Beyond the Formula: Why Pre-Service Teachers Stumble with Mathematical Induction in Word Problems
Abstract
This study examines the challenges pre-service teachers face in using mathematical induction to prove a complex word problem. Problemsolving, particularly with non-routine word problems, develops higher-order thinking skills, and proof, especially mathematical induction, is a core mathematical practice. For students and pre-service teachers, mathematical induction poses major challenges despite its importance. The present study identifies the technical, mathematical and conceptual difficulties that pre-service teachers encounter. A qualitative study was conducted with 34 pre-service teachers (aged 19–20). Data were collected through a written test (a non-routine mathematical induction word problem), questionnaires and semi-structured interviews. The analysis, guided by Avital and Libeskind’s classification, revealed that technical difficulties include incorrect first case determination and failure to generalise patterns in the induction step. Mathematical difficulties stem from misinterpreting the problem and incorrectly defining the proposition P(n). Conceptual difficulties involve misunderstanding the deductive nature of mathematical induction, rigid adherence to a first case of n = 1, and underestimating the importance of the basis step. The findings suggest that targeted pedagogical interventions in teacher training are required in order to improve pre-service teachers’ modelling, conceptual grasp of mathematical induction and pattern-generalisation skills.
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References
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