Conceptual Limitations in Curricular Presentations of Area Measurement: One Nation's Challenges

• Published in: Mathematical thinking and learning Vol. 18; no. 4; pp. 239 - 270
• Main Authors: Smith, John P., Males, Lorraine M., Gonulates, Funda
• Format: Journal Article
• Language: English
• Published: Philadelphia Routledge 01.10.2016; Taylor & Francis Ltd
• Subjects: Content Analysis; Curricula; Educational Principles; Elementary education; Elementary School Students; Geometry; Learning; Mathematical Concepts; Mathematics Curriculum; Mathematics Instruction; Measurement; Statistical Analysis; Teaching Methods; Textbooks
• ISSN: 1098-6065; 1532-7833
• DOI: 10.1080/10986065.2016.1219930

Research has found that elementary students face five main challenges in learning area measurement: (1) conserving area as a quantity, (2) understanding area units, (3) structuring rectangular space into composite units, (4) understanding area formulas, and (5) distinguishing area and perimeter. How well do elementary mathematics curricula address these challenges? A detailed analysis of three U.S. elementary textbook series revealed systematic deficits. Each presented area measurement in strongly procedural terms using a shared sequence of procedures across grades. Key conceptual principles were infrequently expressed and often well after related procedures were introduced. Particularly weak support was given for understanding how the multiplication of lengths produces area measures. The results suggest that the content of written curricula contributes to students' weak learning of area measurement.