title: Supporting students' additive thinking: The use of equal additions for subtraction

authors: Young-Loveridge, Jennifer

subjects: academic achievement

abstract: This paper looks at how teachers can support students' additive thinking. It reports on a study of a lesson designed to teach the equal additions strategy for subtraction, contained in Numeracy Development Project (NDP) Book 5. Nine teachers were observed teaching mathematics. Despite having a strong commitment to promoting conceptual understanding, many teachers struggled with various aspects of the material and resorted to teaching procedurally. We concluded that teachers need to have a deeper, more connected understanding of addition and subtraction in order to develop their pedagogical content knowledge in mathematics.

text: Supporting students' additive thinking: The use of equal additions for subtraction This paper looks at how teachers can support students' additive thinking. It reports on a study of a lesson designed to teach the equal additions strategy for subtraction, contained in Numeracy Development Project (NDP) Book 5. Nine teachers were observed teaching mathematics. Despite having a strong commitment to promoting conceptual understanding, many teachers struggled with various aspects of the material and resorted to teaching procedurally. We concluded that teachers need to have a deeper, more connected understanding of addition and subtraction in order to develop their pedagogical content knowledge in mathematics.

year: 2011

title: Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion

authors: Steyn-Ross, Moira L.

subjects: gap junctions

abstract: In this chapter we describe a continuum model for the cortex that includes both axon-to-dendrite chemical synapses and direct neuron-to-neuron gap-junction diffusive synapses. The effectiveness of chemical synapses is determined by the voltage of the receiving dendrite V relative to its Nernst reversal potential Vrev. Here we explore two alternative strategies for incorporating dendritic reversal potentials, and uncover surprising differences in their stability properties and model dynamics. In the “slow-soma” variant, the (Vrev - V) weighting is applied after the input flux has been integrated at the dendrite, while for “fast-soma”, the weighting is applied directly to the input flux, prior to dendritic integration. For the slow-soma case, we find that–-provided the inhibitory diffusion (via gap-junctions) is sufficiently strong–-the cortex generates stationary Turing patterns of cortical activity. In contrast, the fast-soma destabilizes in favor of standing-wave spatial structures that oscillate at low-gamma frequency (  30-Hz); these spatial patterns broaden and weaken as diffusive coupling increases, and disappear altogether at moderate levels of diffusion. We speculate that the slow- and fast-soma models might correspond respectively to the idling and active modes of the cortex, with slow-soma patterns providing the default background state, and emergence of gamma oscillations in the fast-soma case signaling the transition into the cognitive state.

text: Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion In this chapter we describe a continuum model for the cortex that includes both axon-to-dendrite chemical synapses and direct neuron-to-neuron gap-junction diffusive synapses. The effectiveness of chemical synapses is determined by the voltage of the receiving dendrite V relative to its Nernst reversal potential Vrev. Here we explore two alternative strategies for incorporating dendritic reversal potentials, and uncover surprising differences in their stability properties and model dynamics. In the “slow-soma” variant, the (Vrev - V) weighting is applied after the input flux has been integrated at the dendrite, while for “fast-soma”, the weighting is applied directly to the input flux, prior to dendritic integration. For the slow-soma case, we find that–-provided the inhibitory diffusion (via gap-junctions) is sufficiently strong–-the cortex generates stationary Turing patterns of cortical activity. In contrast, the fast-soma destabilizes in favor of standing-wave spatial structures that oscillate at low-gamma frequency (  30-Hz); these spatial patterns broaden and weaken as diffusive coupling increases, and disappear altogether at moderate levels of diffusion. We speculate that the slow- and fast-soma models might correspond respectively to the idling and active modes of the cortex, with slow-soma patterns providing the default background state, and emergence of gamma oscillations in the fast-soma case signaling the transition into the cognitive state.

year: 2010

title: Kaupapa Māori antenatal wānanga: A solution to refocus New Zealand health service delivery for improved engagement and responsiveness with Māori māmā hapū and pēpi.

