title: Scoping the meaning of 'critical' in mathematical thinking for Initial Teacher Education

authors: Furness, Jane Amanda

abstract: Current strong emphasis on literacy and numeracy in New Zealand educational policy, as elsewhere, reverberates in different ways in institutions charged with children's and adults' learning. A common response is to locate literacy and numeracy centrally in programmes aimed at preparing children for and enhancing adult participation in 21st century life and work. One place these agendas overlap is in preservice teacher education or Initial Teacher Education (ITE). Preservice teachers enter their ITE programmes as adult learners engaged in building literacy and numeracy knowledge and skills for teaching across the curriculum, working with student achievement data and administration, aspects of which may also be useful in their wider lives. These tasks also involve making judgements which require critical thinking, another key policy focus in New Zealand and internationally for children's and adults' learning. As part of a project in which a group of researchers are exploring mathematical thinking and reasoning in initial teacher education (MARKITE) the researchers included critical awareness as one of three dimensions in their definition of mathematical thinking. As the project has progressed our interest in the notion of criticality in mathematics education and its implications for mathematical thinking in the context of the needs of 2 1st century citizens has grown. We have set out in this paper to illuminate what 'critical' in mathematical thinking could mean and what we mean by it in our project. Our aim in this reflective undertaking is to shed light on options and elaborate why we believe developing criticality is important in initial teacher education.
The primary mode of inquiry was a literature search, covering critical theory and critical literacy, critical mathematics and various definitions of mathematics education (critical numeracy, data literacy and quantitative literacy). Next we reviewed current thinking on the context in which ITE takes place, in particular the needs of democratic citizens in the 2 1st century. Ideas gleaned from these documents have been analysed against the Key Competencies Framework and other policy and implementation documents to consider how what is suggested as important in the Mathematics and Statistics learning area (MOE, 2007) provides grounds for the development of criticality in the identification and use of mathematical thinking across an ITE programme. In this examination we were cognisant of the increasing demand for (quantitative) data use in schools.
Our investigations are drawing us towards conclusions that favour quite classic critical theory applications (Freire, 1974), which we see also reflected in current works which explore the link between mathematics and the globally experienced social and environmental conditions of the present and the future (e.g. Atweh & Brady, 2009; Greer & Skovsmose, 2012). Mathematics is deeply involved in framing understanding and solving social, economical and environmental problems. To date we have found very little literature that focuses on the nature of and how to develop student teachers' mathematical thinking beyond a focus on curriculum mathematics. In the National Standards, we find the stem for criteria include a focus on context and problem solving. This creates the potential for critical engagement with the mathematical ideas embedded in real world problems and solutions. However the exemplifications of the standards do not encompass pressing social issues. 
This work brings together current thinking about criticality and critical mathematics/mathematics education in a first attempt to put forward a useful understanding of critical mathematical thinking for ITE. It also brings to the attention of educators the role of mathematics in critical democratic citizenship, alongside the more commonplace focus on critical literacy. The kinds of critical mathematical thinking we have become more specifically interested in are those that enable the inclusion of different culturally based world views am actions, equitable participation and outcomes, and so, justice for all citizens. We propose that the develop in preservice teachers of capacity for critical mathematical thinking is a crucial component of ITE, especially in these times of significant global change which mathematics plays a central yet often hidden re-Critical mathematical thinking holds the potential to facilitate teachers to work actively in pursuit of an inclusive, socially just world.

