Exploring the Commognitive Processes of a Prospective Mathematics Teacher in Mathematical Problem Posing
DOI:
https://doi.org/10.26740/jomp.v7n2.p62-73Keywords:
Commognitive Theory,, Mathematical Problem Posing, Prospective Mathematics Teachers, Qualitative ResearchAbstract
This study aims to explore the commognitive processes of a high-performing prospective mathematics teacher during mathematical problem posing by examining how the four commognitive components word use, visual mediators, routines, and narratives emerge across the orientation, connection, generation, and reflection stages. This study employed a qualitative descriptive approach. The participant was purposively selected based on obtaining the highest score on a mathematical problem-solving test. Data were collected through a problem-solving test, a problem-posing task, and semi-structured interviews. The data were analyzed using data reduction, data display, and conclusion drawing, while credibility was established through data triangulation. The findings revealed that all four commognitive components emerged throughout the mathematical problem-posing process. During the orientation stage, the participant represented mathematical ideas using appropriate mathematical symbols and terminology. During the connection stage, the participant established conceptual relationships by linking derivatives and integrals as inverse operations. During the generation stage, the participant formulated a more sophisticated mathematical problem involving exponential functions. During the reflection stage, the participant verified the solution through substitution and logical justification. These findings indicate that mathematical problem posing is not merely a procedural activity but a commognitive process in which conceptual understanding, mathematical communication, and reasoning interact dynamically. This study extends the application of the commognitive framework to mathematical problem posing and provides pedagogical insights for developing prospective mathematics teachers' problem-posing competencies.
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