Understanding students' hierarchical thinking: a view from continuity, differentiability and integrability

Sevimli E.

TEACHING MATHEMATICS AND ITS APPLICATIONS, vol.37, no.1, pp.1-16, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1093/teamat/hrw028
  • Journal Indexes: Emerging Sources Citation Index, Scopus
  • Page Numbers: pp.1-16


This report examines how students link continuity, differentiability and integrability concepts in their mind maps within the context of hierarchical thinking. A survey research design was used to obtain a large group of participants from three different mathematics departments in Turkey. While primary data acquired with the help of the concept map were analysed using descriptive statistics, secondary data acquired by way of interviews were analysed according to their content. The findings revealed that a great majority of the participants built wrong hierarchies between these concepts. The results also show that the students' epistemological beliefs, or their sequential learning and instrumental understanding instead of relational understanding, hinder building correct hierarchies, and some suggestions show lecturers how to effectively use concept maps and counterexamples.