title: Understanding the beliefs and behaviours of low-skilled adults as they re-engage with mathematics

authors: Whitten, Damon Rodger

subjects: Adult numeracy

abstract: This thesis explored low-skilled adult learners’ beliefs about mathematics and how they engaged with mathematical content delivered as part of foundation-level vocational programmes in New Zealand. It also examined how low-skilled learners holding procedurally-oriented beliefs responded to a classroom environment that emphasised conceptual understanding, collaboration and discourse. An ‘insider research’ approach was adopted to capitalise on the researcher’s prior experience in the sector. Analysis of data utilised an interpretive approach drawing on Bandura’s triadic reciprocal determinant model that posited beliefs, behaviour and the environment as interacting factors. Methods of data collection included surveys, observations, interviews and an intervention in which the researcher took a dual tutor/researcher role. Observation and intervention data were collected through multiple audio-recording devices that recorded private and public utterances as learners participated in lessons.

The survey and interview findings showed that most low-skilled adults believed mathematics to be procedural, performance-oriented, and learned by adopting passive strategies. Many held non-mathematical identities, described school and foundation-level mathematics lessons as potentially shame making, and reported censoring their behaviours to avoid shame.

The use of multiple-recording devices was effective for capturing the complexity of classroom interactions. Learners’ behaviours within lessons were consistent with procedural/calculational beliefs and reflected performance-oriented goals such as completing tasks quickly and accurately. Some learners displayed negative affective responses when expected to engage with mathematical content, and adopted behaviours designed to reduce, or eliminate, public exposure to failure. Group problem-solving was characterised by an unequal division of labour between ‘solvers’ and ‘supporters’. Lower-skilled learners tended to adopt peripheral support roles, while procedurally proficient learners either took, or were assigned, responsibility for all mathematical thinking. These behaviours enabled groups to complete tasks and achieve pseudo-success yet constrained the lower-skilled learners’ engagement in mathematical thinking, while also presenting little mathematical challenge to higher-skilled learners. This pattern appeared to contribute to the maintenance of learners’ low skills and non-mathematical identities by routinising their deferral of agency to more proficient learners.

The intervention indicated that low-skilled procedurally-oriented learners tended to resist conceptually-oriented activities that emphasised mathematical discourse, collaboration, and inquiry. This appeared to be because these activities increased the threat of a shameful episode and were perceived as superfluous to their procedurally-oriented goals. Learners reported that the intervention was more effective than their traditional classes, but attributed this to better tutor explanations, rather than their own active engagement in mathematical thinking. The overall findings indicated that low-skilled procedurally-oriented adults preferred and expected a traditional approach, and many used its familiar routines to reduce their level of engagement and exposure to shame. Implications for educators include the need to differentiate authentic from pseudo-engagement, to understand the impact of shame on behaviour, and establish positive patterns of engagement.

text: Understanding the beliefs and behaviours of low-skilled adults as they re-engage with mathematics This thesis explored low-skilled adult learners’ beliefs about mathematics and how they engaged with mathematical content delivered as part of foundation-level vocational programmes in New Zealand. It also examined how low-skilled learners holding procedurally-oriented beliefs responded to a classroom environment that emphasised conceptual understanding, collaboration and discourse. An ‘insider research’ approach was adopted to capitalise on the researcher’s prior experience in the sector. Analysis of data utilised an interpretive approach drawing on Bandura’s triadic reciprocal determinant model that posited beliefs, behaviour and the environment as interacting factors. Methods of data collection included surveys, observations, interviews and an intervention in which the researcher took a dual tutor/researcher role. Observation and intervention data were collected through multiple audio-recording devices that recorded private and public utterances as learners participated in lessons.

The survey and interview findings showed that most low-skilled adults believed mathematics to be procedural, performance-oriented, and learned by adopting passive strategies. Many held non-mathematical identities, described school and foundation-level mathematics lessons as potentially shame making, and reported censoring their behaviours to avoid shame.

The use of multiple-recording devices was effective for capturing the complexity of classroom interactions. Learners’ behaviours within lessons were consistent with procedural/calculational beliefs and reflected performance-oriented goals such as completing tasks quickly and accurately. Some learners displayed negative affective responses when expected to engage with mathematical content, and adopted behaviours designed to reduce, or eliminate, public exposure to failure. Group problem-solving was characterised by an unequal division of labour between ‘solvers’ and ‘supporters’. Lower-skilled learners tended to adopt peripheral support roles, while procedurally proficient learners either took, or were assigned, responsibility for all mathematical thinking. These behaviours enabled groups to complete tasks and achieve pseudo-success yet constrained the lower-skilled learners’ engagement in mathematical thinking, while also presenting little mathematical challenge to higher-skilled learners. This pattern appeared to contribute to the maintenance of learners’ low skills and non-mathematical identities by routinising their deferral of agency to more proficient learners.

