title: Mathematics in workplace settings: Numeracy in the mechanical engineering trades

authors: Mills, Kelvin Ralph

subjects: Mathematics

abstract: 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.

text: 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.

year: 2022

title: Pontius Pilate and the Imperial Cult in Roman Judaea

authors: Taylor, Joan E.

abstract: While Pontius Pilate is often seen as agnostic, in modern terms, the material evidence of his coinage and the Pilate inscription from Caesarea indicate a prefect determined to promote a form of Roman religion in Judaea. Unlike his predecessors, in the coinage Pilate used peculiarly Roman iconographic elements appropriate to the imperial cult. In the inscription Pilate was evidently responsible for dedicating a Tiberieum to the Dis Augustis. This material evidence may be placed alongside the report in Philo Legatio ad Gaium (299–305) where Pilate sets up shields – likewise associated with the Roman imperial cult –honouring Tiberius in Jerusalem.

text: Pontius Pilate and the Imperial Cult in Roman Judaea While Pontius Pilate is often seen as agnostic, in modern terms, the material evidence of his coinage and the Pilate inscription from Caesarea indicate a prefect determined to promote a form of Roman religion in Judaea. Unlike his predecessors, in the coinage Pilate used peculiarly Roman iconographic elements appropriate to the imperial cult. In the inscription Pilate was evidently responsible for dedicating a Tiberieum to the Dis Augustis. This material evidence may be placed alongside the report in Philo Legatio ad Gaium (299–305) where Pilate sets up shields – likewise associated with the Roman imperial cult –honouring Tiberius in Jerusalem.

year: 2006

title: Ecological modelling of water quality management options in Lake Waahi to support Hauanga Kai species: Technical Report

authors: Allan, Mathew Grant

abstract: This report describes a numerical modelling approach for Lake Waahi to assess the effects of various future scenarios on water quality attributes known to affect the appearance of the lake’s multiple hauanga kai species across differing spatial scales. Hauanga kai refers to customary gathering and use of naturally occurring and cultivated foods. Numerical models were used to support shared learning and development of future scenarios in response to different management options and environmental pressures. The shallow lakes of the Waikato region have been particularly impacted by anthropogenic eutrophication. This is due to the fact that many of these lakes have already undergone a degree of natural eutrophication due to their geomorphic properties, such as their low elevation and shallow depth. The main contributing factors to water quality decline in shallow Waikato lakes have been identified as: high external nutrient and sediment loads, internal loading exacerbated by high sediment resuspension and bioturbation from pest fish (carp), reduced water depth due to installation of water control structures, reduction in wetland filtering potential due to draining, and stock access to wetlands. A 1-D hydrodynamics model, the General Ocean Turbulence Model was coupled to a complex ecological model (PClake) via the Framework for Aquatic Biogeochemical Models (FABM). FABM is an open source FORTAN-based code that facilitates the coupling of hydrodynamic and ecological models. FABM-PCLake is a redesigned PCLake. The consensus from the model simulations carried out in the study suggests that, for Lake Waahi to undergo restoration whereby the lake is restored to clear-water stable state, both external load needs to be reduced significantly by greater than 50%, along with changes in lake ecological structure, resulting from re-establishment of macrophytes aided by the control of carp biomass. These finding supports the general view within the literature that for lake restoration success, external load reduction (catchment load) is critical. Finally, if the ultimate goal of lake restoration in Lake Waahi is to address the decline in tuna (shortfin eel - Anguilla australis) biomass, a return to a clear-water stable state should facilitate improvement in tuna habitat and provide the conditions for development of a healthy eel population. Coupled modelling approaches will provide a more complete picture of potential responses of Hauanga kai species to land and lake management scenarios.

text: Ecological modelling of water quality management options in Lake Waahi to support Hauanga Kai species: Technical Report This report describes a numerical modelling approach for Lake Waahi to assess the effects of various future scenarios on water quality attributes known to affect the appearance of the lake’s multiple hauanga kai species across differing spatial scales. Hauanga kai refers to customary gathering and use of naturally occurring and cultivated foods. Numerical models were used to support shared learning and development of future scenarios in response to different management options and environmental pressures. The shallow lakes of the Waikato region have been particularly impacted by anthropogenic eutrophication. This is due to the fact that many of these lakes have already undergone a degree of natural eutrophication due to their geomorphic properties, such as their low elevation and shallow depth. The main contributing factors to water quality decline in shallow Waikato lakes have been identified as: high external nutrient and sediment loads, internal loading exacerbated by high sediment resuspension and bioturbation from pest fish (carp), reduced water depth due to installation of water control structures, reduction in wetland filtering potential due to draining, and stock access to wetlands. A 1-D hydrodynamics model, the General Ocean Turbulence Model was coupled to a complex ecological model (PClake) via the Framework for Aquatic Biogeochemical Models (FABM). FABM is an open source FORTAN-based code that facilitates the coupling of hydrodynamic and ecological models. FABM-PCLake is a redesigned PCLake. The consensus from the model simulations carried out in the study suggests that, for Lake Waahi to undergo restoration whereby the lake is restored to clear-water stable state, both external load needs to be reduced significantly by greater than 50%, along with changes in lake ecological structure, resulting from re-establishment of macrophytes aided by the control of carp biomass. These finding supports the general view within the literature that for lake restoration success, external load reduction (catchment load) is critical. Finally, if the ultimate goal of lake restoration in Lake Waahi is to address the decline in tuna (shortfin eel - Anguilla australis) biomass, a return to a clear-water stable state should facilitate improvement in tuna habitat and provide the conditions for development of a healthy eel population. Coupled modelling approaches will provide a more complete picture of potential responses of Hauanga kai species to land and lake management scenarios.

year: 2018