UBC Theses and Dissertations
Learning mathematics for the workplace : an activity theory study of pipe trades training LaCroix, Lionel N.
This study examines a single pipe trades pre-apprentice within a one-on-one impromptu tutoring session making sense of fractions-of-an-inch on a measuring tape within the context of a pre-apprenticeship program for the pipe trades. The multi-semiotic analysis of this event is framed using cultural-historical activity theory and Radford’s theory of knowledge objectification. From these complementary perspectives, mathematics is considered a culturally situated purposeful activity. Specifically, mathematics learning involves a cultural-historical, socially, and semiotically mediated process of objectification, (i.e., a process in which one becomes progressively aware and conversant, through one’s actions and interpretations, of a cultural logic of mathematical objects). The analysis focuses on the pre-apprentice’s and tutor’s joint activity during this encounter, drawing on video data and various artifacts used. This entailed slow-motion and frame-by-frame analysis of the video to assess the role and coordination of various semiotic systems, actions, and artifacts. Particular attention is paid to: the semiotic system of cultural signification, norms of practice, contradictions or conflicts that serve to motivate this activity, specific objectives of or sub-goals in the learning process for this student, semiotic processes used both by the student and tutor in the objectification process, as well as changes to the subjectification of both the pre-apprentice and researcher-as-tutor in this process. This analysis informs Radford’s theory of knowledge objectification by showing, through fine-grained analysis, relevant aspects of its dynamics and by calling attention to a new form of iconicity and a process of semiotic extraction, both original contributions to research. It also shows various ways in which a learner’s subjectification is evident in the process of learning mathematics. The results have a number of practical implications for the teaching of mathematics generally, and mathematics for the workplace in particular, by drawing attention to the social, cultural, historical, and mediated dimensions and dynamics of mathematics learning activity. The findings also illustrate the complexity of learning to measure by identifying a number of processes and conflicts involved and practical ways these are negotiated or resolved.
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