Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking

• John Hannah ^[1] ; Sepideh Stewart ^[2] ; Michael Thomas ^[3]
  1. [1] University of Canterbury

     University of Canterbury

     Nueva Zelanda

     
  2. [2] University of Oklahoma

     University of Oklahoma

     Estados Unidos

     
  3. [3] University of Auckland

     University of Auckland

     Nueva Zelanda

     

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• Localización: Teaching mathematics and its applications, ISSN 0268-3679, Vol. 35, Nº. 4, 2016, págs. 216-235
• Idioma: inglés
• DOI: 10.1093/teamat/hrw001
• Texto completo no disponible (Saber más ...)
• Resumen

  • Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall’s three worlds (embodied, symbolic and formal) of mathematical thinking, and use a framework combining these with Dubinsky’s Action, Process, Object and Schema (APOS) theory to analyse students’ resulting levels of understanding. Through interviews and analysis of test and examination scripts, we investigate students’ understanding of the basic concepts of linear algebra, their ability to use and explain these concepts and their relationship to definitional clarity. The results show that, while students tend not to learn definitions by rote and can be imprecise when expressing them in words, they seem to understand the concepts, can talk sensibly about them and are able to use their essential features in solving problems.