Error Patterns in Simplifying Rational Algebraic Expressions among Rural Congolese Students
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Cédric Lukaku
This study investigated the error patterns exhibited by rural Congolese students when simplifying rational algebraic expressions. An exploratory qualitative design within an interpretive research paradigm was employed. The participants were 28 Algebra I students enrolled in a rural secondary school in the Democratic Republic of the Congo during the 2025 academic year. Data were collected using a specialist-validated evaluative test comprising 10 simplification items. The 28 students completed all 10 items, producing 280 responses. Students’ written solutions were examined item by item and classified using an adapted error framework encompassing symbolic, conceptual, reasoning, procedural, and technical difficulties. An error pattern was considered recurrent when it occurred in more than 30% of the participants’ responses. Of the 280 responses, 136 responses (48.6%) contained at least one error, whereas 106 responses (37.9%) were correct and 38 responses (13.6%) were unanswered. The most dominant categories were technical errors and errors associated with insufficient prior knowledge of algebraic facts, skills, and concepts. Recurring difficulties included incorrect factorization, mismanagement of negative signs, inappropriate application of algebraic rules, deficient manipulation of symbols, and difficulties simplifying notable products. These findings indicate that students’ errors were systematic and reflected both conceptual weaknesses and limited procedural fluency. Instruction should therefore emphasize explicit teaching of factorization, sign operations, algebraic equivalence, and step-by-step verification of symbolic procedures, particularly in rural and under-resourced learning environments.
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