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Home ▶ Vol 34, No 2 (2013) ▶	Lloyd
Pam Lloyd1
Vera Frith1
1Numeracy Centre, Academic Development Programme, University of Cape Town, South Africa
Correspondence to:
Pam Lloyd
Private Bag X3, Rondebosch 7701, South Africa
Accepted: 02 Sept. 2013
Published: 10 Oct. 2013
Lloyd, P., & Frith, V. (2013). Proportional reasoning as a threshold to numeracy at university: A framework for analysis. Pythagoras, 34(2), Art. #234, 9 pages. http://dx.doi.org/10.4102/
pythagoras.v34i2.234
© 2013. The Authors. Licensee: AOSIS OpenJournals.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Proportional reasoning as a threshold to numeracy at university: A framework for analysis
In This Original Research...
• The nature of quantitative literacy
• Background to current research question
• The problematic concept
• Theoretical framework
• Method
• Data collection
• Preliminary observations
• Creating the framework
• Using the framework for analysis
• Results and discussion
• Conclusion
• Acknowledgements
• Competing interest
• Authors' contributions
• References
• Footnote
• Appendix 1
• Question 1
There is a generally acknowledged need for students to be quantitatively literate in an increasingly quantitative world. This includes the ability to reason critically about data in context. We have noted that students experience difficulty with the application of certain mathematical and statistical concepts, which in turn impedes progress in the development of students' critical reasoning ability. One such concept, which has the characteristics of a threshold concept, is that of proportional reasoning. The main focus of this article is a description of the development of a framework using an adapted phenomenographic approach that can be used to describe students' experiences in the acquisition of the concept of comparing quantities in relative terms. The framework has also helped to make explicit the elements that constitute a full understanding of the requirements for the proportional comparison of quantities. Preliminary results from using the framework to analyse students' responses to assessment questions showed that many students were challenged by proportional reasoning. When considering the notion of the liminal space that is occupied en route to a full understanding of a threshold concept, about half of the students in the study were at the preliminal stage of understanding the concept and very few were at the threshold.
It is commonly accepted that citizens need to be quantitatively literate (numerate) in order to participate effectively in an increasingly quantitative world (Department of Education, 2003; Gal, 2005; Jablonka, 2003; Steen, 2001). At our university we provide several first-year interventions intended to assist students to develop appropriate quantitative literacy for their disciplines (Frith, 2012). Amongst these is a context-based semester course that caters mainly for students studying law and humanities. The curriculum uses contexts that have a social justice focus in which students are exposed to some of the social issues that are important in a society in transition and that we judge to be relevant to both law and humanities students (Frith et al., 2010). An aim of the course is that students develop the ability to reason critically about quantitative data in such contexts. The focus of this article, which is part of a wider study, is on understanding how students experience the learning and application of a mathematical concept whose difficulty impedes progress in the development of this ability.
The nature of quantitative literacy
There are numerous definitions of quantitative literacy in the literature which emphasise various aspects of this complex concept. We adopt the following definition:
Quantitative literacy is the ability to manage situations or solve problems in practice, and involves responding to quantitative (mathematical and statistical) information that may be presented verbally, graphically, in tabular or symbolic form; it requires the activation of a range of enabling knowledge, behaviours and processes and it can be observed when it is expressed in the form of a communication, in written, oral or visual mode. (Frith & Prince, 2006, p. 30)
The development of this definition was influenced by the definition of numerate behaviour underlying the assessment of numeracy in the Adult Literacy and Lifeskills Survey (Gal, Van Groenestijn, Manly, Schmitt & Tout, 2005) and the view of literacy and numeracy as social practice (Prince & Archer, 2008; Street, 2005; Street & Baker, 2006).
The idea that quantitative literacy is mainly concerned with mathematics and statistics used in context is fundamental to all its definitions. In our definition the statement 'it requires the activation of a range of enabling knowledge, behaviours and processes' refers to the full range of competencies necessary for quantitative literacy practice, including mathematical abilities, logical thinking and thinking critically about data in context. Our definition also emphasises that responding appropriately to quantitative information in a text and communicating quantitative ideas are both essential components of numerate practice.