authors: Barrett, Nikki Maree

subjects: antenatal

abstract: The revitalisation of traditional Māori birthing knowledge and practices is a significant space to enhance Māori maternal and infant health outcomes. This thesis with publications examined the potential of two Kaupapa Māori antenatal wānanga to enhance maternal health outcomes for Māori. Using a mixed methods approach, underpinned by Kaupapa Māori research principles and supported by Māori centred research and a mana wahine theoretical perspective, this thesis reveals transformative solutions to address maternal and infant inequities. 
This thesis explores three key areas. First, maternal and infant education and knowledge during hapūtanga (pregnancy). Second, the connection and engagement of Māori māmā hapū (expectant mothers) and whānau (family) with health and community services, and third, the lived experiences of Māori māmā engaging with community services to identify barriers and enablers of service providers.  
The introductory chapters provide a contextual overview of maternal and infant health. I begin by canvassing traditional and contemporary factors that influence the current state of Indigenous, notably Māori, maternal and infant health. I then present four chapters that have been submitted to academic journals for publication. Each chapter focuses on one or more of the three key areas identified above. The final chapter draws each of the chapters together to demonstrate how Māori led health initiatives work to enhance and improve maternal health .
Chapter 3 provides a rationale for focusing on Indigenous antenatal education. Within Western countries, antenatal education is a recognised and encouraged service provided during pregnancy. Providing education and information, antenatal education is an opportunity for expectant parents to prepare for pregnancy and parenting. With poor maternal and infant health outcomes, Indigenous Peoples from Aotearoa, Australia, Canada, and the United States, are particularly encouraged to attend antenatal education. Yet, the low rates of Indigenous Peoples attending antenatal education (will be interchangeably referred to as childbirth education throughout this thesis) do not reflect this need. Therefore, the first process in this thesis was to explore Indigenous Peoples participation and engagement in antenatal education. Using a standardised protocol, chapter 3 is a systematic review that explored how Indigenous Peoples are involved, prioritised, and privileged in antenatal education. Specifically, this systematic review examined the extent to which Indigenous Peoples, and their aspirations of health, were prioritised in academic scholarship. With only two studies involving Indigenous participants, it was evidenced that the voice of Indigenous Peoples in antenatal education is lacking in academic scholarship. A key finding was that Indigenous antenatal education programmes were not reflected in academic scholarship. Yet, within Aotearoa there are existing Kaupapa Māori antenatal education. Therefore, the next chapter (4) focused on a retrospective audit of Hapū Wānanga, a Kaupapa Māori childbirth education class.  
One reason for undertaking a retrospective audit of Hapū Wānanga (HW) was because I was genuinely interested to understand how other māmā hapū, and their whānau, experienced the programme. I wanted to give voice to these wāhine and was excited to learn whether the programme had similar value to them, as it did for me when I participated in a similar wānanga. This mixed-method interpretive study used retrospective post-course survey data of 1,152 participants over a three-year period from the HW based in the Waikato District Health Board region. This chapter amplified the experiences and voices of HW participants to affirm positive aspects of the class. Participants regarded the information that was shared as life changing, describing the constituents that separated this programme from other health service experiences. Findings revealed that an Indigenous, strengths-based approach to childbirth education service design and delivery, has positive and transformation results for whānau.
Chapter 5 focused on supporting another Kaupapa Māori antenatal wānanga, Whirihia Te Korowai Aroha, to co-design a holistic assessment tool (Whirihia tool). The Whirihia tool aimed to increase access and enhance experiences between health services and māmā hapū by identifying health or social need, then providing a dedicated referral pathway. Using the Indigenous He Pikinga Waiora Implementation (HPW) framework as a guide, this chapter provides an autoethnographic reflective account of the co-design process that led to the development and implementation of the Whirihia tool. This reflective account provides examples of key considerations that align to the HPW framework in the hopes that it will afford some guidance for fellow emerging researchers who wish to undertake ethical co-designed health research with Māori (and non-Māori) communities and organisations. The intention of this chapter is to encourage our research community to provide opportunities and platforms for community health initiatives such as Whirihia Te Korowai Aroha to be foregrounded in academic scholarship. Kaupapa Māori programmes such as these have the solutions to address issues that predominantly affect Māori, however they need the vehicles and tools to make Māori voices, visibility, and vision, heard.   
A cohort study was used to extend on the findings from the autoethnographic co-designed Whirihia tool. This chapter explored the experiences of māmā hapū and their interactions with health and social services immediately after Aotearoa’s first Covid-19 lockdown in March 2020. 17 participants completed the Whirihia tool with a subsequent seven māmā participating in a semi-structured, open-ended telephone interview. Findings showed that when services enabled participants to enact their autonomy and self-determination participants valued their engagement with that service. To be responsive to Māori health needs and aspirations, services must demonstrate empathy and compassion for māmā and operate in a passive role of support rather than a position of authority and power.
The final chapter draws together the findings from the previous chapters and challenges preconceived notions that Māori do not engage with maternal and infant health services. Instead, this thesis demonstrates that Māori-led, designed, and delivered, initiatives attract Māori māmā hapū, wider whānau, and non-Māori engagement and endorsement. Foregrounded by the voice and experiences of Māori māmā hapū and their whānau, I suggest three practical steps that can be enacted immediately at both a health system, and health service delivery level to positively enhance antenatal health. First, determine the extent to which CBE classes are meeting Māori end-user needs. Second, using findings from end-user experiences as a foundation, reorient the Ministry of Health pregnancy and parenting service specifications to ensure appropriate content is prioritised in CBE classes, particularly Māori knowledge. Third, adequately resource CBE providers who can deliver programmes that meet the needs of Māori end-users. With the new Te Whatu Ora Health New Zealand and Te Aka Whai Ora Māori Health Authority, now is the time to deliver on the various strategic documents to authentically meet the needs of māmā hapū and whānau. 
The evidence-based research delivered in this thesis provided the basis for the three recommended changes noted above. These recommendations can be implemented into the health system to enable positive and meaningful change for Māori, in addition to supporting efforts of other Indigenous Peoples to improve Indigenous perinatal health and wellbeing.

