Mapping the sources of mathematical controversy

Research on counterintuitive mathematics tasks describes levels of resolution but rarely distinguishes where a contradiction originates. This qualitative study examines a provisional typology of misleading media, procedures, and operations. Fifty Indonesian pre-service mathematics teachers in a university teacher education programme completed four tasks on percentage growth, fraction representation, algebraic cancellation, and root–exponent rules; 16 joined follow-up interviews. Responses were coded through three cycles. Participants showed different item-level patterns, and combining source and level produced a two-axis diagnostic matrix. Because media and operation were each represented by one task, source cannot be separated from item content or difficulty. The matrix is therefore a heuristic for further validation, not a tested intervention. It may help teacher educators organise analysis of student reasoning.