Students' Differentiated Translation Processes.

Understanding how students translate between mathematical representations is of both practical and theoretical importance. This study examined students’ processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the study suggests that students of different ability levels process translations differently and that students’ apparent difficulties with translations may be directly connected with their processes and obstacles encountered during translations. The study’s novel framework led to identifying aspects of student behavior that were not previously recognized in the literature. In addition to these findings, this study developed an evolution in theoretical frameworks through which to investigate and explain translation actions between representations. The findings of the study have implications for addressing student difficulties in translations among representations. Understanding how students translate between mathematical representations is of both practical and theoretical importance. Educators and researchers recognize the importance of translations in mathematical comprehension and problem solving success. Unfortunately, some studies have reported only a limited understanding of the exact nature of student abilities with the translation process (Kaput, 1989; Knuth, 2000); the intricacies of this process remain mysterious to both students and teachers (Ainsworth & Van Labeke, 2004; Duval, 1999). Kaput (1987a) summarizes that the research literature provides neither a complete picture of the nature of student activities when translating from one representation to another, nor a coherent account of the intricacies of the translation process itself. In an effort to address student translation difficulties, some have argued the need for research that focuses on translation skills and best practices for teaching (Clement et al., 1981; Janvier, 1987). The study in this paper takes steps toward achieving such an understanding by analyzing student translations between representations commonly found in instructional situations (i.e., graphical and symbolic representations). The specific purpose of this study is to better understand how students process translations. Duval (2006) argues that, in order to be genuinely able to see the nature of student abilities and difficulties in translations, one must set up a