Mapping Newman’s Error Analysis to Mathematical Creative Thinking: A Diagnostic Tool for Identifying Cognitive Disruptions - Kartono, Kartono; Suciawati, Vici (FKIP Universitas Lampung, 2025)
This study examines the relationship between Newman’s Error Analysis (NEA) stages and dimensions of Mathematical Creative Thinking (MCT) in solving contextual problems on relations and functions. Using a descriptive qualitative approach, 25 eighth-grade students were analyzed through two open-ended contextual essay items and semi-structured interviews. Errors identified at each NEA stage (reading, comprehension, transformation, process skills, encoding) were mapped to corresponding MCT dimensions to investigate correlations between error patterns and limitations in creative thinking. Findings indicate that students’ primary difficulties emerged at higher-order cognitive stages. Most students succeeded in the reading (23 students on item 1) and comprehension stages (19 students), yet substantial errors occurred during transformation (14 errors), process skills (17 errors), and encoding (20 errors), a pattern similarly observed in Item 2. The narrowing of the Sankey diagram flow suggests that the core difficulties lie not in basic literacy skills but rather in increasing representational and procedural complexity, particularly at the transition from transformation to process skills. Case analyses revealed distinct profiles: high-ability students demonstrated strong fluency and flexibility but experienced a “cognitive transparency illusion” that constrained their elaboration; medium-ability students showed inconsistency in strategic execution due to strategic breakdowns and affective instability; and low-ability students encountered cascading failures beginning from the earliest stages. The study positions the NEA–MCT mapping as an interpretive diagnostic helpful framework for identifying cognitive–affective barriers to mathematical creativity. This framework supports differentiated interventions, including metacommunicative scaffolding for high-ability students, integrated cognitive–strategic–affective support for medium-ability students, and foundational representational instruction with affective scaffolding for low-ability students. Limitations include the small sample size and the narrow task context. Future studies should involve larger and more diverse participants, incorporate real-time think-aloud data, explore additional mathematical domains, and evaluate the framework’s potential in digital learning environments. Keywords: mathematical creative thinking, Newman’s Error Analysis, problem solving, relations and functions.