• Corpus ID: 67813983

Connections Between Qualitative and Quantitative Thinking About Proportion: The Case of Paulina.

@article{Ledesma2004ConnectionsBQ,
  title={Connections Between Qualitative and Quantitative Thinking About Proportion: The Case of Paulina.},
  author={Elena-Fabiola Ruiz Ledesma and Marta Elena Valdemoros {\'A}lvarez},
  journal={International Group for the Psychology of Mathematics Education},
  year={2004}
}

• E. F. Ledesma, M. Álvarez
• Published 1 July 2004
• Education
• International Group for the Psychology of Mathematics Education

The case study presented in this report was part of assessing a teaching proposal on ratio and proportion. A group of sixth-grade students of elementary education in Mexico participated in the implementation of the proposal. The girl of the case study was representative of those students in the group who had a lot of recourse to handling algorithms mechanically and whose elaborations made no sense at all, according to their answers to an initial questionnaire. A didactical program, developed in a problem-solving context for the research study, helped the girl widen her qualitative thinking and strengthen her quantitative thinking about proportion. Analyses of data collected from an initial questionnaire, the teaching process, a final questionnaire, and three interviews evidenced that enriching this girl’s qualitative thinking about proportion allowed her widen quantitative relations and improve her handling of algorithms by providing the setting for meaningful applications. Some theoretical antecedents of the investigation Piaget and Inhelder (1978) pointed out, as a result of their experimental researches in education, that children acquire qualitative identity sooner than quantitative conservation. Thus, these authors made a distinction between qualitative comparisons and true quantification. According to Piaget and Inhelder (1972), the acquisition of the notion of proportion always starts in a qualitative and logical form before it becomes quantitatively structured. Piaget defined what is qualitative by using categories or classes of words. Our own interpretation of what is qualitative refers to what is based on linguistic recognitions by creating comparison categories such as big or small. Our interpretation is that what is qualitative consists of intuitive and empirical aspects as well, which are provided by our senses. Piaget (1978) pointed out that the idea of order emerges during the transition from the qualitative to the quantitative realm, although the idea of quantity is not yet present. Piaget called these situations intensive quantifications. For us, this is what makes the transition from qualitative to quantitative thinking stand out. On their part, Van den Brink and Streefland (1979) agreed with Piaget as to their research findings that qualitative aspects of thinking occur sooner than quantitative ones. However, Streefland usually had recourse to these findings in teaching contexts. In our approach for the designing of the didactical program as well as in the development of interviews for the case study of educational research we present in this report, we used that contribution by Streefland. Research findings reported by Streefland (1984; 1985) emphasized that the early teaching of ratio and proportion topics must depart from qualitative levels of recognizing them. For that purpose, Streefland made use of didactical resources, which strengthen the development of perceptual patterns for supporting the corresponding processes of quantification. Streefland stated that qualitative reasoning evolves as the thinking of the child advances and he or she is capable of incorporating