Ninth-Grade Students’ Conceptual Understanding of the Number Line

Authors

  • Zehra E. Ünal
    Department of Psychological Sciences, University of Missouri, Columbia, MO, USA
  • Aslı M. Ala
    Department of Mathematics Education, Erzincan University, Erzincan, Turkey
  • Gamze Kartal
    Department of Educational Psychology, University of Illinois, Urbana-Champaign, IL, USA
  • Serkan Özel
    Department of Mathematics and Science Education, Bogazici University, Istanbul, Turkey
  • David C. Geary
    Department of Psychological Sciences, University of Missouri, Columbia, MO, USA

Abstract

Sixty (35 girls and 25 boys) 9th-grade students’ conceptual understanding of the number line was qualitatively assessed through verbal explanations and visual representations. The assessment included an open-ended question focused on students’ number line descriptions and the explanations coalesced around six features: sequential ordering (i.e., numbers are sequentially represented), positivity-negativity of numbers (i.e., the number line contains positive and negative numbers), non-centrality (i.e., zero does not have to be in the center), infinity, increment flexibility (i.e., number line increments can vary), and continuity (i.e., numbers can be placed anywhere between minus infinity and plus infinity without breaks). The students’ explanations show that these six features emerge in five successive stages in the conceptual understanding of the number line. These stages are (1) no knowledge, (2) sequential ordering and positivity-negativity, (3) infinity and non-centrality, (4) incremental flexibility, and (5) continuity. The last two stages were not found in most descriptions. The results suggest that students’ understanding of the number line is incomplete and may be overestimated by commonly used quantitative assessments of number line knowledge.