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: Investigation of Microcystin Processing, Production and Export by Microcystis sp.

authors: Rogers, Shelley

subjects: microcystin

abstract: During this study, the effect of different processing methods on the microcystin quota (microcystins per cell) was investigated.  Microcystins from two Microcystis strains and one Planktothrix strain were quantified using liquid chromatography-mass spectrometry (LC-MS) after processing via; (1) direct freezing (no prior cell concentration) and extraction by freeze-thaw cycles, (2) cell concentration by centrifugation and extraction in methanol and (3) cell concentration by filtration and extraction in methanol. Microcystin quotas were lower for samples concentrated by filtration compared with the other two methods.  

In order to distinguish between extracellular microcystins actively exported from cells and those that are present as a result of cell lysis, a comparative microcystin export (CME) assay was developed using LC-MS to compare the proportion of extracellular microcystins with the proportion of extracellular non-ribosomal peptide which does not get actively exported. A culture-based experiment using the CME assay demonstrated the utility of this method and indicated that export from one of the Microcystis strains had occurred. With further validation experiments, the CME assay has the potential to be a valuable new tool for determining the occurrence of microcystin export. 

An in situ experiment was carried out in Lake Rotorua, Kaikoura, New Zealand, using mesocosms to study the effect of Microcystis sp. cell density on microcystin production, while measuring a wide array of abiotic parameters (temperature, light intensity, pH, dissolved oxygen and nutrients). Lake water was added to ‘control’ mesocosms in which cells were concentrated to different levels and added to ‘medium cell addition’ and ‘high cell addition’ mesocosms. The microcystin quota remained relatively constant throughout the study, despite induced changes in cell density and associated environmental parameters. These results indicate that cell density is not the only factor responsible for increased microcystin synthesis and that further investigation into the effect of stress inducing abiotic parameters such as pH and dissolved oxygen concentration may be required.

text: Investigation of Microcystin Processing, Production and Export by Microcystis sp. During this study, the effect of different processing methods on the microcystin quota (microcystins per cell) was investigated.  Microcystins from two Microcystis strains and one Planktothrix strain were quantified using liquid chromatography-mass spectrometry (LC-MS) after processing via; (1) direct freezing (no prior cell concentration) and extraction by freeze-thaw cycles, (2) cell concentration by centrifugation and extraction in methanol and (3) cell concentration by filtration and extraction in methanol. Microcystin quotas were lower for samples concentrated by filtration compared with the other two methods.  

In order to distinguish between extracellular microcystins actively exported from cells and those that are present as a result of cell lysis, a comparative microcystin export (CME) assay was developed using LC-MS to compare the proportion of extracellular microcystins with the proportion of extracellular non-ribosomal peptide which does not get actively exported. A culture-based experiment using the CME assay demonstrated the utility of this method and indicated that export from one of the Microcystis strains had occurred. With further validation experiments, the CME assay has the potential to be a valuable new tool for determining the occurrence of microcystin export. 

An in situ experiment was carried out in Lake Rotorua, Kaikoura, New Zealand, using mesocosms to study the effect of Microcystis sp. cell density on microcystin production, while measuring a wide array of abiotic parameters (temperature, light intensity, pH, dissolved oxygen and nutrients). Lake water was added to ‘control’ mesocosms in which cells were concentrated to different levels and added to ‘medium cell addition’ and ‘high cell addition’ mesocosms. The microcystin quota remained relatively constant throughout the study, despite induced changes in cell density and associated environmental parameters. These results indicate that cell density is not the only factor responsible for increased microcystin synthesis and that further investigation into the effect of stress inducing abiotic parameters such as pH and dissolved oxygen concentration may be required.

year: 2014

title: A wiggle-match date for Polynesian settlement of New Zealand

authors: Hogg, Alan G.

subjects: East Polynesia

abstract: Dating initial colonisation and environmental impacts by Polynesians in New Zealand is controversial. A key horizon is provided by the Kaharoa Tephra, deposited from an eruption of Mt Tarawera, because just underneath this layer are the first signs of forest clearance which imply human settlement. The authors used a log of celery pine from within Kaharoa deposits to derive a new precise date for the eruption via "wiggle-matching" – matching the radiocarbon dates of a sequence of samples from the log with the Southern Hemisphere calibration curve. The date obtained was 1314 ± 12 AD (2σ error), and the first environmental impacts and human occupation are argued to have occurred in the previous 50 years, i.e. in the late 13th – early 14th centuries AD. This date is contemporary with earliest settlement dates determined from archaeological sites in the New Zealand archipelago.

text: A wiggle-match date for Polynesian settlement of New Zealand Dating initial colonisation and environmental impacts by Polynesians in New Zealand is controversial. A key horizon is provided by the Kaharoa Tephra, deposited from an eruption of Mt Tarawera, because just underneath this layer are the first signs of forest clearance which imply human settlement. The authors used a log of celery pine from within Kaharoa deposits to derive a new precise date for the eruption via "wiggle-matching" – matching the radiocarbon dates of a sequence of samples from the log with the Southern Hemisphere calibration curve. The date obtained was 1314 ± 12 AD (2σ error), and the first environmental impacts and human occupation are argued to have occurred in the previous 50 years, i.e. in the late 13th – early 14th centuries AD. This date is contemporary with earliest settlement dates determined from archaeological sites in the New Zealand archipelago.

year: 2002