FORMULATING THE GENETIC DECOMPOSITION FOR PROBABILITY CONSTRUCTION BASED ON STUDENT DESCONSTRUCTED PROBLEM-SOLVING PROCESS
DOI:
https://doi.org/10.24127/ajpm.v14i4.14367Keywords:
APOS, Genetic Decomposition, Mental Mechanism, Mental Structure, ProbabilityAbstract
Probability theory is inherently abstract and structurally complex, often creating substantial cognitive barriers for students when solving problems. This study aims to formulate a genetic decomposition of core probability concepts based on the mental structures constructed by undergraduate learners. Guided by the APOS (Action–Process–Object–Schema) theoretical framework, the research employed a three-phase methodological cycle: (1) epistemological analysis of fundamental probability concepts, (2) design and administration of diagnostic and instructional instruments, and (3) analysis and validation of students’ cognitive structures. The study was conducted at two universities in Central Java, Indonesia, involving four mathematics education undergraduates enrolled in an introductory probability course. Data were collected through content analysis, domain-specific assessment instruments, and semi-structured interviews. The APOS framework was used to trace students’ mental constructions in relation to classical probability, independence, conditional probability, total probability, and Bayes’ theorem. The results reveal that students had not fully internalized the mental objects and schemas required to coordinate these concepts during problem-solving activities. Their reasoning remained largely at the process level, particularly in representing sample spaces, applying counting techniques, and thematizing probability structures. Nonetheless, several elements of their cognitive behavior aligned with the refined genetic decomposition. The findings highlight the necessity of strengthening students’ APOS-based mental constructions to support the development of coherent probabilistic schemas and enhance conceptual as well as procedural fluency.
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