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Abstract

In understanding upper secondary school students' interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in symbolic representations of different phenomena. Two theoretical perspectives have been used to conduct the analysis: Tall and Vinner's theoretical perspectives on learning and Gray's & Tall's theory of three mathematical worlds together with Hähkiöniemi's interpretation of these three worlds. The findings provide evidence that a detailed analyse of student's utterances show difference in quality related to student's interpretations of a distance-time relation. The qualities were related to student's concept images of functions and derivatives.Keywords: Conceptual development, symbolical representations, interpretations REDIMAT, Vol. 6 No. 2 Junio 2017 pp. 138-135 ResumenEn la comprensión de las interpretaciones de los estudiantes de la escuela secundaria en representaciones simbólicas de una relación distancia-tiempo, se ha prestado poca atención al análisis de la condición del desarrollo conceptual relacionado con los enunciados. Entender esto mejor puede ayudar a mejorar la enseñanza del atributo y de la información en representaciones simbólicas de diferentes fenómenos. Se han utilizado dos perspectivas teóricas para llevar a cabo el análisis: las perspectivas teóricas de Tall y Vinner sobre el aprendizaje y la teoría de Gray y Tall de tres mundos matemáticos junto con la interpretación de Hähkiöniemi de estos tres mundos. Los hallazgos proporcionan evidencia de que un análisis detallado de los enunciados de los estudiantes muestra diferencias en calidad relacionadas con las interpretaciones de los estudiantes de la relación distancia-tiempo. Las cualidades estaban relacionadas con las imágenes conceptuales de funciones y de sus derivadas.Palabras clave: Desarrollo conceptual, representaciones simbólicas, interpretaciones. Lingefjärd & Farahani -The Symbolic World of Mathematics118 athematical representations such as diagrams, histograms, functions, graphs, tables and symbols facilitate understanding and communication of abstract mathematical concepts or other phenomenon described in mathematical terms (Elby, 2000; Leinhardt, Zaslavsky, & Stein 1990). Nevertheless, humans of today are facing a world that is shaped by increasingly complex, dynamic, and powerful systems of information that we meet through various media.An important aspect of the problem we gave the students is that it is a symbolical representation of a theoretical physical concept's motion. Being able to interpret, understand, and work with symbolical representations involves mathematical processes and concepts the student needs to appreciate and comprehend and can address when facing interpretation challenges (Friel, Curcio & Bright, 2001).For mathematics education in an elementary, middle, ...