Responding appropriately to quantitative information includes the ability to think critically about the meaning of such information. Most numeracy practitioners would agree that a disposition and ability to think critically about quantitative information is an essential aspect of numerate practice (Best, 2008; Jablonka, 2003; Johnston & Yasukawa, 2001; Steen, 2001). For example, Johnston (2007) defines numeracy as 'a critical awareness that builds bridges between mathematics and the real world' (p. 54) and for Boersma and Willard (2008) the term quantitative literacy refers to 'the ability to reason critically with quantitative information' (p. 1). The literature on critical thinking (e.g. Facione, 2013) suggests that this critical awareness consists of mental abilities or cognitive skills, such as interpretation, analysis, inference, evaluation, explanation and self-regulation, and the disposition or habit of mind to use these mental abilities. According to Facione (2013, p. 10), '[t]he ideal critical thinker can be characterised not merely by her or his cognitive skills but also by how she or he approaches life and living in general.' Writers about numeracy have also stressed the importance of this critical habit of mind as a necessary attribute of a numerate individual (Dingman & Madison, 2010; Steen, 2001).
The example presented in Figure 1 illustrates the interplay of the three facets of quantitatively literate behaviour outlined above, namely the application of mathematical concepts in context, critical reasoning and communication. When presented with data about the take-up rates of the Child Support Grant (CSG) in the various provinces of South Africa in 2005 and 2006, a spontaneous response by a quantitatively literate student could be the posing of the question: 'Which province was most successful in increasing the take-up rate of the CSG from 2005 to 2006?'
FIGURE 1: Example of a data representation requiring critical interpretation.
The process of answering this question involves reasoning about the size of the percentage change in each province by using information gained from the graphical representation and then communicating the result of this reasoning. The development of a framework to describe this ability in students is the focus of this article.
Background to current research question
The initial aim of our research project was to determine to what extent we were effectively achieving the outcome that students are able to reason critically about data in context. However, once we began to consider our context-based learning materials, our classroom interactions and the students' responses to assessment questions it became apparent that the students in these courses were hardly ever thinking critically in the way that we would like.
Reflection on why this was the case led to the realisation that too many of the students were still struggling at the level of understanding the mathematical concepts and techniques to allow for us to focus effectively on developing their critical awareness. Most of the classroom time was used for students to learn the basic mathematical and statistical concepts, leaving little time for drawing on these concepts in the process of thinking more critically about the contexts.
Steen (2001) defines numeracy as:
[a]n aggregate of skills, knowledge, beliefs, dispositions, habits of mind, communication capabilities, and problem solving skills that people need in order to engage effectively in quantitative situations arising in life and work. (p. 7)
Drawing on this definition, we argue that our students in fact still need to acquire the skills and knowledge before we can effectively facilitate the development of appropriate habits of mind, communication capabilities and problem-solving skills. It is argued, for example by Bailin, Case, Coombs and Daniels (1999), that the extent to which one is able to think critically in a certain context, even if one possesses the cognitive skills and disposition to do so, will be determined by one's depth of knowledge and understanding of that context. In the case of quantitative literacy, this means that the critical awareness that is fundamental to numerate behaviour depends heavily on a sound knowledge and understanding of some basic mathematical and statistical concepts.
We thus decided that it would be more productive to first focus our attention on how students attempt to make sense of the mathematical concepts that they find to be difficult, with the ultimate aim of establishing more effective ways of teaching them.
The problematic concept
Through many years of teaching quantitative literacy courses we have repeatedly identified the concept of proportion and proportional reasoning as being problematic for first-year university students. Consequently, the curriculum of the course recognises that fractions, percentages and proportions are concepts that require revisiting – in various forms, at intervals, and in different contexts, with attention being paid to appropriate language use. Continual emphasis is placed on the use of the proportion concept in the comparison of quantities. Students are regularly exposed to situations where comparing quantities in absolute terms will give a very different impression from that gained by expressing each quantity as a fraction of some relevant base value before making the comparison. For example, one country may spend vastly more on health care than another with a similar population size, but as a proportion of its gross domestic product it could be spending far less. We believe that being able to move beyond thinking about quantities in absolute terms is crucial to the development of critical reasoning: the understanding of the concept of comparing quantities in relative terms and being able to identify situations where it may be relevant to do so is a very important tool for thinking critically about quantitative information. Ultimately we would like our students to spontaneously recognise when it would be appropriate to ask questions such as: Yes, this quantity is bigger than the other, but is it bigger in relative terms?
