title: Row-column block designs: Efficiency and structure

authors: Nie, Xiao

subjects: Latin Squares

abstract: A row-column design is any rearrangement of the blocks of a combinatorial design into a rectangular array. A row-column block design is a row-column design in which the blocks form a balanced incomplete block design; that is, each pair of elements occurs in a constant number of blocks. In this thesis we study the efficiency and structure of row-column block designs. In particular, we use solutions to Heffter’s difference problem to give construct row-column block designs with 3 elements per cell with optimal regularity in rows and columns.
In Section 1 we review definitions and theorems related to Latin squares. We introduce related concepts of balanced incomplete block designs and incidence matrix and concurrence matrix of designs. In Section 2 we give our main results of row-column block designs with block size 3. In Section 3 we use Heffter’s difference problem to give some solutions. In Section 4 we explain efficiency measures for block designs. In Section 5 we introduce Trojan semi-Latin squares. We give efficiency measures for Trojan semi-Latin squares. In Section 6 we show the applications to experimental design. Original results are given in the following theorems: Theorem 2.9, Theorem 3.1, Theorem 3.3, Theorem 3.4, Theorem 4.2, Theorem 5.2, Theorem 5.12.
Results from Section 2 and Section 3 have been submitted as a manuscript for publication [17] (Xiao Nie, Row-column block designs with blocks of size three, Ars Combinatoria, submitted).

text: Row-column block designs: Efficiency and structure A row-column design is any rearrangement of the blocks of a combinatorial design into a rectangular array. A row-column block design is a row-column design in which the blocks form a balanced incomplete block design; that is, each pair of elements occurs in a constant number of blocks. In this thesis we study the efficiency and structure of row-column block designs. In particular, we use solutions to Heffter’s difference problem to give construct row-column block designs with 3 elements per cell with optimal regularity in rows and columns.
In Section 1 we review definitions and theorems related to Latin squares. We introduce related concepts of balanced incomplete block designs and incidence matrix and concurrence matrix of designs. In Section 2 we give our main results of row-column block designs with block size 3. In Section 3 we use Heffter’s difference problem to give some solutions. In Section 4 we explain efficiency measures for block designs. In Section 5 we introduce Trojan semi-Latin squares. We give efficiency measures for Trojan semi-Latin squares. In Section 6 we show the applications to experimental design. Original results are given in the following theorems: Theorem 2.9, Theorem 3.1, Theorem 3.3, Theorem 3.4, Theorem 4.2, Theorem 5.2, Theorem 5.12.
Results from Section 2 and Section 3 have been submitted as a manuscript for publication [17] (Xiao Nie, Row-column block designs with blocks of size three, Ars Combinatoria, submitted).

year: 2024-09-23

title: Teachers’ reflecting on professional knowledge in the numeracy (mathematics) classroom

authors: Mills, Judith Patricia

abstract: New Zealand primary school teachers are expected to regularly reflect on their teaching practice in order to consider the implications of past teaching on future planning. Aligned to teachers’ ongoing reflection, the New Zealand Curriculum (Ministry of Education, 2007) contains a section on effective pedagogy—teacher actions promoting student learning, which includes a Teaching as Inquiry Cycle (pp. 34–35). Embedded within their inquiry, teachers consider the teaching-learning relationship and often turn to frameworks of knowledge for guidance. This article shares the implications of using a framework of teacher knowledge in research. While the framework used contained much detail for the researcher, it overlapped categories and at the same time lacked acknowledgement of some important concepts for teachers in classroom practice. Findings from using a framework in this research were combined with findings from previous research to formulate the Wheel of Professional Knowledge, which was developed for mathematics teachers to use when reflecting on their practice.

