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Mathematics in workplace settings: Numeracy in the mechanical engineering trades

While mathematics is an essential tool for both professional and trades mechanical engineers, little is known about how mathematics is used and learned in the mechanical engineering trades. Using an interpretivist paradigm and informed by a social constructivist epistemology, this mixed methods study aimed to identify key features of mathematical learning in the New Zealand mechanical engineering trades: specifically, the nature of the mathematical knowledge and skills, and how they are applied and developed. A purposive sample of 199 apprentices, skilled tradespersons and mechanical engineering trades educators completed a questionnaire about the mathematics and numeracy skills they used, how they used and learned those skills, and the role of ancillary skills such as higher-order thinking and social interaction. Seventeen of these participants also took part in semi-structured interviews. The data were analysed thematically using Engeström’s (1987) Cultural Historical Activity Theory (CHAT) and Lave and Wenger’s (1991) Situated Learning as theoretical frameworks. Regarding the mathematics skills employed in the mechanical engineering trades, the study found that a thorough knowledge of, and proficiency in, basic mathematics and numeracy skills were essential. In addition, those basic mathematical skills were frequently used in sophisticated, real-life contexts involving higher-order thinking skills such as problem-solving, creativity, and extended reasoning, as well as metacognitive skills, such as critical thinking, learning to learn, working in teams, and planning. However, many engineering decisions were made not on mathematical considerations alone, but using non-formal heuristics and engineering judgment following particular rules generated and accepted by the engineering communities. Regarding developing the mathematical skills, learning at both individual and community levels appeared to be done eclectically. Learning and knowledge creation took place both formally and informally, whether in the classroom or on-the-job, and hence by acquisition and participation as well as by individual reflection. This study contributes to our knowledge of the role of mathematics in mechanical engineering trades. It does this through its demonstration of the importance of basic mathematics and numeracy skills and the new insights gained into the interconnectedness of these basic skills with higher-order thinking and metacognitive skills. Moreover, this study contributes to our knowledge of the influences of social interaction, collaboration, and communication as important tools for learning, problem-solving, and creating new knowledge in workplaces’ communities of practice. Therefore, learning is revealed as an iterative process involving developing relationships between tools and subjects as part of an evolving historical process where communities play a central role. The study should be of interest to mechanical engineering communities and other vocations that are high users of mathematics because of the interconnections the study makes between physical tools and higher-order thinking skills situated in real contexts, the learning needed to change school habits and perspectives regarding well-developed numeracy and mental calculation skills for the workplace, ongoing professional development of mathematics knowledge skills related to real contexts, and conceptual understanding of the holistic interconnectedness of mathematics within workplace contexts. The study also has implications for other vocations because it demonstrates that developing workplace mathematics knowledge and skills is a much more complex process than a simple transference of school mathematics skills. Successful practice depends on combining technical skills with higher-order thinking, metacognitive skills, social interaction, collaboration and communication.
Type of thesis
The University of Waikato
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