Educational Studies in Mathematics

, Volume 40, Issue 2, pp 173–196 | Cite as

Structure sense: The relationship between algebraic and numerical contexts

  • Liora Linchevski
  • Drora Livneh
Article

Abstract

Several researchers suggest that students' difficulties with the algebraic structure are in part due to their lack of understanding of structural notions in arithmetic. They assume that the algebraic system used by students inherits structural properties associated with the number system with which students are familiar. This study explored this assumption. In an attempt to discover whether wrong interpretations of the algebraic structure found in an algebraic context occur in a purely numerical one, we interviewed 53 sixth-graders individually. The assessment confirms the assumption: students' difficulties with the algebraic structure were found in purely numerical contexts. However, the study also confirms two, seemingly, contradictory observations. On the one hand, the students' interpretations of the structures of the expressions were very consistent; that is, the same tendencies were found in many students' answers. In this sense the students' behaviour was consistent. On the other hand, it was clearly observed that the same student may give an incorrect answer in one context and a correct answer in another. In this sense, it often seemed that the students were inconsistent.

Keywords

Structural Property Correct Answer Algebraic Structure Algebraic System Number System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Liora Linchevski
    • 1
  • Drora Livneh
    • 1
  1. 1.School of EducationThe Hebrew University of Jerusalem, Mount ScopusJerusalemIsrael

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