Despite the fact that almost all of our students have a school background that includes 12 years of Mathematics or nine years of Mathematics and three years of Mathematical Literacy, we have found that, for many of our students, even a basic understanding of the proportion concept and its use is lacking. Despite mediation during the course the problem is pervasive and persistent. In her work describing the challenges involved in understanding ratio by South African school learners, Long (2009, p. 34) notes that the development of proficiency in concepts such as fraction, ratio and rate is not confined to the early grades but continues through high school and beyond. Analysis of test items involving ratio, proportion and percentage revealed that, in general, Grade 8 learners in South African schools do not have an operational understanding of these concepts and are unable to solve problems in which these concepts are embedded (Long, 2009).
This problem is not confined to South Africa: research over a 30-year period by the Rational Number Project (n.d.) in the United States of America (USA) has resulted in over 90 publications focusing on the theory and practice of the teaching and learning of fractions in schools. It has been found that the representation of ratios and proportions as percentages presents particular difficulties. A review of research conducted in schools in the USA into the inadequate performance with percentages revealed that 'percent is a topic in which students have displayed inadequate performance, and in some cases utter confusion, for over 60 years' (Parker & Leinhardt, 1995, p. 422). Investigating the difficulty in the learning of percentage, these authors drew attention to the mathematical complexity of the concept and the different ways in which it is used – to indicate a part-whole relationship; as a number, fraction or decimal; as an operator; and as a statistic or function. They also highlighted that the language of percentage uses concise and elegant linguistic forms requiring attention to unstated relationships and that this language is often in conflict with everyday language. In addition, they suggested that percentage is poorly taught and there is evidence that many teachers are also confused about the concept (Parker & Leinhardt, 1995).
One of the strategies that many of our students appear to have adopted in order to cope with difficult mathematical concepts is to apply learned rules and procedures without much attempt at understanding. Parker and Leinhardt (1995) identify a problem in the teaching of percentage by means of fixed procedures that leads to students approaching problems by attempting to manipulate given numbers by rule, rather than by reason. We have observed that most of our students, when explicitly asked to do so, are able to calculate fractions such as percentage change by means of a formula when given the relevant quantities. That is, they are able to produce the 'ritual knowledge' described as the 'routine that we execute to get a particular result' (Perkins, 1999, cited in Meyer & Land, 2006, p. 10).
However, the troublesome nature of proportion becomes apparent when students are asked to reason about change in a quantity as a percentage change, that is as a fraction, without doing calculations and then to describe in words, using appropriate language, their reasoning. Behr, Harel, Post and Lesh (1992) describe this kind of thinking as 'qualitative reasoning'.
We use the term 'proportional comparison' to describe the comparison of fractions that requires qualitative reasoning. Mastery of proportional comparison can be demonstrated when a student can compare change in two quantities in relative rather than absolute terms without making use of a formula or numerical values and can then use appropriate language to describe this reasoning. Typically, we have been interested in whether students are able to reason qualitatively about the effect that a change in the size of the numerator and/or denominator of a fraction has on the size of the fraction. An illustration of this is a question that we have asked students about the data for two of the provinces in the chart shown earlier in Figure 1. Since the data in the example is presented in graphical form it is possible, for example in the case of Limpopo and North West, to decide, without doing any calculations, which province experienced the greater percentage increase in CSG take-up rate. This is because both have experienced the same absolute change, but North West had a smaller take-up rate in 2005, resulting in a larger percentage increase for this province.
In order to ascertain the extent to which students have developed the ability to reason with proportions we examined students' answers to two assessment questions requiring the application of proportional comparison. In this article we focus on describing the development of the framework for elucidating the elements contributing to successful reasoning about proportional change. We then demonstrate the use of this framework to analyse student responses.
In developing our method of analysis we used the threshold concepts framework as described by Meyer and Land (2003) and a phenomenographic type of analysis (Marton & Booth, 1997).
