ANALISIS KESALAHAN DAN SARAN PERBAIKAN PADA BUKU MULTIVARIABLE CALCULUS KARYA DON SHIMAMATO
DOI:
https://doi.org/10.23969/jp.v10i04.36811Keywords:
multivariable calculus, textbook analysis, conceptual errors, ontological errors, suggestions for improvement.Abstract
Textbooks play a central role in multivariable calculus instruction because they are the main reference for lecturers and students to understand important concepts such as vector spaces, linear transformations, multivariable functions, parametric curves, curvature, and coordinate systems. Inaccuracies in the presentation of concepts, definitions, or examples in textbooks can potentially cause long-lasting misconceptions and hinder successful learning at the university level. Given this urgency, this study aims to analyze errors and formulate suggestions for improvement for the textbook Multivariable Calculus by Don Shimamato, so that the content quality and its suitability as a textbook can be assessed more systematically and objectively.
This research uses a qualitative approach with a library-research design and content analysis technique. The main data source is the full text of Multivariable Calculus by Don Shimamato, while supporting data sources include standard textbooks in calculus, analysis, linear algebra, topology, and differential geometry, as well as relevant mathematics education journal articles. Data were collected through thorough reading, identification of sections potentially containing errors, systematic recording, and directed comparison with standard reference works.
The results indicate that the book contains various forms of errors, which can be classified into four main categories: (1) conceptual errors, related to formulations and explanations of concepts that are not aligned with standard definitions; (2) ontological errors, consisting of misinterpretations concerning the type and status of mathematical objects; (3) terminological errors, concerning the use of mathematical terminology and language that are imprecise or inconsistent; and (4) technical errors, consisting of mistakes in calculations, notation, and examples. Such errors have the potential to cause misconceptions and obscure students’ understanding if the book is used without additional clarification or correction.
Based on these findings, the study formulates several suggestions for improvement in the form of rewriting definitions, explanations, and examples in accordance with standard literature and the characteristics of undergraduate students. In general, the results of this research emphasize the importance of critical review and academic scrutiny of mathematics textbooks used in teaching, and show that error analysis of textbooks is an important step in the effort to improve the quality of multivariable calculus teaching at universities.
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