Area as a geometric quantity: PCN and BNCC guidelines with an emphasis on semiotic representations

Abstract: The purpose of this paper is to analyze how the concept of area of plane figures and how it is grasped within Elementary School, according to the Parâmetros Curriculares Nacionais (PCN) and the Base Nacional Comum Curricular (BNCC). To that end, it is based on the theoretical model proposed by Douady and Perrin-Glorian, exposed in Bellemain and Lima, that is related to the teaching of geometric quantities and according to the assumptions of semiotic representation registers by Duval. Characterized as qualitative research of the documental kind, the study is grounded in principles of the content analysis. The findings show that both the PCN and the BNCC emphasize the importance of using different mathematical representations. In both documents, the concepts/contents of area, in their majority, are in the content block/thematic unit of Quantities and Measurements. It appears that the BNCC, in addition to indications of figurative, numerical, algebraic and graphic registers as in PCN, also favors registers in natural language. There are indications, in both documents, of sequential, perceptive, discourse and operative intake.

摘要：本文旨在依据《国家课程参数》（Parâmetros Curriculares Nacionais，PCN）与《国家共同基础教育课程基准》（Base Nacional Comum Curricular，BNCC），探析平面图形面积的概念及其在小学教育阶段的掌握路径。为此，本研究依托杜阿迪（Douady）与佩兰-格洛里安（Perrin-Glorian）提出的理论模型——该模型由贝尔曼（Bellemain）与利马（Lima）阐释，与几何量教学领域相关——并遵循迪瓦尔（Duval）的符号表征寄存器理论假设。本研究属于文献型质性研究，以内容分析法的研究原则为支撑。研究结果表明，《国家课程参数》与《国家共同基础教育课程基准》均强调运用多元数学表征的重要性。两份文件中，面积相关概念与内容大多归入“量与测量”这一内容模块或主题单元。相较于仅提及形象、数值、代数与图形表征的《国家课程参数》，《国家共同基础教育课程基准》还支持自然语言表征。两份文件均体现出对面积概念的序列性、感知性、话语性与操作性的理解与习得路径。