text: Scoping the meaning of 'critical' in mathematical thinking for Initial Teacher Education Current strong emphasis on literacy and numeracy in New Zealand educational policy, as elsewhere, reverberates in different ways in institutions charged with children's and adults' learning. A common response is to locate literacy and numeracy centrally in programmes aimed at preparing children for and enhancing adult participation in 21st century life and work. One place these agendas overlap is in preservice teacher education or Initial Teacher Education (ITE). Preservice teachers enter their ITE programmes as adult learners engaged in building literacy and numeracy knowledge and skills for teaching across the curriculum, working with student achievement data and administration, aspects of which may also be useful in their wider lives. These tasks also involve making judgements which require critical thinking, another key policy focus in New Zealand and internationally for children's and adults' learning. As part of a project in which a group of researchers are exploring mathematical thinking and reasoning in initial teacher education (MARKITE) the researchers included critical awareness as one of three dimensions in their definition of mathematical thinking. As the project has progressed our interest in the notion of criticality in mathematics education and its implications for mathematical thinking in the context of the needs of 2 1st century citizens has grown. We have set out in this paper to illuminate what 'critical' in mathematical thinking could mean and what we mean by it in our project. Our aim in this reflective undertaking is to shed light on options and elaborate why we believe developing criticality is important in initial teacher education.
The primary mode of inquiry was a literature search, covering critical theory and critical literacy, critical mathematics and various definitions of mathematics education (critical numeracy, data literacy and quantitative literacy). Next we reviewed current thinking on the context in which ITE takes place, in particular the needs of democratic citizens in the 2 1st century. Ideas gleaned from these documents have been analysed against the Key Competencies Framework and other policy and implementation documents to consider how what is suggested as important in the Mathematics and Statistics learning area (MOE, 2007) provides grounds for the development of criticality in the identification and use of mathematical thinking across an ITE programme. In this examination we were cognisant of the increasing demand for (quantitative) data use in schools.
Our investigations are drawing us towards conclusions that favour quite classic critical theory applications (Freire, 1974), which we see also reflected in current works which explore the link between mathematics and the globally experienced social and environmental conditions of the present and the future (e.g. Atweh & Brady, 2009; Greer & Skovsmose, 2012). Mathematics is deeply involved in framing understanding and solving social, economical and environmental problems. To date we have found very little literature that focuses on the nature of and how to develop student teachers' mathematical thinking beyond a focus on curriculum mathematics. In the National Standards, we find the stem for criteria include a focus on context and problem solving. This creates the potential for critical engagement with the mathematical ideas embedded in real world problems and solutions. However the exemplifications of the standards do not encompass pressing social issues. 
This work brings together current thinking about criticality and critical mathematics/mathematics education in a first attempt to put forward a useful understanding of critical mathematical thinking for ITE. It also brings to the attention of educators the role of mathematics in critical democratic citizenship, alongside the more commonplace focus on critical literacy. The kinds of critical mathematical thinking we have become more specifically interested in are those that enable the inclusion of different culturally based world views am actions, equitable participation and outcomes, and so, justice for all citizens. We propose that the develop in preservice teachers of capacity for critical mathematical thinking is a crucial component of ITE, especially in these times of significant global change which mathematics plays a central yet often hidden re-Critical mathematical thinking holds the potential to facilitate teachers to work actively in pursuit of an inclusive, socially just world.

year: 2015

title: Evaluation of vegetation and stream health within sites supported by the Hamilton City Council Plants for Gullies Programme

authors: Bylsma, Rebecca Johanna

abstract: Between August 2012 and March 2013, the Environmental Research Institute, University of Waikato, conducted a survey of randomly selected Hamilton gully sites which had received plants from the Hamilton City Council’s Plants for Gullies Programme. This survey assessed recent plantings, existing gully vegetation and stream health, along with property owner awareness and engagement with the key restoration principles. 
The Plants for Gullies Programme has been extremely well received by the Hamilton community and gully owners. Survey participants were actively restoring their gully sites with the most common goal (c. 40%) being the establishment of native plant dominance within 10 years. Gully owners have a good understanding of restoration theory and practise; on average, plant placement in the gullies scored 15.7 out of 20 with consideration of plant environmental requirements and the concept of ecosourcing was understood by c. 76% of landowners surveyed. Also, most of the interviewed participants (c. 80%) were active in seeking guidance from other gullies, often through organised tours. 
Current stream health was qualitatively assessed and characterised at each of the gully sites. Results provide baseline data for future monitoring. The majority of surveyed sites (c. 50%) had sand or silt substrate and the Bankwood gully had the best features for fauna habitat (e.g. debris and areas of low flow). At the time of visit, c. 60% of surveyed streams had clear water clarity. The poorest water clarity scores were in the Waitawhiriwhiri gully. When assessed on width, length and density, the average riparian buffer score was 12.8 out of 20 while the average stream shading score was 12.7 out of 20. The average bank stability score was 13.1 out of 20, reflecting an erosion problem that many gully owners talked about. 
Surveyed gullies were diverse in terms of native and exotic vegetation structure and composition; native species contributed between c. 30% to 100% of surveyed trees and shrubs, whereas groundcovers were predominantly exotic. This assessment of gully sites has shown that the Plants for Gullies Programme improves native species diversity through the re-introduction of species that are not naturally regenerating. The Plants for Gullies programme is a powerful tool for engaging private landowners and making cost-effective change to Hamilton City’s native biodiversity. There is now a community of willing gully owners who will continue to restore their gullies with the support of a programme or network. It is our recommendation that the Plants for Gullies Programme is reinstated before this community loses momentum.

