Analyzing students’ errors and misconceptions in proof construction in abstract algebra course
DOI:
https://doi.org/10.30872/primatika.v14i2.6217Keywords:
Errors, Misconceptions, Abstract algebra, Proof construction, IsomorphismAbstract
This study aimed to identify and describe the types of errors and misconceptions made by students in the process of constructing proofs. Using a qualitative approach with a case study design, the subjects were fifth-semester students enrolled in the Abstract Algebra course at Mulawarman University. Three student responses showing significant error patterns regarding the Fundamental Isomorphism Theorem were purposively selected and analyzed based on the Selden & Selden framework. The results indicated that students faced notation, logical, and structural obstacles. Dominant errors included notation inflexibility (E3), reversed logic in surjective proofs due to quantifier neglect (E8), and structural misconceptions in defining kernel and image (M7). Additionally, over-generalization of real number rules in group operations (M5) was observed. These findings suggested that students remained at the procedural-thinking stage and had not yet reached the "Object" stage in their cognitive schema, resulting in a failure to build rigorous deductive arguments. This study recommends instructional interventions emphasizing the visualization of abstract structures and strengthening quantifier logic to minimize students' future epistemological obstacles.
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