title: Transit time distributions are not L-shaped

authors: Bardsley, W. Earl

subjects: transit time distribution

abstract: A probability density function f(t) with origin at t = 0 is defined here as being ‘L-shaped’if f ʹ(t) ≤ 0 for t ≥ 0. L-shaped probability density functions, such as exponential distributions, are often employed as transit time distributions in hydrological modelling. However, the use of L-shaped transit time distributions implies including tracer particles that were already present at the observation point at time t = 0. These passive particles have no transit history by definition because ‘transit’ implies some history of movement of a particle through a hydrological system, however small that movement may be. That is, the particle must have reached the observation point by moving to it for some non-zero time and over some non-zero distance through a hydrological system such as a catchment or aquifer. By this argument, particles that happen to be already at the observation point at time t = 0 represent background noise.
The distinction between the inclusion or not of particles already at the observation point might seem pedantic but does have an important implication: if transit time distributions in the hydrological environment are defined to not include non-transiting particles, they must have the property f ( 0) = 0. This negates the possibility of L-shaped transit time distributions. The exclusion of non-transiting particles also has the implication that transit time distributions must have at least one mode at t > 0, which may or may not be identifiable from field measurements.

text: Transit time distributions are not L-shaped A probability density function f(t) with origin at t = 0 is defined here as being ‘L-shaped’if f ʹ(t) ≤ 0 for t ≥ 0. L-shaped probability density functions, such as exponential distributions, are often employed as transit time distributions in hydrological modelling. However, the use of L-shaped transit time distributions implies including tracer particles that were already present at the observation point at time t = 0. These passive particles have no transit history by definition because ‘transit’ implies some history of movement of a particle through a hydrological system, however small that movement may be. That is, the particle must have reached the observation point by moving to it for some non-zero time and over some non-zero distance through a hydrological system such as a catchment or aquifer. By this argument, particles that happen to be already at the observation point at time t = 0 represent background noise.
The distinction between the inclusion or not of particles already at the observation point might seem pedantic but does have an important implication: if transit time distributions in the hydrological environment are defined to not include non-transiting particles, they must have the property f ( 0) = 0. This negates the possibility of L-shaped transit time distributions. The exclusion of non-transiting particles also has the implication that transit time distributions must have at least one mode at t > 0, which may or may not be identifiable from field measurements.

year: 2018

title: Scientists’ habits of mind as evidenced by the interaction between their science training and religious beliefs

authors: Coll, Richard K.

subjects: science training

abstract: The science education literature suggests that the public and students often hold narrow stereotypical views of scientists and science. Here we argue that it is important that students and the public understand the basis on which scientists make scientific claims. The inquiry sought to develop an understanding of the scientific mind, explored through Gauld’s (2005) notion of ‘habits of mind’. The vehicle used to explore these ideas consisted of an inquiry into how scientists rationalise conflicts between scientific theories and religious beliefs which are not in agreement with consensually‐accepted scientific theories. Twenty scientists from different scientific disciplines and levels of seniority were interviewed using as a basis an instrument containing a series of religious‐based item statements that a panel of scientific and religious experts considered were in agreement with a variety of religious doctrines yet in disagreement with current scientific thinking, or for which there is at present no supporting evidence from a variety of scientific disciplines. These statements acted as an interview protocol and formed the basis for interactive discourse, which was audio‐taped, transcribed verbatim and participant‐validated. These data provide a window into scientific thinking as practiced by modern scientists, and helps develop a picture of these scientists’ ‘habits of mind’. The findings suggest that these scientists, unlike their stereotype, hold idiosyncratic views of what constitutes good scientific evidence and sound, credible testimony.

text: Scientists’ habits of mind as evidenced by the interaction between their science training and religious beliefs The science education literature suggests that the public and students often hold narrow stereotypical views of scientists and science. Here we argue that it is important that students and the public understand the basis on which scientists make scientific claims. The inquiry sought to develop an understanding of the scientific mind, explored through Gauld’s (2005) notion of ‘habits of mind’. The vehicle used to explore these ideas consisted of an inquiry into how scientists rationalise conflicts between scientific theories and religious beliefs which are not in agreement with consensually‐accepted scientific theories. Twenty scientists from different scientific disciplines and levels of seniority were interviewed using as a basis an instrument containing a series of religious‐based item statements that a panel of scientific and religious experts considered were in agreement with a variety of religious doctrines yet in disagreement with current scientific thinking, or for which there is at present no supporting evidence from a variety of scientific disciplines. These statements acted as an interview protocol and formed the basis for interactive discourse, which was audio‐taped, transcribed verbatim and participant‐validated. These data provide a window into scientific thinking as practiced by modern scientists, and helps develop a picture of these scientists’ ‘habits of mind’. The findings suggest that these scientists, unlike their stereotype, hold idiosyncratic views of what constitutes good scientific evidence and sound, credible testimony.

year: 2009

title: The teaching, learning and testing of te reo Māori in tertiary institutions in Aotearoa/New Zealand

authors: Tihema, Ngaire L. A.