The intervention indicated that low-skilled procedurally-oriented learners tended to resist conceptually-oriented activities that emphasised mathematical discourse, collaboration, and inquiry. This appeared to be because these activities increased the threat of a shameful episode and were perceived as superfluous to their procedurally-oriented goals. Learners reported that the intervention was more effective than their traditional classes, but attributed this to better tutor explanations, rather than their own active engagement in mathematical thinking. The overall findings indicated that low-skilled procedurally-oriented adults preferred and expected a traditional approach, and many used its familiar routines to reduce their level of engagement and exposure to shame. Implications for educators include the need to differentiate authentic from pseudo-engagement, to understand the impact of shame on behaviour, and establish positive patterns of engagement.

year: 2018

title: The influence of sediment nutrient dynamics on the response of lake ecosystems to restoration and climate change

authors: Trolle, Dennis

subjects: Sediment

abstract: Human activities such as urban settlement, farming, forestry and recreation, have caused deterioration of water quality in many freshwater lakes worldwide. Apart from anthropogenic impacts, it is also recognized that climate has a direct influence on lake water temperature, nutrient loads, phytoplankton abundance and chemistry. However, little is known about the potential effects of future climate change on lake water quality. Understanding the dynamics, abundance and availability of nutrient pools in lake bottom sediments is fundamentally important for predicting how, and over what time-scales, lake ecosystems will respond to future scenarios such as climate change, in-lake restoration or altered external nutrient loading. Through a sediment field study on 14 different lakes, and applications of complex lake ecosystem models to three New Zealand lakes, this study examined the spatial and temporal dynamics of sediment nutrient concentrations, and made considerations of the effects of restoration measures and future climate change on lake water quality.

To gain insight into processes influencing the dynamics of horizontal and vertical gradients of sediment nutrient concentrations, intact sediment cores were collected from twelve lakes within the Bay of Plenty province, North Island of New Zealand. In addition, intact sediment cores were collected from shallow Lake Te Waihora (Ellesmere) in the Canterbury province, South Island of New Zealand and shallow Lake Taihu in the Jaingsu province, China. The observed vertical concentration profiles of total phosphorus (TP) in the sediments revealed that the shape of these profiles can be similar across gradients of widely differing trophic status. Empirical and mechanistic steady state profile models were derived to describe the vertical distribution of total carbon (TC), total nitrogen (TN) and TP concentrations in the sediments. These models revealed that density-driven burial and biodiffusive mixing, which in the models also includes effects of redox-driven gradients, are strongly correlated with vertical gradients of sediment TC, TN and TP content, whereas lake trophic status was not.

Despite enhancing knowledge of the processes influencing vertical gradients of sediment nutrient concentrations, little is known about the rates at which sediment nutrient concentrations may change as a response to changes in external loading or climate. Studies into the composition of bottom sediments have been undertaken intermittently over the past three decades for the 12 lakes in the Bay of Plenty. These studies, together with the data collected in this study, were used to quantify temporal changes in sediment chemistry across the lakes. Comparison of the data collected in this study with results from a survey in 1995 showed that surficial sediment (0-2 cm) TP concentrations have increased in three of the 12 lakes, at rates ranging from 27.5 to 114.4 mg P kg-1 dry wt yr-1. TN concentrations in surficial sediments have increased in nine of the 12 lakes at rates ranging from 51.8 to 869.2 mg N kg-1 dry wt yr-1. A correlation analysis revealed that temporal changes in sediment TP and TN concentrations were not significantly linearly related (pgt0.05) to catchment area or temporal changes of different water column indices considered to reflect lake trophic state, including annual mean water column concentrations of TP, TN or chlorophyll a (Chl a).

