Students’ Recognition of Function Transformations’ Themes Associated with the Algebraic Representation

The topic of function transformations is a difficult mathematical topic for school and college students. On the other hand, GeoGebra is a new technological tool for mathematics teaching and learning, so we wanted to experiment with this new tool in teaching non-basic function transformations to middle school students. Specifically, we wanted to examine how students conceive function transformations after working with GeoGebra, when this conceiving relates to the algebraic representation. The research participants were 19 ninth grade high achieving students who learned, with the help of GeoGebra translations, reflection and stretch. During their learning, the participants worked with transformations on the absolute function, the cubic function, and the quartic function. After they finished the transformation unit, the participants solved mathematics problems by means of function transformations. This research is interested in the participants’ solution of problems that included two non-basic functions: the absolute value of the quadratic function and the rationale function. The research findings show that the participants were generally able to solve successfully mathematical problems, by means of transformations on new and non-basic functions. Furthermore, the participants encountered difficulties in working with translations. These difficulties were due to the special algebraic form of the functions. We recommend that mathematics teachers expose middle school students to transformations on different types of non-basic function during learning this mathematical topic. Future researches could examine the impact of activities that include such functions and that are GeoGebra based on students’ conceptions and behavior when performing translations is involved

Students’ Recognition of Function Transformations’ Themes Associated with the Algebraic Representation

The topic of function transformations is a difficult mathematical topic for school and college students. On the other hand, GeoGebra is a new technological tool for mathematics teaching and learning, so we wanted to experiment with this new tool in teaching non-basic function transformations to middle school students. Specifically, we wanted to examine how students conceive function transformations after working with GeoGebra, when this conceiving relates to the algebraic representation. The research participants were 19 ninth grade high achieving students who learned, with the help of GeoGebra translations, reflection and stretch. During their learning, the participants worked with transformations on the absolute function, the cubic function, and the quartic function. After they finished the transformation unit, the participants solved mathematics problems by means of function transformations. This research is interested in the participants’ solution of problems that included two non-basic functions: the absolute value of the quadratic function and the rationale function. The research findings show that the participants were generally able to solve successfully mathematical problems, by means of transformations on new and non-basic functions. Furthermore, the participants encountered difficulties in working with translations. These difficulties were due to the special algebraic form of the functions. We recommend that mathematics teachers expose middle school students to transformations on different types of non-basic function during learning this mathematical topic. Future researches could examine the impact of activities that include such functions and that are GeoGebra based on students’ conceptions and behavior when performing translations is involved.Las transformaciones de las funciones es un tema difícil de matemáticas tanto para estudiantes en la escuela, como en la universidad. En este artículo examinamos cómo los estudiantes conciben las transformaciones de las funciones después de trabajar con GeoGebra, cuando esta concepción se relaciona con la representación algebraica. Los participantes en la investigación fueron 19 niños/as de noveno curso con un promedio alto, que estaban aprendiendo, con ayuda de GeoGebra, traslaciones, reflexiones y prolongaciones. Los participantes trabajaron con transformaciones sobre funciones absoluta, cúbica y cuadrática. Cuando terminaron la unidad sobre funciones, resolvieron problemas de matemáticas usando transformaciones de funciones. Los resultados muestran que generalmente fueron capaces de resolver de manera satisfactoria los problemas de matemáticas, usando transformaciones de funciones nuevas y no-básicas. Futuras investigaciones podrían examinar el impacto de las actividades que incluyen este tipo de funciones en GeoGebra que están basadas en las concepciones de los estudiantes y en su comportamiento cuando involucran transformaciones