text: Kaupapa Māori antenatal wānanga: A solution to refocus New Zealand health service delivery for improved engagement and responsiveness with Māori māmā hapū and pēpi. The revitalisation of traditional Māori birthing knowledge and practices is a significant space to enhance Māori maternal and infant health outcomes. This thesis with publications examined the potential of two Kaupapa Māori antenatal wānanga to enhance maternal health outcomes for Māori. Using a mixed methods approach, underpinned by Kaupapa Māori research principles and supported by Māori centred research and a mana wahine theoretical perspective, this thesis reveals transformative solutions to address maternal and infant inequities. 
This thesis explores three key areas. First, maternal and infant education and knowledge during hapūtanga (pregnancy). Second, the connection and engagement of Māori māmā hapū (expectant mothers) and whānau (family) with health and community services, and third, the lived experiences of Māori māmā engaging with community services to identify barriers and enablers of service providers.  
The introductory chapters provide a contextual overview of maternal and infant health. I begin by canvassing traditional and contemporary factors that influence the current state of Indigenous, notably Māori, maternal and infant health. I then present four chapters that have been submitted to academic journals for publication. Each chapter focuses on one or more of the three key areas identified above. The final chapter draws each of the chapters together to demonstrate how Māori led health initiatives work to enhance and improve maternal health .
Chapter 3 provides a rationale for focusing on Indigenous antenatal education. Within Western countries, antenatal education is a recognised and encouraged service provided during pregnancy. Providing education and information, antenatal education is an opportunity for expectant parents to prepare for pregnancy and parenting. With poor maternal and infant health outcomes, Indigenous Peoples from Aotearoa, Australia, Canada, and the United States, are particularly encouraged to attend antenatal education. Yet, the low rates of Indigenous Peoples attending antenatal education (will be interchangeably referred to as childbirth education throughout this thesis) do not reflect this need. Therefore, the first process in this thesis was to explore Indigenous Peoples participation and engagement in antenatal education. Using a standardised protocol, chapter 3 is a systematic review that explored how Indigenous Peoples are involved, prioritised, and privileged in antenatal education. Specifically, this systematic review examined the extent to which Indigenous Peoples, and their aspirations of health, were prioritised in academic scholarship. With only two studies involving Indigenous participants, it was evidenced that the voice of Indigenous Peoples in antenatal education is lacking in academic scholarship. A key finding was that Indigenous antenatal education programmes were not reflected in academic scholarship. Yet, within Aotearoa there are existing Kaupapa Māori antenatal education. Therefore, the next chapter (4) focused on a retrospective audit of Hapū Wānanga, a Kaupapa Māori childbirth education class.  
One reason for undertaking a retrospective audit of Hapū Wānanga (HW) was because I was genuinely interested to understand how other māmā hapū, and their whānau, experienced the programme. I wanted to give voice to these wāhine and was excited to learn whether the programme had similar value to them, as it did for me when I participated in a similar wānanga. This mixed-method interpretive study used retrospective post-course survey data of 1,152 participants over a three-year period from the HW based in the Waikato District Health Board region. This chapter amplified the experiences and voices of HW participants to affirm positive aspects of the class. Participants regarded the information that was shared as life changing, describing the constituents that separated this programme from other health service experiences. Findings revealed that an Indigenous, strengths-based approach to childbirth education service design and delivery, has positive and transformation results for whānau.