subjects: tertiary educational institutions

abstract: Additional language teaching and learning is fraught with problems the world over and Aotearoa/New Zealand is not immune to these issues.  This doctoral research investigates current practices of teaching and learning te reo Māori (the Māori language) as an additional language in tertiary educational institutions and explores the appropriacy of measuring the language proficiency of speakers and learners of te reo Māori by using a variation of the C-test principle.  The first chapter (Chapter One) sets the context by providing an overview of post-colonial historical events in Aotearoa/New Zealand that led to a language shift which would result in many Māori learning te reo Māori as a second language.  The literature review (Chapter Two) provides an historical overview of additional language teaching methods and approaches since the 18th century and critiques some language teaching methods/approaches – found to be outdated, teacher-centred and/or too limited in scope – that are currently used to teach the Māori language in tertiary institutions.  The next two chapters report on responses from a questionnaire-based survey (Chapter Three) and semi-structured interviews (Chapter Four) with tertiary teachers of te reo Māori, which found that most teachers are largely untrained and unqualified in the area of additional language teaching and learning.  The chapter that follows (Chapter Five) provides an analysis of a textbook series – reported to be the most widely used Māori language resources in tertiary institutions – which was found to be largely influenced by an eclectic approach to textbook design that includes grammar translation and audiolingual methods.  For the next chapter (Chapter Six), the development of a particular type of Māori language proficiency test (variant C-test) is discussed, along with the findings and results of its trial, which was done, firstly, with a sample of highly proficient speakers of te reo and, secondly, with a small sample of second language learners of te reo, prior to a pilot of the test which was conducted with a second sample of tertiary learners of te reo Māori.  While analyses of test scores reveal that satisfactory reliability coefficients were obtained, more research is required, not only to investigate the validity of this particular C-test variant, but also to further explore the appropriacy of applying the (variant) C-test principle to measuring general Māori language proficiency.  This chapter (Chapter Six) concludes with a discussion of the questionnaire responses about the educational backgrounds, language backgrounds, motivations and attitudes of the samples of learners, approximately half of whom are additional language learners and the other half of whom have been raised with te reo Māori as (one of) their main language.  An overview of the research findings and its limitations is provided in the final chapter (Chapter Seven), along with potential contributions of the research and further recommendations for future research.  The challenge that each issue raised in this thesis places on teachers, students and the revitalisation movement of te reo Māori in tertiary institutions, is one which needs to be further explored and addressed.

text: The teaching, learning and testing of te reo Māori in tertiary institutions in Aotearoa/New Zealand Additional language teaching and learning is fraught with problems the world over and Aotearoa/New Zealand is not immune to these issues.  This doctoral research investigates current practices of teaching and learning te reo Māori (the Māori language) as an additional language in tertiary educational institutions and explores the appropriacy of measuring the language proficiency of speakers and learners of te reo Māori by using a variation of the C-test principle.  The first chapter (Chapter One) sets the context by providing an overview of post-colonial historical events in Aotearoa/New Zealand that led to a language shift which would result in many Māori learning te reo Māori as a second language.  The literature review (Chapter Two) provides an historical overview of additional language teaching methods and approaches since the 18th century and critiques some language teaching methods/approaches – found to be outdated, teacher-centred and/or too limited in scope – that are currently used to teach the Māori language in tertiary institutions.  The next two chapters report on responses from a questionnaire-based survey (Chapter Three) and semi-structured interviews (Chapter Four) with tertiary teachers of te reo Māori, which found that most teachers are largely untrained and unqualified in the area of additional language teaching and learning.  The chapter that follows (Chapter Five) provides an analysis of a textbook series – reported to be the most widely used Māori language resources in tertiary institutions – which was found to be largely influenced by an eclectic approach to textbook design that includes grammar translation and audiolingual methods.  For the next chapter (Chapter Six), the development of a particular type of Māori language proficiency test (variant C-test) is discussed, along with the findings and results of its trial, which was done, firstly, with a sample of highly proficient speakers of te reo and, secondly, with a small sample of second language learners of te reo, prior to a pilot of the test which was conducted with a second sample of tertiary learners of te reo Māori.  While analyses of test scores reveal that satisfactory reliability coefficients were obtained, more research is required, not only to investigate the validity of this particular C-test variant, but also to further explore the appropriacy of applying the (variant) C-test principle to measuring general Māori language proficiency.  This chapter (Chapter Six) concludes with a discussion of the questionnaire responses about the educational backgrounds, language backgrounds, motivations and attitudes of the samples of learners, approximately half of whom are additional language learners and the other half of whom have been raised with te reo Māori as (one of) their main language.  An overview of the research findings and its limitations is provided in the final chapter (Chapter Seven), along with potential contributions of the research and further recommendations for future research.  The challenge that each issue raised in this thesis places on teachers, students and the revitalisation movement of te reo Māori in tertiary institutions, is one which needs to be further explored and addressed.

year: 2018