• Article  

      Knowledge construction and diverging thinking in elementary & advanced mathematics 

      Gray, Eddie M.; Pinto, Marcia; Pitta-Pantazi, Demetra; Tall, David (1999)
      This paper begins by considering the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum. We base our theoretical development on fundamental ...
    • Article  

      Objects, Actions, and Images: A Perspective on Early Number Development 

      Gray, Eddie M.; Pitta-Pantazi, Demetra; Tall, David (2000)
      It is the purpose of this article to present a review of research evidence that indicates the existence of qualitatively different thinking in elementary number development. In doing so, the article summarizes empirical ...
    • Article  

      Symbols and the bifurcation between procedural and conceptual thinking 

      Tall, David; Gray, Eddie M.; Ali, Maselan Bin; Crowley, Lillie; DeMarois, Phil; McGowen, Mercedes; Pitta-Pantazi, Demetra; Pinto, Marcia; Thomas, Michael; Yusof, Yudariah (2001)
      Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this article we ...