text: Teachers’ reflecting on professional knowledge in the numeracy (mathematics) classroom New Zealand primary school teachers are expected to regularly reflect on their teaching practice in order to consider the implications of past teaching on future planning. Aligned to teachers’ ongoing reflection, the New Zealand Curriculum (Ministry of Education, 2007) contains a section on effective pedagogy—teacher actions promoting student learning, which includes a Teaching as Inquiry Cycle (pp. 34–35). Embedded within their inquiry, teachers consider the teaching-learning relationship and often turn to frameworks of knowledge for guidance. This article shares the implications of using a framework of teacher knowledge in research. While the framework used contained much detail for the researcher, it overlapped categories and at the same time lacked acknowledgement of some important concepts for teachers in classroom practice. Findings from using a framework in this research were combined with findings from previous research to formulate the Wheel of Professional Knowledge, which was developed for mathematics teachers to use when reflecting on their practice.

year: 2020

title: He Pikinga Waiora Implementation Framework: A tool for chronic disease intervention effectiveness in Maori and other indigenous communities

authors: Oetzel, John G.

subjects: Science & Technology

abstract: Introduction: Health outcomes for Māori are significantly worse than non-Maori in New Zealand; these inequities mirror those found in indigenous communities elsewhere. Evidence-based interventions with established efficacy may not be effective in indigenous communities without addressing specific implementation challenges. We present an implementation framework for chronic condition interventions for Māori.

Theory/Methods: The He Pikinga Waiora Implementation Framework has indigenous self-determination at its core and consists of four elements: cultural-centeredness, community engagement, systems thinking, and integrated knowledge translation.  All elements have demonstrated evidence of positive implementation outcomes.  A coding scheme derived from the Framework was applied to 13 studies of diabetes prevention in indigenous communities from a systematic review.

Results: Cross-tabulations demonstrated that culture-centeredness (p=.008) and community engagement (p=.009) explained differences in diabetes outcomes and community engagement (p=.098) explained difference in blood pressure outcomes.

Discussion and Conclusions: The He Pikinga Waiora Implementation Framework is well suited to advance implementation science for Māori and other indigenous communities. The framework has promise as a policy and planning tool to evaluate and design effective interventions for chronic disease prevention.

Lessons Learned: We needed to revise the coding framework in order to make the implication framework concrete.

Limitations: This study has a limitation in that we coded information about interventions from the published articles and not the interventions themselves. Additionally, the study only included 13 interventions.

Suggestions for Future Direction: Further research should provide stronger evidence of the usefulness of the framework particularly with Māori end-users. There will also be a need to understand the differential contribution of each of the four elements to health outcomes.

text: He Pikinga Waiora Implementation Framework: A tool for chronic disease intervention effectiveness in Maori and other indigenous communities Introduction: Health outcomes for Māori are significantly worse than non-Maori in New Zealand; these inequities mirror those found in indigenous communities elsewhere. Evidence-based interventions with established efficacy may not be effective in indigenous communities without addressing specific implementation challenges. We present an implementation framework for chronic condition interventions for Māori.

Theory/Methods: The He Pikinga Waiora Implementation Framework has indigenous self-determination at its core and consists of four elements: cultural-centeredness, community engagement, systems thinking, and integrated knowledge translation.  All elements have demonstrated evidence of positive implementation outcomes.  A coding scheme derived from the Framework was applied to 13 studies of diabetes prevention in indigenous communities from a systematic review.

Results: Cross-tabulations demonstrated that culture-centeredness (p=.008) and community engagement (p=.009) explained differences in diabetes outcomes and community engagement (p=.098) explained difference in blood pressure outcomes.

Discussion and Conclusions: The He Pikinga Waiora Implementation Framework is well suited to advance implementation science for Māori and other indigenous communities. The framework has promise as a policy and planning tool to evaluate and design effective interventions for chronic disease prevention.

Lessons Learned: We needed to revise the coding framework in order to make the implication framework concrete.

Limitations: This study has a limitation in that we coded information about interventions from the published articles and not the interventions themselves. Additionally, the study only included 13 interventions.

Suggestions for Future Direction: Further research should provide stronger evidence of the usefulness of the framework particularly with Māori end-users. There will also be a need to understand the differential contribution of each of the four elements to health outcomes.

year: 2018