title: Investigating the Professional Knowledge of New Zealand Primary School Teachers when Teaching Mathematics for Numeracy

authors: Mills, Judith Patricia

abstract: This research investigated the relationship between teachers’ espoused professional knowledge, professional knowledge in practice, and student learning, when teaching ‘mathematics for numeracy’ in the New Zealand primary school classroom. The focus was on teaching within the multiplicative and proportional domains, as research at the time the study commenced indicated that these areas of mathematics were problematic for many teachers. The purpose of the research was to identify strengths, weaknesses, and inconsistencies in teachers’ practice; links between espoused views and actions; and to consider the usefulness of a framework for investigating teacher knowledge in practice. This study is intended to inform teacher reflection and professional development, and contribute to improvements in teaching practice and student achievement.
A multiple-case study design, underpinned by an interpretivist paradigm, was used, which included four case-study teachers from two primary schools: School A, was a central city full primary school (Years 1 to 8) and School B, a rural town primary school (Years 1 to 6). The study aligned with a social constructivist perspective on teaching and learning. The data were obtained through four main sources: (1) pre-unit and post-unit student assessment tasks; (2) recorded observations; (3) semi-structured interviews); and (4) teacher questionnaires. 
Comparison between students’ initial and final assessment data showed little progress in understanding of multiplication and division, with a more noticeable improvement in fractional understanding. Classroom observations were analysed under three broad categories: content knowledge, pedagogical knowledge, and pedagogical content knowledge, and highlighted important issues relating to the professional knowledge of teachers and the contribution this made to student learning. Results indicated that the mathematical content knowledge of the teachers was stronger than their content knowledge in a pedagogical context. While teaching for conceptual understanding frequently challenged the teachers, they recognised the importance of conceptual understanding prior to procedural learning for their students. They struggled with on-the-spot identification of the next steps of learning for individual students and there was little evidence of focus on questioning that extended students’ thinking that might have assisted in overcoming misconceptions and confusions with concepts. There were times when the teachers’ espoused theories differed from their theory-in-practice, while at times they were similar to each other.
The research concluded that in teaching practice the many facets of PCK, within the broader construct of professional knowledge, were more than topic-specific. Instead, they were person-specific and lesson-specific, with different categories coming to the fore in different proportions, for different reasons, including: lesson structure, context, problem types, the opportunities afforded students for conversation, and use of manipulatives. While not all categories of professional knowledge were evident in every lesson, they combined over a period to underscore the complexities of teaching and ultimately have an effect on student learning. 
An outcome of the study was a Wheel of Knowledge designed for teachers, identifying key areas of knowledge to be addressed in mathematics teaching. Alongside this, a more detailed Professional Knowledge Framework was created for researchers, based on categories identified from this research as important in identifying teacher professional knowledge in classroom practice. Both models have the potential to identify areas of teacher professional knowledge required to improve students’ mathematical understanding.

text: Investigating the Professional Knowledge of New Zealand Primary School Teachers when Teaching Mathematics for Numeracy This research investigated the relationship between teachers’ espoused professional knowledge, professional knowledge in practice, and student learning, when teaching ‘mathematics for numeracy’ in the New Zealand primary school classroom. The focus was on teaching within the multiplicative and proportional domains, as research at the time the study commenced indicated that these areas of mathematics were problematic for many teachers. The purpose of the research was to identify strengths, weaknesses, and inconsistencies in teachers’ practice; links between espoused views and actions; and to consider the usefulness of a framework for investigating teacher knowledge in practice. This study is intended to inform teacher reflection and professional development, and contribute to improvements in teaching practice and student achievement.
A multiple-case study design, underpinned by an interpretivist paradigm, was used, which included four case-study teachers from two primary schools: School A, was a central city full primary school (Years 1 to 8) and School B, a rural town primary school (Years 1 to 6). The study aligned with a social constructivist perspective on teaching and learning. The data were obtained through four main sources: (1) pre-unit and post-unit student assessment tasks; (2) recorded observations; (3) semi-structured interviews); and (4) teacher questionnaires. 
Comparison between students’ initial and final assessment data showed little progress in understanding of multiplication and division, with a more noticeable improvement in fractional understanding. Classroom observations were analysed under three broad categories: content knowledge, pedagogical knowledge, and pedagogical content knowledge, and highlighted important issues relating to the professional knowledge of teachers and the contribution this made to student learning. Results indicated that the mathematical content knowledge of the teachers was stronger than their content knowledge in a pedagogical context. While teaching for conceptual understanding frequently challenged the teachers, they recognised the importance of conceptual understanding prior to procedural learning for their students. They struggled with on-the-spot identification of the next steps of learning for individual students and there was little evidence of focus on questioning that extended students’ thinking that might have assisted in overcoming misconceptions and confusions with concepts. There were times when the teachers’ espoused theories differed from their theory-in-practice, while at times they were similar to each other.
The research concluded that in teaching practice the many facets of PCK, within the broader construct of professional knowledge, were more than topic-specific. Instead, they were person-specific and lesson-specific, with different categories coming to the fore in different proportions, for different reasons, including: lesson structure, context, problem types, the opportunities afforded students for conversation, and use of manipulatives. While not all categories of professional knowledge were evident in every lesson, they combined over a period to underscore the complexities of teaching and ultimately have an effect on student learning. 
An outcome of the study was a Wheel of Knowledge designed for teachers, identifying key areas of knowledge to be addressed in mathematics teaching. Alongside this, a more detailed Professional Knowledge Framework was created for researchers, based on categories identified from this research as important in identifying teacher professional knowledge in classroom practice. Both models have the potential to identify areas of teacher professional knowledge required to improve students’ mathematical understanding.

