title: Maximum margin principal components

authors: Luo, Xianghui

subjects: Machine learning

abstract: Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first $K$ principal components minimizes the sum of squared errors between the original data and the projected data over all possible rank $K$ projections. Thus, PCA provides optimal low-rank representations of data for least-squares linear regression under standard modeling assumptions. On the other hand, when the loss function for a prediction problem is not the least-squares error, PCA is typically a heuristic choice of dimensionality reduction -- in particular for classification problems under the zero-one loss. In this paper we target classification problems by proposing a straightforward alternative to PCA that aims to minimize the difference in margin distribution between the original and the projected data. Extensive experiments show that our simple approach typically outperforms PCA on any particular dataset, in terms of classification error, though this difference is not always statistically significant, and despite being a filter method is frequently competitive with Partial Least Squares (PLS) and Lasso on a wide range of datasets.

text: Maximum margin principal components Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first $K$ principal components minimizes the sum of squared errors between the original data and the projected data over all possible rank $K$ projections. Thus, PCA provides optimal low-rank representations of data for least-squares linear regression under standard modeling assumptions. On the other hand, when the loss function for a prediction problem is not the least-squares error, PCA is typically a heuristic choice of dimensionality reduction -- in particular for classification problems under the zero-one loss. In this paper we target classification problems by proposing a straightforward alternative to PCA that aims to minimize the difference in margin distribution between the original and the projected data. Extensive experiments show that our simple approach typically outperforms PCA on any particular dataset, in terms of classification error, though this difference is not always statistically significant, and despite being a filter method is frequently competitive with Partial Least Squares (PLS) and Lasso on a wide range of datasets.

year: 2017

title: Learning in the 21st century: Empowering student-centred practices through curriculum integration

authors: Morgan, Jason

subjects: student-centred

abstract: The New Zealand Curriculum [NZC] provides a framework for schools to design and implement the curriculum at three levels: Nationally, school- wide, and in the classroom (Ministry of Education [MoE], 2007). Through a student-centred approach, which the NZC supports, a culturally-responsive curriculum that integrates subject matter from the learning areas with the ‘front-end’ values and key competencies is advocated, promoting the interests of students, their whānau and communities (Dowden, 2010; Fraser & Paraha, 2002). Curriculum integration [CI] is a curriculum design theory, which values students and the world they live in as the main source of curriculum, and as a result of the democratic teaching pedagogy that underpins this practice, acknowledges students as active collaborators throughout the learning process (Brough, 2008a). When students are positioned as curriculum decision-makers and have their voice heard and valued, equal power relationships can be established, enriching and positively influencing student motivation, achievement, and engagement (Brough, 2012).

As Beane (1995) explains, CI is a fundamental realignment of thinking about the purpose of schools, and the sources and purposes of curriculum and knowledge. When students are actively encouraged to engage with learning experiences relevant to their lives, knowledge is acquired in an organic way and developed through meaningful, real-life purposes. When a school’s curriculum is designed to relate to both students’ and their communities’ needs and interests, students are no longer placed as consumers of information, but rather as producers of knowledge (Boyd, 2013). By integrating powerful learning environments in their classes which values students’ voice and supports active, autonomous and collaborative learning, teachers and students are engaged in open-ended, democratic decision- making around curriculum decisions. This can enable the fostering of confident, connected, actively involved, lifelong learners (Brough, 2008b; MoE, 2007).

The aim of this thesis was to explore how teachers in the primary school, in particular the senior setting of primary schools, are integrating the curriculum to encourage student-centred practices. It is hoped that this study will illuminate potential ways classroom practice can empower student-centred pedagogy and position students at the centre of educational decision-making. It was anticipated this project would contribute to the limited research in this field in both the primary and New Zealand school contexts.

A critical theoretical framework underpinned this study as it naturally aligned with the research question and the project’s aims. A case study methodology was adopted which used a variety of methods, including semi- structured interviews, naturalistic observations, photographs and documentation.