text: Evaluation of vegetation and stream health within sites supported by the Hamilton City Council Plants for Gullies Programme Between August 2012 and March 2013, the Environmental Research Institute, University of Waikato, conducted a survey of randomly selected Hamilton gully sites which had received plants from the Hamilton City Council’s Plants for Gullies Programme. This survey assessed recent plantings, existing gully vegetation and stream health, along with property owner awareness and engagement with the key restoration principles. 
The Plants for Gullies Programme has been extremely well received by the Hamilton community and gully owners. Survey participants were actively restoring their gully sites with the most common goal (c. 40%) being the establishment of native plant dominance within 10 years. Gully owners have a good understanding of restoration theory and practise; on average, plant placement in the gullies scored 15.7 out of 20 with consideration of plant environmental requirements and the concept of ecosourcing was understood by c. 76% of landowners surveyed. Also, most of the interviewed participants (c. 80%) were active in seeking guidance from other gullies, often through organised tours. 
Current stream health was qualitatively assessed and characterised at each of the gully sites. Results provide baseline data for future monitoring. The majority of surveyed sites (c. 50%) had sand or silt substrate and the Bankwood gully had the best features for fauna habitat (e.g. debris and areas of low flow). At the time of visit, c. 60% of surveyed streams had clear water clarity. The poorest water clarity scores were in the Waitawhiriwhiri gully. When assessed on width, length and density, the average riparian buffer score was 12.8 out of 20 while the average stream shading score was 12.7 out of 20. The average bank stability score was 13.1 out of 20, reflecting an erosion problem that many gully owners talked about. 
Surveyed gullies were diverse in terms of native and exotic vegetation structure and composition; native species contributed between c. 30% to 100% of surveyed trees and shrubs, whereas groundcovers were predominantly exotic. This assessment of gully sites has shown that the Plants for Gullies Programme improves native species diversity through the re-introduction of species that are not naturally regenerating. The Plants for Gullies programme is a powerful tool for engaging private landowners and making cost-effective change to Hamilton City’s native biodiversity. There is now a community of willing gully owners who will continue to restore their gullies with the support of a programme or network. It is our recommendation that the Plants for Gullies Programme is reinstated before this community loses momentum.

year: 2013

title: Listening to the Winds of Change: Assessing culturally responsive and relational pedagogy

authors: Thin-Rabb, Polly

subjects: Culturally responsive and relational pedagogy

abstract: This thesis examines how the Rongohia te Hau tools were used to capture a snapshot of the extent that culturally responsive and relational pedagogies were occurring within classrooms in two English-medium secondary schools in Aotearoa, New Zealand. In this study, school leaders used Rongohia te Hau to measure changes in the educational experiences of Māori learners over twelve to eighteen-months, to prioritise next steps in addressing the educational inequities that were evident. 

With the contribution of teachers, leaders and kaitoro (Kia Eke Panuku facilitators), this research investigates the purpose and place of Rongohia te Hau within the Kia Eke Panuku professional learning and development context. It also presents and discusses the pedagogical shifts that occurred in these two schools over the period of this research, as evidenced by quantitative and qualitative Rongohia te Hau data. Furthermore, the learning implications that arose out of this research are analysed to help generate new questions and considerations, to enable continuing conversations for these schools, other schools, professional learning and development providers and researchers.

text: Listening to the Winds of Change: Assessing culturally responsive and relational pedagogy This thesis examines how the Rongohia te Hau tools were used to capture a snapshot of the extent that culturally responsive and relational pedagogies were occurring within classrooms in two English-medium secondary schools in Aotearoa, New Zealand. In this study, school leaders used Rongohia te Hau to measure changes in the educational experiences of Māori learners over twelve to eighteen-months, to prioritise next steps in addressing the educational inequities that were evident. 

With the contribution of teachers, leaders and kaitoro (Kia Eke Panuku facilitators), this research investigates the purpose and place of Rongohia te Hau within the Kia Eke Panuku professional learning and development context. It also presents and discusses the pedagogical shifts that occurred in these two schools over the period of this research, as evidenced by quantitative and qualitative Rongohia te Hau data. Furthermore, the learning implications that arose out of this research are analysed to help generate new questions and considerations, to enable continuing conversations for these schools, other schools, professional learning and development providers and researchers.

year: 2017