While vertical profiles of sediment nutrient concentrations can be used to provide information about historical changes of trophic status in lakes, little is known about horizontal variability of sediment nutrient concentrations, including possibly relationships with horizontal variations in water column variables. In the large, shallow and eutrophic Lake Taihu, China, there are distinct horizontal water column concentration gradients of nutrients and Chl a. Concentrations are generally high in the north, where some of the major polluted tributaries enter the lake, and relatively low in the south, where macrophytes generally are abundant. To test whether these water column concentration gradients are similarly reflected in spatial heterogeneity of nutrient concentrations within the bottom sediments of Lake Taihu, I examined correlations between concentrations of TP and TN in surficial sediments (0-2 cm) and TP, TN and Chl a concentrations in water column samples determined for 32 sites in 2005. Linear correlation analysis revealed that surficial sediment TP concentrations across the 32 stations were related significantly, though weakly, to annual mean water column concentrations of TP and TN as well as Chl a. Correlations of surficial sediment TN with water column variables were, however, not significant (p gt 0.05).
To better understand the effects of future climate change on lakes of different trophic status, I applied the one-dimensional lake ecosystem model, DYRESM-CAEDYM, to oligo-mesotrophic Lake Okareka, eutrophic Lake Rotoehu and highly eutrophic Lake Te Waihora. All three models were calibrated based on a three-year period (July 2002 - June 2005) and validated on a separate two-year period (July 2005 - June 2007). The model simulations generally showed good agreement with observed data for temperature, dissolved oxygen (DO), and total nutrient and Chl a concentrations. To represent a possible future climate of 2100, temperature predictions were derived from the regional climate model, DARLAM, based on the Intergovernmental Panel on Climate Change (IPCC) A2 scenario, which suggests that air temperatures by the year 2100 will increase by an average of 2.5 'C and 2.7 'C for the Bay of Plenty and the Canterbury province, respectively, relative to the base scenario (years 2002-2007). Model simulations of the future climate scenarios indicate that climatic changes generally will lead to a degradation of lake water quality in all three lakes, especially during summer months, and further suggest that the effects on annual mean surface concentrations of TP, TN and Chl a will be equivalent to an increase in external TN and TP loading by 25-50%. Simulations for Lake Rotoehu, where diatoms and cyanophytes were represented in the conceptual model, further suggest that cyanophytes will be more abundant in the future, increasing by gt15% in annual mean biomass. Although the effects of climate change may be delayed or slightly mediated by the chemical resilience of the sediment nutrient pools, the effects of climate change on lake water quality in the New Zealand lakes will be of a magnitude that should be considered as management strategies are planned and implemented, thus increasing the probability of successful preservation or improvement in water quality in future decades.

text: The influence of sediment nutrient dynamics on the response of lake ecosystems to restoration and climate change Human activities such as urban settlement, farming, forestry and recreation, have caused deterioration of water quality in many freshwater lakes worldwide. Apart from anthropogenic impacts, it is also recognized that climate has a direct influence on lake water temperature, nutrient loads, phytoplankton abundance and chemistry. However, little is known about the potential effects of future climate change on lake water quality. Understanding the dynamics, abundance and availability of nutrient pools in lake bottom sediments is fundamentally important for predicting how, and over what time-scales, lake ecosystems will respond to future scenarios such as climate change, in-lake restoration or altered external nutrient loading. Through a sediment field study on 14 different lakes, and applications of complex lake ecosystem models to three New Zealand lakes, this study examined the spatial and temporal dynamics of sediment nutrient concentrations, and made considerations of the effects of restoration measures and future climate change on lake water quality.

To gain insight into processes influencing the dynamics of horizontal and vertical gradients of sediment nutrient concentrations, intact sediment cores were collected from twelve lakes within the Bay of Plenty province, North Island of New Zealand. In addition, intact sediment cores were collected from shallow Lake Te Waihora (Ellesmere) in the Canterbury province, South Island of New Zealand and shallow Lake Taihu in the Jaingsu province, China. The observed vertical concentration profiles of total phosphorus (TP) in the sediments revealed that the shape of these profiles can be similar across gradients of widely differing trophic status. Empirical and mechanistic steady state profile models were derived to describe the vertical distribution of total carbon (TC), total nitrogen (TN) and TP concentrations in the sediments. These models revealed that density-driven burial and biodiffusive mixing, which in the models also includes effects of redox-driven gradients, are strongly correlated with vertical gradients of sediment TC, TN and TP content, whereas lake trophic status was not.

Despite enhancing knowledge of the processes influencing vertical gradients of sediment nutrient concentrations, little is known about the rates at which sediment nutrient concentrations may change as a response to changes in external loading or climate. Studies into the composition of bottom sediments have been undertaken intermittently over the past three decades for the 12 lakes in the Bay of Plenty. These studies, together with the data collected in this study, were used to quantify temporal changes in sediment chemistry across the lakes. Comparison of the data collected in this study with results from a survey in 1995 showed that surficial sediment (0-2 cm) TP concentrations have increased in three of the 12 lakes, at rates ranging from 27.5 to 114.4 mg P kg-1 dry wt yr-1. TN concentrations in surficial sediments have increased in nine of the 12 lakes at rates ranging from 51.8 to 869.2 mg N kg-1 dry wt yr-1. A correlation analysis revealed that temporal changes in sediment TP and TN concentrations were not significantly linearly related (pgt0.05) to catchment area or temporal changes of different water column indices considered to reflect lake trophic state, including annual mean water column concentrations of TP, TN or chlorophyll a (Chl a).