Through this study it was found student-centred curriculum integration can provide a powerful and motivating curriculum framework and pedagogy for learning in the 21st century. Through a pedagogy that is underpinned by democratic principles and practices, students can develop critical and creative thinking skills. These skills empower students to ‘perform’ knowledge across authentic, real-life contexts. This not only prepares students to lead fulfilling and rewarding lives as active participants within society, but promotes emancipatory ideals leading to beneficial outcomes for communities. This study argues how through curriculum integration, teachers can find ways to empower student-centred practices.

text: Learning in the 21st century: Empowering student-centred practices through curriculum integration The New Zealand Curriculum [NZC] provides a framework for schools to design and implement the curriculum at three levels: Nationally, school- wide, and in the classroom (Ministry of Education [MoE], 2007). Through a student-centred approach, which the NZC supports, a culturally-responsive curriculum that integrates subject matter from the learning areas with the ‘front-end’ values and key competencies is advocated, promoting the interests of students, their whānau and communities (Dowden, 2010; Fraser & Paraha, 2002). Curriculum integration [CI] is a curriculum design theory, which values students and the world they live in as the main source of curriculum, and as a result of the democratic teaching pedagogy that underpins this practice, acknowledges students as active collaborators throughout the learning process (Brough, 2008a). When students are positioned as curriculum decision-makers and have their voice heard and valued, equal power relationships can be established, enriching and positively influencing student motivation, achievement, and engagement (Brough, 2012).

As Beane (1995) explains, CI is a fundamental realignment of thinking about the purpose of schools, and the sources and purposes of curriculum and knowledge. When students are actively encouraged to engage with learning experiences relevant to their lives, knowledge is acquired in an organic way and developed through meaningful, real-life purposes. When a school’s curriculum is designed to relate to both students’ and their communities’ needs and interests, students are no longer placed as consumers of information, but rather as producers of knowledge (Boyd, 2013). By integrating powerful learning environments in their classes which values students’ voice and supports active, autonomous and collaborative learning, teachers and students are engaged in open-ended, democratic decision- making around curriculum decisions. This can enable the fostering of confident, connected, actively involved, lifelong learners (Brough, 2008b; MoE, 2007).

The aim of this thesis was to explore how teachers in the primary school, in particular the senior setting of primary schools, are integrating the curriculum to encourage student-centred practices. It is hoped that this study will illuminate potential ways classroom practice can empower student-centred pedagogy and position students at the centre of educational decision-making. It was anticipated this project would contribute to the limited research in this field in both the primary and New Zealand school contexts.

A critical theoretical framework underpinned this study as it naturally aligned with the research question and the project’s aims. A case study methodology was adopted which used a variety of methods, including semi- structured interviews, naturalistic observations, photographs and documentation.

Through this study it was found student-centred curriculum integration can provide a powerful and motivating curriculum framework and pedagogy for learning in the 21st century. Through a pedagogy that is underpinned by democratic principles and practices, students can develop critical and creative thinking skills. These skills empower students to ‘perform’ knowledge across authentic, real-life contexts. This not only prepares students to lead fulfilling and rewarding lives as active participants within society, but promotes emancipatory ideals leading to beneficial outcomes for communities. This study argues how through curriculum integration, teachers can find ways to empower student-centred practices.

year: 2014

title: Popoia te reo kia penapena: Nurture the language

authors: Berryman, Mere

subjects: Maori language

abstract: Research to develop a Māori language screening tool (Specialist Education Services, 2001), identified that students entering Māori Medium at five, could be classified into one of four Māori language competency, groups. Concurrently, teachers raised their need to identify the Māori language proficiency of five year olds entering Māori Medium so that more appropriate teaching strategies could be incorporated in preparation for literacy.
Accordingly, three Māori oral-language assessment tools, to help identify the Māori language competency of students entering Māori Medium settings at five years of age and provide formative information, were developed in response to this need. This paper details the development and trial of these tools.

text: Popoia te reo kia penapena: Nurture the language Research to develop a Māori language screening tool (Specialist Education Services, 2001), identified that students entering Māori Medium at five, could be classified into one of four Māori language competency, groups. Concurrently, teachers raised their need to identify the Māori language proficiency of five year olds entering Māori Medium so that more appropriate teaching strategies could be incorporated in preparation for literacy.
Accordingly, three Māori oral-language assessment tools, to help identify the Māori language competency of students entering Māori Medium settings at five years of age and provide formative information, were developed in response to this need. This paper details the development and trial of these tools.

year: 2009