We find that the threshold concepts approach provides a useful guide for thinking about how students understand concepts that are the foundations of numerate practice in higher education. According to Meyer and Land (2003),
[a] threshold concept can be considered as akin to a portal, opening up a new and previously inaccessible way of thinking about something. It represents a transformed way of understanding, or interpreting, or viewing something without which the learner cannot progress. As a consequence of comprehending a threshold concept there may thus be a transformed internal view of subject matter, subject landscape, or even world view. This transformation may be sudden or it may be protracted over a considerable period of time, with the transition to understanding proving troublesome. Such a transformed view or landscape may represent how people 'think' in a particular discipline, or how they perceive, apprehend, or experience particular phenomena within that discipline (or more generally). (p. 1)
These concepts are characterised as, amongst others, likely to be troublesome for the student; transformative, leading to a shift in perception and use of language; irreversible in that the change in perspective is unlikely to be forgotten; and integrative, in the way they link to other concepts in the discipline. So threshold concepts can be seen as gateways to thinking and practising and communicating authentically in a particular discourse.
The time taken for the process of internalising a threshold concept and thus effecting a transition from one way of thinking to another will vary depending on how troublesome the concept is for a student. During this time of transition a student may experience uncertainty and a sense of being stuck between a limited, superficial understanding of the concept and a full understanding; a student may well oscillate between stages of understanding. This conceptual space that is occupied by a learner is described by Meyer and Land as the 'liminal space':
Difficulty in understanding threshold concepts may leave the learner in a state of liminality (Latin limen – 'threshold') a suspended state in which understanding approximates to a kind of mimicry or lack of authenticity. (Meyer & Land, 2003, p. 10)
Prior to the emergence of the threshold concepts theory, research in school mathematics education identified proportional reasoning as being both difficult for many students and as taking a long time to develop (Behr et al., 1992; Cramer & Post, 1993; Karplus, Pulos & Stage, 1983). More recently it has been recognised that fractions, ratios and proportions are amongst the most challenging mathematical concepts to learn and to teach (Lamon, 2007) and Long (2011, p. 211) asserts that there is 'agreement generally that proportional reasoning is a threshold concept'.
Given that many students entering higher education have not yet gained this threshold in school mathematics, we take the view that proportional reasoning is one of many mathematical and statistical concepts that often deny students access to numerate 'ways of thinking and practising' (Meyer & Land, 2003, p. 12) in academic disciplines. This view is supported by the work of researchers in the sciences who have identified proportional reasoning as a threshold concept in their discipline. Ross et al. (2010) hypothesise that there is a 'web of threshold concepts' or 'epistemes', including proportional reasoning, that underlie difficult (in this case, biological) concepts.
Data was obtained from the written assessments of students in the law course in the form of their responses to two assessment questions that required them to reason about percentage change. Permission for use of student work was obtained from students via a signed consent form in accordance with the requirements of the Research Ethics Committee of the Centre for Higher Education Development at our university. Students were informed that consent was voluntary and that anonymity would be respected. The work of students whose consent was not given was not used in this study.
The data was collected in two batches: we recorded each student's written response to a particular question in each of two assessments that were six weeks apart. Students regularly encounter contexts throughout the course where they are required to work with percentage change in various ways. Students continued to be exposed to contexts involving percentage change between the two assessments; however, we made no specific changes to the curriculum as a result of their performance in the first assessment. The intention of the questions was to assess students' ability to reason proportionally about data in previously unseen situations. The data in the assessment questions was presented graphically and students were instructed not to do any calculations but to explain their reasoning in a written response. In each case the reasoning required the comparison of the sizes of two fractions, the relative sizes of the fractions being apparent from the geometry of the graphical representation. Students had not previously discussed similar questions in which the data was presented graphically. See Appendix 1 for the actual questions.
Question 1 was set in the context of children's rights, specifically dealing with CSGs in South Africa and the take-up rates of CSGs in the different provinces. The chart used in this question is that shown in Figure 1. Although students had spent about five hours in class working with quantitative issues that arise in allocating resources for social services for children, including CSGs, the issue of take-up rate had not previously been encountered in classroom materials. However, in other contexts students had calculated percentage changes in quantities that were themselves percentages and been introduced to the difference between percentage change and change in percentage points. In Question 1, students were required to compare the percentage change in take-up rate for two specific provinces, North West and Limpopo. Careful observation of the graphs would show that the absolute change for both provinces was essentially the same, but for one province the percentage change was clearly calculated off a lower base.
