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: Late Miocene to early Pliocene stratigraphic record in northern Taranaki Basin: Condensed sedimentation ahead of Northern Graben extension and progradation of the modern continental margin

authors: Hansen, Rochelle J.

subjects: Taranaki Basin

abstract: The middle Pliocene-Pleistocene progradation of the Giant Foresets Formation in Taranaki Basin built up the modern continental margin offshore from western North Island. The late Miocene to early Pliocene interval preceding this progradation was characterised in northern Taranaki Basin by the accumulation of hemipelagic mudstone (Manganui Formation), volcaniclastic sediments (Mohakatino Formation), and marl (Ariki Formation), all at bathyal depths. The Manganui Formation has generally featureless wireline log signatures and moderate to low amplitude seismic reflection characteristics. Mohakatino Formation is characterised by a sharp decrease in the GR log value at its base, a blocky GR log motif reflecting sandstone packets, and erratic resistivity logs. Seismic profiles show bold laterally continuous reflectors. The Ariki Formation has a distinctive barrel-shaped to blocky GR log motif. This signature is mirrored by the SP log and often by an increase in resistivity values through this interval. The Ariki Formation comprises (calcareous) marl made up of abundant planktic foraminifera, is 109 m thick in Ariki-1, and accumulated over parts of the Western Stable Platform and beneath the fill of the Northern Graben. It indicates condensed sedimentation reflecting the distance of the northern region from the contemporary continental margin to the south.

text: Late Miocene to early Pliocene stratigraphic record in northern Taranaki Basin: Condensed sedimentation ahead of Northern Graben extension and progradation of the modern continental margin The middle Pliocene-Pleistocene progradation of the Giant Foresets Formation in Taranaki Basin built up the modern continental margin offshore from western North Island. The late Miocene to early Pliocene interval preceding this progradation was characterised in northern Taranaki Basin by the accumulation of hemipelagic mudstone (Manganui Formation), volcaniclastic sediments (Mohakatino Formation), and marl (Ariki Formation), all at bathyal depths. The Manganui Formation has generally featureless wireline log signatures and moderate to low amplitude seismic reflection characteristics. Mohakatino Formation is characterised by a sharp decrease in the GR log value at its base, a blocky GR log motif reflecting sandstone packets, and erratic resistivity logs. Seismic profiles show bold laterally continuous reflectors. The Ariki Formation has a distinctive barrel-shaped to blocky GR log motif. This signature is mirrored by the SP log and often by an increase in resistivity values through this interval. The Ariki Formation comprises (calcareous) marl made up of abundant planktic foraminifera, is 109 m thick in Ariki-1, and accumulated over parts of the Western Stable Platform and beneath the fill of the Northern Graben. It indicates condensed sedimentation reflecting the distance of the northern region from the contemporary continental margin to the south.

year: 2004-12-01

title: Cultural Justice and Ethics

authors: Nikora, Linda Waimarie

subjects: Maori

abstract: Contains the complete proceedings of the Cultural Justice and Ethics symposium held within the Annual Conference of the New Zealand Psychological Society, Wellington, 23rd-24th August, 1993. The responsibility for ensuring that the discipline of psychology is culturally just, is not only that of Maori or some other non-dominant group - the responsibility belongs to all involved in psychology. This collection of papers is about questioning and challenging the psychology that has been adopted from other settings. It is about nurturing and valuing the development of local and indigenous psychologies. It is about developing psychological tools and methods of application that are culturally compatible. It is an invitation to become excited about and instrumental in building a profession and practice in Aotearoa, for Aotearoa.

text: Cultural Justice and Ethics Contains the complete proceedings of the Cultural Justice and Ethics symposium held within the Annual Conference of the New Zealand Psychological Society, Wellington, 23rd-24th August, 1993. The responsibility for ensuring that the discipline of psychology is culturally just, is not only that of Maori or some other non-dominant group - the responsibility belongs to all involved in psychology. This collection of papers is about questioning and challenging the psychology that has been adopted from other settings. It is about nurturing and valuing the development of local and indigenous psychologies. It is about developing psychological tools and methods of application that are culturally compatible. It is an invitation to become excited about and instrumental in building a profession and practice in Aotearoa, for Aotearoa.

year: 1993