Exploring Students’ Mathematical Reasoning Behavior in Junior High Schools: A Grounded Theory
Abstract
:1. Introduction
2. Theoretical Framework
2.1. Mathematical Reasoning
 Recognizing reasoning and proof as essential aspects of mathematics.
 Constructing and finding mathematical conjectures.
 Developing and assessing arguments.
 Choosing and using various types of reasoning and methods of proof.
2.2. MetaReasoning
2.3. Affective Aspect in Mathematical Reasoning
2.4. Mathematical Reasoning Behavior
3. Materials and Methods
3.1. Selection of Subjects
3.2. Tasks
3.3. Data Analysis
4. Results
4.1. Student with Imitative Reasoning Behavior (IS)
4.1.1. Drawing Logical Conclusions
4.1.2. Constructing and Testing Conjectures
4.1.3. Composing Valid Arguments
4.1.4. Monitoring and Control Metacognitive
4.1.5. SelfConfidence
4.2. Student with Algorithmic Reasoning Behavior (AS)
4.2.1. Drawing Logical Conclusions
4.2.2. Constructing and Testing Conjectures
4.2.3. Composing Valid Arguments
4.2.4. Monitoring and Control Metacognitive
4.2.5. SelfConfidence
4.3. Student with SemiCreative Reasoning Behavior (SS)
4.3.1. Drawing Logical Conclusions
4.3.2. Constructing and Testing Conjectures
4.3.3. Composing Valid Arguments
4.3.4. Monitoring and Control Metacognitive
4.3.5. SelfConfidence
4.4. Student with Creative Reasoning Behavior (CS)
4.4.1. Drawing Logical Conclusions
4.4.2. Constructing and Testing Conjectures
4.4.3. Composing Valid Arguments
4.4.4. Monitoring and Control Metacognitive
4.4.5. SelfConfidence
5. Discussion
5.1. Drawing Logical Conclusions
5.2. Constructs and Tests Conjectures
5.3. Constructing Valid Arguments
5.4. Monitoring and Control Metacognitive
5.4.1. Metacognitive Monitoring
5.4.2. Metacognitive Control
5.5. SelfConfidence
6. Conclusions
7. Limitations and Future Research
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
No  Problems 

1.  Matchsticks are arranged in the following way.

2.  Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 in the following circles so the sum of the numbers along each line of four is 23! 
3.  Consider 3^{1} = 3, 3^{2} = 9, 3^{3} = 27, 3^{4} = 81, 3^{5} = 243, 3^{6} = 729, 3^{7} = 2187, 3^{8} = 6561. Perhaps the ones digits of these numbers form a pattern that can be used to predict the ones digit of 3^{99}. Find the ones digit in 3^{99}! 
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Aspect  Indicator  Students’ Mathematical Reasoning Behavior  

Imitative  Algorithmic  SemiCreative  Creative  
Cognitive  Drawing logical conclusions  Only capable of utilizing the information provided but not yet capable of selecting a set of rules to reach a logical conclusion.  Can deduce logical relationships between number sequences and object configuration sequences based on the pattern and object configuration sequences.  Able to utilize the information provided, choose several sets of rules, and arrive at a logical conclusion with the help of directions from the teacher.  Capable of utilizing the information provided and establishing their own rules to arrive at logical conclusions. 
Constructing and testing conjectures  Capable of utilizing known data but unable to choose a set of rules to construct and test conjectures.  Generate and test hypotheses by arranging numbers into a specified amount using the rules provided for number patterns problems.  Able to utilize the information provided, choose several sets of rules, and reach the preparation and testing of conjectures with the direction of the teacher.  Capable of utilizing available data and establishing their own rules to construct and test conjectures.  
Composing valid arguments  Only capable of utilizing the information provided, but not yet capable of selecting a set of rules to prepare valid arguments.  Can develop valid arguments on the material of number patterns and object configuration by explaining the strategy selected and implemented as well as the reasons it worked or not.  Able to utilize the information provided and be able to choose several suitable sets of rules and arrive at the preparation of valid arguments with directions from the teacher.  Capable of utilizing the information provided to develop their own set of rules to construct valid arguments.  
Metareasoning  Metacognitive monitoring  Have a single rule or strategy to solve nonroutine problems and adhere to the strategy even when all indicators show it is incorrect.  Have a single rule or strategy to solve nonroutine problems but willing to try other rules or strategies to obtain the correct result.  Have more than one rule (strategy) in solving nonroutine problems and have the desire to try other rules (strategies) and find the right solution, but must be guided by the teacher.  Capable of developing novel rules or strategies to resolve nonroutine problems and obtain the desired results. 
Metacognitive Control (In writing)  Metacognitive control was not observed in writing during the compilation or assembly of the intermediate targets or rules used from the information provided in the questions.  Metacognitive control was observed in writing during the compilation or assembly of the intermediate targets, or the rules used but not up to the final target.  Metacognitive control has been seen in writing when compiling or arranging intermediate targets (rules used), as well as arriving at the final target with directions from the teacher.  Metacognitive control was demonstrated in writing during the process of compiling or assembling intermediate targets or the rules used and obtaining the final target.  
Metacognitive Control (In oral)  Capable of communicating thoughts and the results of the reasoning verbally only on a portion of the information provided.  Capable of communicating thoughts and outcome of reasoning verbally using several sets of rules selected but was unable to reach the correct conclusion on the final target.  Able to convey thoughts (results of their reasoning) verbally regarding several sets of rules they choose but are not able to make the correct conclusions on the final target with direction from the teacher.  Capable of communicating thoughts and the outcome of reasoning orally, coherently completely, and systematically, and provides correct conclusions regarding the final objective.  
Affective  Self Confidence  Have selfconfidence as indicated by the provision of answers quickly even when they are not sure the rules selected are correct or incorrect.  Frequently demonstrates selfconfidence when solving mathematical reasoning problems but cannot reach the correct conclusions.  Often shows confidence in solving mathematical reasoning problems and can draw the correct conclusions with directions from the teacher.  Demonstrates selfconfidence and makes sound judgments. 
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Rohati, R.; Kusumah, Y.S.; Kusnandi, K. Exploring Students’ Mathematical Reasoning Behavior in Junior High Schools: A Grounded Theory. Educ. Sci. 2023, 13, 252. https://doi.org/10.3390/educsci13030252
Rohati R, Kusumah YS, Kusnandi K. Exploring Students’ Mathematical Reasoning Behavior in Junior High Schools: A Grounded Theory. Education Sciences. 2023; 13(3):252. https://doi.org/10.3390/educsci13030252
Chicago/Turabian StyleRohati, Rohati, Yaya S. Kusumah, and Kusnandi Kusnandi. 2023. "Exploring Students’ Mathematical Reasoning Behavior in Junior High Schools: A Grounded Theory" Education Sciences 13, no. 3: 252. https://doi.org/10.3390/educsci13030252