year: 2018

title: Developing an understanding of higher education science and engineering learning communities

authors: Coll, Richard K.

subjects: higher education

abstract: This article sets the scene for this special issue of Research in Science & Technological Education, dedicated to understanding higher education science and engineering learning communities. We examine what the literature has to say about the nature of, and factors influencing, higher education learning communities. A discussion of issues in, and synthesis of, research into higher education learning communities completes the paper. This paper clearly identifies a need to better understand higher education learning communities: their nature, influential factors and forces that shape our higher education learning communities.

text: Developing an understanding of higher education science and engineering learning communities This article sets the scene for this special issue of Research in Science & Technological Education, dedicated to understanding higher education science and engineering learning communities. We examine what the literature has to say about the nature of, and factors influencing, higher education learning communities. A discussion of issues in, and synthesis of, research into higher education learning communities completes the paper. This paper clearly identifies a need to better understand higher education learning communities: their nature, influential factors and forces that shape our higher education learning communities.

year: 2008

title: Identifying fisheries regions in New Zealand: Some conceptual difficulties

authors: Rennie, Hamish Gordon

subjects: Fisheries

abstract: The importance of fisheries to nations is reflected in the production and employment statistics of the country. It is also reflected in socio-cultural symbols (for instance songs, tales), and in socio-political hegemonies.  Just as these may vary from one nation to another, they may also vary from region to region within a nation.  Several nations speak openly in terms of 'fisheries regions' and there have been a number of attempts to identify such regions in the social science literature. An understanding of these regions is seen as step towards defining appropriate policies for the sustainable management of their resources.

In 1986, New Zealand established an innovative fishery management system based on individually transferable quota (ITQ), and subsequently removed the (never-implemented) region-based, fishery management planning structure from the statutes.  These changes might be indicative of a loss of geography, a flattening of the nation's "fishing topography", and might be expected to result in significant changes to the nature and location of fisheries regions.

This paper outlines the changes in the management structure of New Zealand's fisheries. We then attempt a preliminary analysis of fisheries regions in New Zealand as the basis for a "new regional" geography of New Zealand's fisheries. In the process we discuss various criteria for defining fishery regions and present our initial categorisation of New Zealand into those regions. The relationship between these regions and related institutional structures is then discussed. This raises a number of additional questions regarding the concept of a fisheries region, especially in the context of a resurgent indigenous (Maaori) culture, the emergence of new fishing peoples in New Zealand, and the respective size of recreational and commercial fishing sectors.

text: Identifying fisheries regions in New Zealand: Some conceptual difficulties The importance of fisheries to nations is reflected in the production and employment statistics of the country. It is also reflected in socio-cultural symbols (for instance songs, tales), and in socio-political hegemonies.  Just as these may vary from one nation to another, they may also vary from region to region within a nation.  Several nations speak openly in terms of 'fisheries regions' and there have been a number of attempts to identify such regions in the social science literature. An understanding of these regions is seen as step towards defining appropriate policies for the sustainable management of their resources.

In 1986, New Zealand established an innovative fishery management system based on individually transferable quota (ITQ), and subsequently removed the (never-implemented) region-based, fishery management planning structure from the statutes.  These changes might be indicative of a loss of geography, a flattening of the nation's "fishing topography", and might be expected to result in significant changes to the nature and location of fisheries regions.

This paper outlines the changes in the management structure of New Zealand's fisheries. We then attempt a preliminary analysis of fisheries regions in New Zealand as the basis for a "new regional" geography of New Zealand's fisheries. In the process we discuss various criteria for defining fishery regions and present our initial categorisation of New Zealand into those regions. The relationship between these regions and related institutional structures is then discussed. This raises a number of additional questions regarding the concept of a fisheries region, especially in the context of a resurgent indigenous (Maaori) culture, the emergence of new fishing peoples in New Zealand, and the respective size of recreational and commercial fishing sectors.

year: 1998-06-01