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: Agglomeration elasticities and firm heterogeneity

authors: Maré, David C.

subjects: agglomeration

abstract: This paper examines three key issues encountered when estimating the relationship between agglomeration and multi factor productivity ('agglomeration elasticities'): the sorting of heterogeneous firms, the convexity of agglomeration effects, and the challenges of identifying the impact of persistent spatial differences in effective density. We use a firm-level panel containing production data together with detailed information on the geographic location of employment, covering a high proportion of the New Zealand economy. We are able to control for heterogeneity along firm, region, and industry dimensions, and to estimate separate agglomeration elasticities across industries and regions. Sorting leads to upward biased elasticity estimates but using firm fixed effects can lead to downward bias due to the highly persistent nature of agglomeration variables. Our preferred estimates control for sorting across regions and industries. Overall, we find a positive agglomeration elasticity of 0.066. Within industries and, to a lesser extent within regions, there is pronounced variation in the strength of agglomeration effects, and evidence of decreasing returns to agglomeration. High density areas attract firms that benefit most from agglomeration.

text: Agglomeration elasticities and firm heterogeneity This paper examines three key issues encountered when estimating the relationship between agglomeration and multi factor productivity ('agglomeration elasticities'): the sorting of heterogeneous firms, the convexity of agglomeration effects, and the challenges of identifying the impact of persistent spatial differences in effective density. We use a firm-level panel containing production data together with detailed information on the geographic location of employment, covering a high proportion of the New Zealand economy. We are able to control for heterogeneity along firm, region, and industry dimensions, and to estimate separate agglomeration elasticities across industries and regions. Sorting leads to upward biased elasticity estimates but using firm fixed effects can lead to downward bias due to the highly persistent nature of agglomeration variables. Our preferred estimates control for sorting across regions and industries. Overall, we find a positive agglomeration elasticity of 0.066. Within industries and, to a lesser extent within regions, there is pronounced variation in the strength of agglomeration effects, and evidence of decreasing returns to agglomeration. High density areas attract firms that benefit most from agglomeration.

year: 2013

title: What is Māori typography?

authors: Kennedy, Nikki Eileen

subjects: Māori Design

abstract: Te Reo Māori was traditionally an oral language similar to many indigenous cultures. Writing systems were not familiar to Māori until 1769 where Māori were introduced to the written language by Pākehā. Early Māori writing can be found printed, carved and painted in a number of different parts of Māori society. These myriad texts were strongly influenced and inspired by Pākehā biblical texts and newspapers. The influence of Pākehā texts meant that overtime the written language of Te Reo Māori had a Pākehā visual identity.

To date, there is minimal research about the history and visual identity of Māori typography. The lack of research and resources about Māori typography confirms how underdeveloped Māori typography is and highlights the potential for research and development in this space.

This thesis aims to explore Māori typography. In particular, this thesis will provide an understanding of how Māori typography has evolved, addressing the perceptions of Māori text features and advice on design guidance of Māori typography.

Two studies within this thesis involved analysing the text-based features in 21 Māori newspapers dated from 1842-1935. Māori newspapers are a valuable resource that captured moments in history and also early displays of Māori text. The second study involved interviews with 50 participants — Māori and non-Māori, from a range of different backgrounds — who provided their understandings and perceptions surrounding the features of Māori text.

The results from these studies have shown that the serif typeface classification was commonly used in early print such as Māori newspapers. Serif lettering also reminded participants in our studies of early Māori texts such as old text books and newspapers. This appears to be the reason as to why, a strong theme of serifs and the style of Didone typefaces have been used throughout Māori typography and by default are recognised features of Māori typefaces today.

Having analysed Māori newspapers, an unexpected finding appeared in the 1908 Te Pipiwharauroa newspaper. Two unique letter characters were found that was revolution for Te Reo Māori text of the time. This oddity combined the ‘ng’ letters into one letter character and the ‘wh’ letters into one letter character also. The aim in combining the two letters together was to emphasise the one sound that the ‘ng’ and the ‘wh’ make to avoid confusion in the pronunciation of Māori words. The results showed that these two letter characters appeared from 1908 through to 1912. There is no evidence of these characters appearing after 1912 and also appearing in other newspapers. The two characters were a rare appearance of its time.

As a result of this research it is clear that the visual identity of Te Reo Māori remains unclear and was highly influenced by serif lettering. This thesis highlights the need for more research about Māori typography and design guidance for developing appropriate Māori typefaces that are influenced and inspired by Maori culture.

text: What is Māori typography? Te Reo Māori was traditionally an oral language similar to many indigenous cultures. Writing systems were not familiar to Māori until 1769 where Māori were introduced to the written language by Pākehā. Early Māori writing can be found printed, carved and painted in a number of different parts of Māori society. These myriad texts were strongly influenced and inspired by Pākehā biblical texts and newspapers. The influence of Pākehā texts meant that overtime the written language of Te Reo Māori had a Pākehā visual identity.

To date, there is minimal research about the history and visual identity of Māori typography. The lack of research and resources about Māori typography confirms how underdeveloped Māori typography is and highlights the potential for research and development in this space.

This thesis aims to explore Māori typography. In particular, this thesis will provide an understanding of how Māori typography has evolved, addressing the perceptions of Māori text features and advice on design guidance of Māori typography.

Two studies within this thesis involved analysing the text-based features in 21 Māori newspapers dated from 1842-1935. Māori newspapers are a valuable resource that captured moments in history and also early displays of Māori text. The second study involved interviews with 50 participants — Māori and non-Māori, from a range of different backgrounds — who provided their understandings and perceptions surrounding the features of Māori text.

The results from these studies have shown that the serif typeface classification was commonly used in early print such as Māori newspapers. Serif lettering also reminded participants in our studies of early Māori texts such as old text books and newspapers. This appears to be the reason as to why, a strong theme of serifs and the style of Didone typefaces have been used throughout Māori typography and by default are recognised features of Māori typefaces today.

Having analysed Māori newspapers, an unexpected finding appeared in the 1908 Te Pipiwharauroa newspaper. Two unique letter characters were found that was revolution for Te Reo Māori text of the time. This oddity combined the ‘ng’ letters into one letter character and the ‘wh’ letters into one letter character also. The aim in combining the two letters together was to emphasise the one sound that the ‘ng’ and the ‘wh’ make to avoid confusion in the pronunciation of Māori words. The results showed that these two letter characters appeared from 1908 through to 1912. There is no evidence of these characters appearing after 1912 and also appearing in other newspapers. The two characters were a rare appearance of its time.

As a result of this research it is clear that the visual identity of Te Reo Māori remains unclear and was highly influenced by serif lettering. This thesis highlights the need for more research about Māori typography and design guidance for developing appropriate Māori typefaces that are influenced and inspired by Maori culture.

year: 2020