title: On the distances between Latin squares and the smallest defining set size

authors: Cavenagh, Nicholas J.

subjects: mathematics

abstract: We show that for each Latin square L of order n ≥ 2 , there exists a Latin square  L’ ≠ L of order n such that L and L’  differ in at most 8√n̅ cells. Equivalently, each Latin square of order n contains a Latin trade of size at most 8√n̅ . We also show that the size of the smallest defining set in a Latin square is Ω(n³/²).

text: On the distances between Latin squares and the smallest defining set size We show that for each Latin square L of order n ≥ 2 , there exists a Latin square  L’ ≠ L of order n such that L and L’  differ in at most 8√n̅ cells. Equivalently, each Latin square of order n contains a Latin trade of size at most 8√n̅ . We also show that the size of the smallest defining set in a Latin square is Ω(n³/²).

year: 2016

title: Developing statistical literacy with Year 9 students: a collaborative research project

authors: Sharma, Sashi

abstract: Advances in technology and communication have increased the amount of statistical information delivered through everyday media. The importance of statistics in everyday life has led to calls for increased attention to statistical literacy in the mathematics curriculum (Watson 2006). Gal (2004) sees statistical literacy as the need for students to be able to interpret results from studies and media reports and to be able to pose critical and reflective questions about those reports. Aspects of Gal’s notion of statistical literacy have been incorporated in the New Zealand Curriculum (Ministry of Education 2007).

text: Developing statistical literacy with Year 9 students: a collaborative research project Advances in technology and communication have increased the amount of statistical information delivered through everyday media. The importance of statistics in everyday life has led to calls for increased attention to statistical literacy in the mathematics curriculum (Watson 2006). Gal (2004) sees statistical literacy as the need for students to be able to interpret results from studies and media reports and to be able to pose critical and reflective questions about those reports. Aspects of Gal’s notion of statistical literacy have been incorporated in the New Zealand Curriculum (Ministry of Education 2007).

year: 2013

title: Barriers and facilitators to colorectal cancer diagnosis in New Zealand: a qualitative study

authors: Blackmore, Tania Louise

subjects: Science & Technology

abstract: Background: New Zealand (NZ) has high rates of colorectal cancer but low rates of early diagnosis. Due to a lack of understanding of the pre-diagnostic experience from the patient’s perspective, it is necessary to investigate potential patient and health system factors that contribute to longer diagnostic intervals. Previous qualitative studies have discussed delays using The Model of Pathways to Treatment, but this has not been explored in the NZ context. This study aimed to understand the patient experience and perception of their general practitioner (GP) through the diagnostic process in the Waikato region of NZ. In particular, we sought to investigate potential barriers and facilitators that contribute to longer diagnostic intervals. 
Methods: Ethical approval for this study was granted by the New Zealand Health and Disability Ethics Committee. Twenty-eight participants, diagnosed with colorectal cancer, were interviewed about their experience. Semi-structured interviews were audio recorded, transcribed verbatim and analysed thematically using The Model of Pathways to Treatment framework (intervals: appraisal, help-seeking, diagnostic). 
Results: Participant appraisal of symptoms was a barrier to prompt diagnosis, particularly if symptoms were normalised, intermittent, or isolated in occurrence. Successful self-management techniques also resulted in delayed help-seeking. However if symptoms worsened, disruption to work and daily routines were important facilitators to seeking a GP consultation. Participants positively appraised GPs if they showed good technical competence and were proactive in investigating symptoms. Negative GP appraisals were associated with a lack of physical examinations and misdiagnosis, and left participants feeling dehumanised during the diagnostic process. However high levels of GP interpersonal competence could override poor technical competence, resulting in an overall positive experience, even if the cancer was diagnosed at an advanced stage. Māori participants often appraised symptoms inclusive of their sociocultural environment and considered the impact of their symptoms in relation to family. 
Conclusions: The findings of this study highlight the importance of tailored colorectal cancer symptom communication in health campaigns, and indicate the significance of the interpersonal competence aspect of GP-patient interactions. These findings suggest that interpersonal competence be overtly displayed in all GP interactions to ensure a higher likelihood of a positive experience for the patient.

text: Barriers and facilitators to colorectal cancer diagnosis in New Zealand: a qualitative study Background: New Zealand (NZ) has high rates of colorectal cancer but low rates of early diagnosis. Due to a lack of understanding of the pre-diagnostic experience from the patient’s perspective, it is necessary to investigate potential patient and health system factors that contribute to longer diagnostic intervals. Previous qualitative studies have discussed delays using The Model of Pathways to Treatment, but this has not been explored in the NZ context. This study aimed to understand the patient experience and perception of their general practitioner (GP) through the diagnostic process in the Waikato region of NZ. In particular, we sought to investigate potential barriers and facilitators that contribute to longer diagnostic intervals. 
Methods: Ethical approval for this study was granted by the New Zealand Health and Disability Ethics Committee. Twenty-eight participants, diagnosed with colorectal cancer, were interviewed about their experience. Semi-structured interviews were audio recorded, transcribed verbatim and analysed thematically using The Model of Pathways to Treatment framework (intervals: appraisal, help-seeking, diagnostic). 
Results: Participant appraisal of symptoms was a barrier to prompt diagnosis, particularly if symptoms were normalised, intermittent, or isolated in occurrence. Successful self-management techniques also resulted in delayed help-seeking. However if symptoms worsened, disruption to work and daily routines were important facilitators to seeking a GP consultation. Participants positively appraised GPs if they showed good technical competence and were proactive in investigating symptoms. Negative GP appraisals were associated with a lack of physical examinations and misdiagnosis, and left participants feeling dehumanised during the diagnostic process. However high levels of GP interpersonal competence could override poor technical competence, resulting in an overall positive experience, even if the cancer was diagnosed at an advanced stage. Māori participants often appraised symptoms inclusive of their sociocultural environment and considered the impact of their symptoms in relation to family. 
Conclusions: The findings of this study highlight the importance of tailored colorectal cancer symptom communication in health campaigns, and indicate the significance of the interpersonal competence aspect of GP-patient interactions. These findings suggest that interpersonal competence be overtly displayed in all GP interactions to ensure a higher likelihood of a positive experience for the patient.

year: 2020-10-01