Chapter 5 focused on supporting another Kaupapa Māori antenatal wānanga, Whirihia Te Korowai Aroha, to co-design a holistic assessment tool (Whirihia tool). The Whirihia tool aimed to increase access and enhance experiences between health services and māmā hapū by identifying health or social need, then providing a dedicated referral pathway. Using the Indigenous He Pikinga Waiora Implementation (HPW) framework as a guide, this chapter provides an autoethnographic reflective account of the co-design process that led to the development and implementation of the Whirihia tool. This reflective account provides examples of key considerations that align to the HPW framework in the hopes that it will afford some guidance for fellow emerging researchers who wish to undertake ethical co-designed health research with Māori (and non-Māori) communities and organisations. The intention of this chapter is to encourage our research community to provide opportunities and platforms for community health initiatives such as Whirihia Te Korowai Aroha to be foregrounded in academic scholarship. Kaupapa Māori programmes such as these have the solutions to address issues that predominantly affect Māori, however they need the vehicles and tools to make Māori voices, visibility, and vision, heard.   
A cohort study was used to extend on the findings from the autoethnographic co-designed Whirihia tool. This chapter explored the experiences of māmā hapū and their interactions with health and social services immediately after Aotearoa’s first Covid-19 lockdown in March 2020. 17 participants completed the Whirihia tool with a subsequent seven māmā participating in a semi-structured, open-ended telephone interview. Findings showed that when services enabled participants to enact their autonomy and self-determination participants valued their engagement with that service. To be responsive to Māori health needs and aspirations, services must demonstrate empathy and compassion for māmā and operate in a passive role of support rather than a position of authority and power.
The final chapter draws together the findings from the previous chapters and challenges preconceived notions that Māori do not engage with maternal and infant health services. Instead, this thesis demonstrates that Māori-led, designed, and delivered, initiatives attract Māori māmā hapū, wider whānau, and non-Māori engagement and endorsement. Foregrounded by the voice and experiences of Māori māmā hapū and their whānau, I suggest three practical steps that can be enacted immediately at both a health system, and health service delivery level to positively enhance antenatal health. First, determine the extent to which CBE classes are meeting Māori end-user needs. Second, using findings from end-user experiences as a foundation, reorient the Ministry of Health pregnancy and parenting service specifications to ensure appropriate content is prioritised in CBE classes, particularly Māori knowledge. Third, adequately resource CBE providers who can deliver programmes that meet the needs of Māori end-users. With the new Te Whatu Ora Health New Zealand and Te Aka Whai Ora Māori Health Authority, now is the time to deliver on the various strategic documents to authentically meet the needs of māmā hapū and whānau. 
The evidence-based research delivered in this thesis provided the basis for the three recommended changes noted above. These recommendations can be implemented into the health system to enable positive and meaningful change for Māori, in addition to supporting efforts of other Indigenous Peoples to improve Indigenous perinatal health and wellbeing.

year: 2023