Question 2 was part of a later assessment at the end of the course. The context here was the real disposable income of South Africans and how this has changed over time. The data was again shown graphically, this time in the form of four time series, one for each of the different race groups1. The question itself required the consideration of the real disposable incomes of two of the groups, and how these had changed from 1960 to 2005. Students had been exposed to the concept of real income but had not previously compared relative changes in real income. As before, the absolute change for each group was approximately the same, but one clearly came off a lower base.
Preliminary observations
From a preliminary examination of student responses it was clear that most students had not reasoned about percentage change in the way we had expected. Many students compared the absolute changes instead of the relative changes and based their conclusion on the former comparison. Others based their argument on the comparison of only the absolute sizes of the quantities (without even considering the absolute change). In order to reason correctly about the relative changes, both of these elements must be taken into appropriate consideration. However, we observed that many of the students were focusing on only one or two elements of the necessary evidence and then jumping to a conclusion. They would also frequently not link the elements they identified in a logical way, and many did not use appropriate quantitative language to describe their observations.
We also realised that in both questions there was a large number of students who were distracted by the context in which similar questions had previously been experienced. For example, in Question 1 many students used arguments based on not knowing the population sizes of the different provinces. We suggest that the reason for this is that when they had previously been exposed to examples where they had to reason about proportions it was in situations where the quantities under consideration were percentages of a population. For example: in a tutorial, students studied a table in which the percentage of households with television was higher in Mpumalanga than in KwaZulu-Natal. They were then required to discuss the following question: 'Does this mean that Mpumalanga has more households with TV than does KwaZulu-Natal? Explain.' In the later question many students were distracted by the nature of the data representation. Much of their previous exposure to the interpretation of line charts involved making observations about trends and rates of change, and so it seems that many of them assumed that this kind of thinking was required in order to answer this question.
Creating the framework
We required a more precise description of students' understanding of proportional comparison. The framework for identifying and describing the elements that are required when reasoning about proportional comparison emerged from further examination of the data and applications of phenomenography suggested by the literature.
The phenomenographic method of analysis (Marton & Booth, 1997) enables the description of the variety of ways in which people experience a phenomenon. This is usually achieved by means of open-ended interviews in which students reflect on their understanding of the phenomenon. The transcribed interviews are studied with the aim of categorising the descriptions of experiences in a way that will provide a limited, but complete, set of categories that covers all the variations. An iterative process is then embarked on where the interview data is re-examined using the categories and the categories are modified to ensure consistency with the data. The process continues until stability is achieved. The categories can often be arranged hierarchically, and a participant's experience may be described by one or more categories.
We adapted this approach by examining the written responses to assessment questions with the view to observing and categorising the ways in which students experienced proportional comparison. The variation in the ways of understanding the concept was described by an iterative process in which we read the students' responses and defined categories describing the different 'objects of focal awareness' (Marton & Booth, 1997, p. 112) as experienced by students in their written responses, refined these categories and then coded students' responses according to these categories. This process is described below.
For the 36 responses to Question 1 and the 32 responses to Question 2, we independently identified preliminary descriptive categories and then coded student responses according to these categories. On comparing our categories we found that they were in effect the same and that our initial codings using our respective preliminary categories were very similar. At this stage it became apparent that the main categories were essentially descriptions of the elements required in the reasoning towards a correct answer: a consideration of the size of the absolute change, the size of the base from which the absolute change occurred, then a comparison of sizes of the resulting fractions.
These insights informed the development of new category descriptions that were general enough to be used to code the responses to both questions. This resulted in the framework outlined in Table 1. Using the framework and the coding key shown in the table we then independently re-coded the student answers. Agreement on a final coding was reached after further discussion. The stability of the framework was confirmed when, after a few months' break from the data and the framework, the coding exercise was repeated and only a few changes were made.
TABLE 1: Coding key for Question 1 and Question 2.
Using the framework for analysis
Codes A, B, C and D are elements of a correct answer. Responses whose reasoning exhibited all four elements as well as the correct conclusion that the fraction with the smaller base will yield the larger percentage were coded only as G. Responses that showed incomplete reasoning were given one or more codes identifying the particular elements. In addition, responses of students who were distracted by the context in which they had previously been asked similar questions were coded as F and those whose reasoning was based on an incorrect understanding of fractions were coded as E. Those responses that we found incomprehensible or unable to classify were coded only as H.
