Revisiting the place value concept in the workplace context: the issue of transfer development

In this paper, we studied the transferring process of five apprentice engineering students concerning the place value concept in a telecommunication workplace setting. In this setting, a physical material, a telecommunication closet (TC), appearing as a concrete representation of the ten-numeration system, supported the process of generating composite units in a sequential way. The data were generated by conducting an interview with each student based on two tasks. In the first task, students were asked to locate the place of a particular wire pair on the telecommunication closet representation (TC representation). In the second task, students were asked to determine the range of values that generate this composite unit. Our theoretical and analytical framework is guided by the three levels of students’ generalization activity by Radford (2003) and the work on developmental transfer by Engeström (2001). By identifying shifts in the students’ activity (from factual to contextual and from contextual to symbolic), we recognized three transferring cases: the immediate transfer case, the developmental transfer case, and the nondevelopmental transfer case. By comparing and contrasting the different cases, we identified four factors that seem to facilitate or constrain the transfer development. These are the use of metaphors, the development of problem solving strategies, the context dependency, and the students’ motivation. In conclusion, we discuss the educational implications of our findings.