While vertical profiles of sediment nutrient concentrations can be used to provide information about historical changes of trophic status in lakes, little is known about horizontal variability of sediment nutrient concentrations, including possibly relationships with horizontal variations in water column variables. In the large, shallow and eutrophic Lake Taihu, China, there are distinct horizontal water column concentration gradients of nutrients and Chl a. Concentrations are generally high in the north, where some of the major polluted tributaries enter the lake, and relatively low in the south, where macrophytes generally are abundant. To test whether these water column concentration gradients are similarly reflected in spatial heterogeneity of nutrient concentrations within the bottom sediments of Lake Taihu, I examined correlations between concentrations of TP and TN in surficial sediments (0-2 cm) and TP, TN and Chl a concentrations in water column samples determined for 32 sites in 2005. Linear correlation analysis revealed that surficial sediment TP concentrations across the 32 stations were related significantly, though weakly, to annual mean water column concentrations of TP and TN as well as Chl a. Correlations of surficial sediment TN with water column variables were, however, not significant (p gt 0.05).
To better understand the effects of future climate change on lakes of different trophic status, I applied the one-dimensional lake ecosystem model, DYRESM-CAEDYM, to oligo-mesotrophic Lake Okareka, eutrophic Lake Rotoehu and highly eutrophic Lake Te Waihora. All three models were calibrated based on a three-year period (July 2002 - June 2005) and validated on a separate two-year period (July 2005 - June 2007). The model simulations generally showed good agreement with observed data for temperature, dissolved oxygen (DO), and total nutrient and Chl a concentrations. To represent a possible future climate of 2100, temperature predictions were derived from the regional climate model, DARLAM, based on the Intergovernmental Panel on Climate Change (IPCC) A2 scenario, which suggests that air temperatures by the year 2100 will increase by an average of 2.5 'C and 2.7 'C for the Bay of Plenty and the Canterbury province, respectively, relative to the base scenario (years 2002-2007). Model simulations of the future climate scenarios indicate that climatic changes generally will lead to a degradation of lake water quality in all three lakes, especially during summer months, and further suggest that the effects on annual mean surface concentrations of TP, TN and Chl a will be equivalent to an increase in external TN and TP loading by 25-50%. Simulations for Lake Rotoehu, where diatoms and cyanophytes were represented in the conceptual model, further suggest that cyanophytes will be more abundant in the future, increasing by gt15% in annual mean biomass. Although the effects of climate change may be delayed or slightly mediated by the chemical resilience of the sediment nutrient pools, the effects of climate change on lake water quality in the New Zealand lakes will be of a magnitude that should be considered as management strategies are planned and implemented, thus increasing the probability of successful preservation or improvement in water quality in future decades.

year: 2009

title: The COVID-19 domestic vaccine pass: Implications for Māori

authors: Kukutai, Tahu

abstract: The New Zealand government has introduced a COVID-19 domestic vaccine pass to be used in conjunction with the COVID-19 Protection Framework. The Framework is likely to be activated soon after Cabinet meets on 29 November 2021. The pass will be necessary to access places and events that require proof of vaccination under the Framework.
This brief does not argue for or against the introduction of a domestic vaccine pass, but rather discusses key issues that it raises for Māori, and suggests actions to address them. We see four key issues:
• the lack of Māori involvement, as a Tiriti partner, on either the design or implementation of the COVID-19 domestic vaccine pass;
• disproportionate restriction on Māori mobility due to lower Māori vaccination rates;
• privacy and data security concerns;
• uneven implementation that could increase discrimination against Māori and other groups considered to pose a risk to others’ safety.
To respond to these issues we recommend that the implementation of the pass be designed in partnership with Māori and comply with Māori data sovereignty requirements. As Tiriti partners, Māori should expect that the pass will keep their communities safe, while providing opportunities to enact manaakitanga in the matrix of care, and the mana to manage their own affairs.

text: The COVID-19 domestic vaccine pass: Implications for Māori The New Zealand government has introduced a COVID-19 domestic vaccine pass to be used in conjunction with the COVID-19 Protection Framework. The Framework is likely to be activated soon after Cabinet meets on 29 November 2021. The pass will be necessary to access places and events that require proof of vaccination under the Framework.
This brief does not argue for or against the introduction of a domestic vaccine pass, but rather discusses key issues that it raises for Māori, and suggests actions to address them. We see four key issues:
• the lack of Māori involvement, as a Tiriti partner, on either the design or implementation of the COVID-19 domestic vaccine pass;
• disproportionate restriction on Māori mobility due to lower Māori vaccination rates;
• privacy and data security concerns;
• uneven implementation that could increase discrimination against Māori and other groups considered to pose a risk to others’ safety.
To respond to these issues we recommend that the implementation of the pass be designed in partnership with Māori and comply with Māori data sovereignty requirements. As Tiriti partners, Māori should expect that the pass will keep their communities safe, while providing opportunities to enact manaakitanga in the matrix of care, and the mana to manage their own affairs.

year: 2021-11-30