy 

Dimension: Mathematical metacognitive knowledge (55 points)  
Subdimension: Knowledge about individuals (25 points)  
Middlelevel students (13 ≤ X < 17):


Subdimension: Knowledge about tasks (15 points)  
Middlelevel students (8 ≤ X < 10):


Subdimension: Knowledge about strategies (15 points)  
Middlelevel students (8 ≤ X < 10):


Dimension: Mathematical metacognitive experience (35 points)  
Subdimension: Cognitive experience (20 points)  
Middlelevel students (11 ≤ X < 14):


Subdimension: Affective experience (15 points)  
Middlelevel students (8 ≤ X < 10):


Dimension: Mathematical metacognitive monitoring (65 points)  
Subdimension: Planning (10 points)  
Middlelevel students (5 ≤ X < 7): There is room for improvement in working out math learning plans. Lowlevel students (X < 5): Are weak in working out math learning plans. 

Subdimension: Regulation (20 points)  
Middlelevel students (11 ≤ X < 14):


Subdimension: Evaluation (10 points)  
Middlelevel students (5 ≤ X < 7):


Subdimension: Inspection (15 points)  
Middlelevel students (8 ≤ X < 11):


Subdimension: Management (10 points)  
Middlelevel students (5 ≤ X < 7):


N  Min  Max  Mean (M)  Standard Deviation  Dimension Full Score  Scoring Rate (S)  

Mathematical metacognition  2100  31  155  121.3605  18.59534  155  78.30% 
MMK  2100  11  63  44.1105  7.56249  55  80.20% 
MME  2100  7  35  25.0095  3.49106  35  71.46% 
MMM  2100  13  75  52.2405  8.99428  65  80.37% 
N  Min  Max  Mean (M)  Standard Deviation  Dimension Full Score  Scoring Rate (S)  

KI  2100  5.00  25.00  20.5338  3.53100  25  82.14% 
KT  2100  3.00  39.00  12.2988  2.23434  15  81.99% 
KS  2100  3.00  39.00  11.2780  2.64080  15  75.19% 
CE  2100  4.00  20.00  14.3033  2.28116  20  71.52% 
AE  2100  3.00  15.00  10.7062  1.89552  15  71.37% 
Planning  2100  2.00  36.00  7.6064  1.92350  10  76.06% 
Regulation  2100  4.00  20.00  16.6011  2.80477  20  83.01% 
Evaluation  2100  2.00  10.00  7.8237  1.69608  10  78.24% 
Inspection  2100  3.00  15.00  11.6604  2.53955  15  77.74% 
Management  2100  2.00  10.00  8.5488  1.41231  10  85.49% 
Student  Raw Score  TScore  Norm Level  Scoring Rate (S) 

A  108  59.9  Average  69.67% 
B  111  61.3  Average  71.61% 
C  110  60.9  Average  70.97% 
D  108  59.9  Average  69.67% 
E  110  60.9  Average  70.97% 
F  108  59.9  Average  69.67% 
Dimension  Student  Raw Score  TScore  Norm Level  Scoring Rate (S) 

MMK  A  34  51.9  Average $(29\le X<38$)  61.82% 
B  42  61.9  Above average $(38\le X<45$)  76.36%  
C  43  63.5  Above average $(38\le X<45$)  78.18%  
D  36  54.4  Average $(29\le X<38$)  65.45%  
E  40  59.5  Above average $(38\le X<45)$  72.73%  
F  43  62.82  Above average $(38\le X<45$)  78.18%  
MME  A  21  49.2  Average $(19\le X<24$)  60.00% 
B  16  39.3  Below average $(14\le X<19$)  45.71%  
C  24  56.1  Above average $(24\le X<31$)  68.57%  
D  23  54.0  Average $(19\le X<24)$  65.71%  
E  18  43.3  Below average $(14\le X<19$)  51.43%  
F  23  54.0  Average $(19\le X<24$)  65.71%  
MMM  A  53  67.1  Above average $(44\le X<54$)  81.54% 
B  53  67.1  Above average $\text{}(44\le X54$)  81.54%  
C  43  55.9  Average $(34\le X<44$)  66.15%  
D  49  62.7  Above average $(44\le X<54$)  75.38%  
E  52  65.8  Above average $(44\le X<54$)  80.00%  
F  42  54.1  Average $(34\le X<44$)  64.62% 
Mean  N  Standard Deviation  t  df  p  

Result 1  80.870  568  15.593  −1.154  567  0.249 
Result 2  81.324  568  17.827 
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Wang, G.; Kang, Y.; Jiao, Z.; Chen, X.; Zhen, Y.; Zhang, D.; Su, M. Development and Application of Intelligent Assessment System for Metacognition in Learning Mathematics among Junior High School Students. Sustainability 2022, 14, 6278. https://doi.org/10.3390/su14106278
Wang G, Kang Y, Jiao Z, Chen X, Zhen Y, Zhang D, Su M. Development and Application of Intelligent Assessment System for Metacognition in Learning Mathematics among Junior High School Students. Sustainability. 2022; 14(10):6278. https://doi.org/10.3390/su14106278
Chicago/Turabian StyleWang, Guangming, Yueyuan Kang, Zicong Jiao, Xia Chen, Yiming Zhen, Dongli Zhang, and Mingyu Su. 2022. "Development and Application of Intelligent Assessment System for Metacognition in Learning Mathematics among Junior High School Students" Sustainability 14, no. 10: 6278. https://doi.org/10.3390/su14106278