Ratio and Proportion

Razones, proporciones y proporcionalidad constituyen un campo ampliamente investigado en los últimos cincuenta años. Evaluaciones recientes muestran que estos objetos de conocimiento siguen siendo difíciles de aprender para la mayoría de los estudiantes, lo que constituye un certero indicador de la necesidad de hacer mayor investigación didáctica que permita nuevas comprensiones de dicha problemática y, por esa vía, lograr mayores impactos en el sistema educativo. En este artículo se revisan y comentan algunas investigaciones recientes sobre razón, proporción y proporcionalidad. De acuerdo con la perspectiva de análisis, se agrupan en tres momentos: cognitivo, epistémico y semióticoantropológico. Finalmente, se plantean algunos problemas de investigación a manera de conclusión.

We believe that the problem of teacher preparation is one of development of “pedagogical content knowledge” rather than “subject knowledge” per se. It has been found that even experienced teachers may not be aware of the misconceptions that learners tend to exhibit, or at what stage of development and in what areas of the curriculum these are likely to be manifested. This pedagogical knowledge is, we believe, important to teachers’ mental models of their learners, and hence their teaching effectiveness. In this study, we aim to contribute to teachers’ awareness of their pupils’ strategies and misconceptions in the field of “ratio”: a topic that is difficult to teach and learn in the middle school years. Towards this aim, we constructed a diagnostic instrument which reveals children's proportional thinking. Our instrument contains two versions, one with “models” thought to be of service to children’s proportional reasoning and one without. It is also designed to function as a que...