Newman’s Error Analysis of Trigonometry: Critical Thinking Perspective
), Erik Santoso(2)
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Country:
(1) Department of Mathematics Education, Universitas Majalengka, Indonesia
(2) Department of Mathematics Education, Universitas Majalengka, Indonesia
Corresponding Author
Trigonometry is a fundamental topic in secondary mathematics, yet many students still experience difficulties that lead to various errors. This study applies Newman's Error Analysis (NEA) to analyze trigonometry errors and qualitatively link each error stage to critical thinking indicators. The findings show that fewer Newman’s errors correspond to stronger critical thinking performance, as S1 made minimal errors across all stages and correctly answered nearly all items aligned with critical thinking indicators. Participants were 29 grade XII students from a senior high school in Majalengka, West Java, Indonesia, selected purposively. The study employed a descriptive, qualitative design, supported by quantitative item analysis. Critical thinking skills were assessed through five open-ended trigonometry questions, aligned with reasoning, inference, clarification, and problem-solving indicators, and validated by experts for content and construct accuracy. Semi-structured interviews involved three students representing high, medium, and low ability levels. The interviews revealed that high-achieving students mainly struggled to express conclusions, while medium- and low-achieving students had broader difficulties in applying concepts and reasoning. The most frequent errors occurred in encoding (up to 100%), followed by process skills (82.7%–96.5%), moderate transformation (≤96.5%), comprehension (34.5%–100%), and fewer reading errors (86.2%). The findings indicate that NEA is effective in diagnosing students’ specific cognitive barriers and mapping their weaknesses in critical thinking. The findings show that each of Newman’s stages corresponds to critical thinking weaknesses, with reading and comprehension exhibiting weak clarification, transformation showing weak inference, process skills demonstrating weak reasoning and logical evaluation, and encoding displaying poor evaluation and difficulty in expressing conclusions. The study concludes that mathematics instruction should focus on strengthening process skills and training students in clear mathematical communication to minimize encoding errors. It also recommends integrating visual or manipulative learning media that address these errors, as many process and encoding mistakes stem from students’ difficulty visualizing angle–side relationships in trigonometric problems.
Keywords: newman’s error analysis, critical thinking, trigonometry, student errors.
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