Calculus students’ understanding of the vertex of the quadratic function in relation to the concept of derivative

• Annie Burns-Childers ^[1] ; Draga Vidakovic ^[2]
  1. [1] University of Arkansas at Little Rock

     University of Arkansas at Little Rock

     Township of Big Rock, Estados Unidos

     
  2. [2] Georgia State University

     Georgia State University

     Estados Unidos

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 49, Nº. 5, 2018, págs. 660-679
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The purpose of this study was to gain insight into 30, first year calculus students’ understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up group interviews. Students’ personal meanings of the vertex, including misconceptions, were explored, along with students’ understanding to solve problems pertaining to the derivative of a quadratic function. Results give evidence of students’ weak schema of the vertex, lack of connection between different problem types and the importance of linguistics in relation to levels of APOS theory. A preliminary genetic decomposition was developed based on the results. Future research is suggested as a continuation to improve student understanding of the relationship between the vertex of quadratic functions and the derivative.