We then further classified students' responses in relation to the liminal space. Land, Meyer and Baillie (2010) describe the variation in the understanding of threshold concepts in terms of a journey through the preliminal, liminal and postliminal stages of conceptual development. According to our categories, codes A, B and C refer to answers in which students did not recognise that proportions were involved and referred only to absolute quantities or absolute changes. When viewed using the threshold concepts framework, these responses indicate that students do not appear to have engaged at all with the concept of proportional comparison and their understanding of the concept can be regarded as being at the preliminal stage. Codes D, E and F for Question 1 (and D and E for Question 2), sometimes in combination with codes A, B and C, represent understandings that are at various stages within the liminal space and G represents an answer indicating that, at least in terms of the specific context of the question, the student has demonstrated mastery of the concept and its associated language. In this case their understanding can be considered to be at the threshold or, possibly, postliminal.
In this section we present the results of an analysis, largely in order to illustrate the usefulness of the framework. For this reason we do not discuss the implications of the results in great depth. A summary of the coding of the responses to the questions is shown in Table 2. The total of the percentages is not 100%, as many responses had multiple codes.
TABLE 2: Results of coding of responses to Question 1 (N = 36) and Question 2 (N = 32).
In Question 1, only 11% of students, and in Question 2 only 3%, correctly reasoned that it is the data category with the lowest initial value that has the greatest percentage change, given that in both cases the absolute changes were roughly equal. These responses indicate students being 'at the threshold'.
Table 3 shows a summary of the classification of responses as preliminal, liminal and 'at the threshold'.
TABLE 3: Classification of responses to Question 1 (N = 36) and Question 2 (N = 32).
More than one third of the students (42% for Question 1 and 34% for Question 2) considered only the size of the absolute changes or did not consider change at all (and compared the size of the absolute quantities) and so did not recognise the need to compare fractions. We suggest that this demonstrates an understanding that is in the preliminal stage: the concept of proportional comparison did not 'come into view' (Meyer & Land, 2005, p. 384). In particular, in Question 1, one quarter of the students argued that neither province had the greater change as the absolute change was the same for the two provinces (see Table 2). On the other hand, in Question 2, none of the students recognised that the absolute changes were essentially the same. Also, for this question we included in the preliminal classification those answers coded F, responses that indicated a focus on irrelevant trends shown by the graphs.
More than one third of the students' responses in Question 1, and only one quarter in Question 2, showed an understanding that fractions needed to be considered. Some of these responses also noted the size of the absolute change but did not follow through with the correct argument. These understandings were considered to be in the liminal stage.
In the case of Question 1, one quarter of the students were distracted by the context and, instead of arguing using the data presented in the graph, tried to argue that the population size of the province would influence the percentage increase in take-up rate. As previously noted, the context of Question 2 appears to have been even more distracting, with half of the students including in their arguments irrelevant observations about the trends shown in the chart.
In this more distracting question some students, who were initially considered to be at the threshold, appear to have returned to the liminal stage, illustrating the observation of Land et al. (2010, p. xi) that 'the acquisition of threshold concepts often involves a degree of recursiveness', that is, a student's journey through the liminal space is not necessarily direct. We observed that not all students for whom understanding in Question 1 seemed to be at the threshold were (irreversibly) over the threshold and could therefore not be regarded as being in the postliminal stage.
One of the attributes of a quantitatively literate person is the ability to think critically about data in context. The outcomes of a quantitative literacy intervention at tertiary level that seeks to promote access to ways of thinking and practising in academic disciplines would include this ability. However, this particular outcome is unattainable if students are unable first to cross certain conceptual thresholds, one of which is that of proportional reasoning.
The development and application of a framework for the detailed analysis of student understanding of proportional comparison has enabled a systematic description of the range of student experiences in the process of gaining a full understanding of the concept. The development of this framework has made explicit the elements required when reasoning about proportions. It has also enabled the classification of student responses in relation to the liminal space that is occupied en route to a full understanding of proportional comparison.
Our study has shown that, throughout the course, and despite repeated exposure to the concept, most of the students retained an incomplete understanding of proportional comparison and almost half of the students remained in the preliminal stage. The study confirms the tenaciously troublesome nature of the concept and has implications for our teaching practice and the curriculum. These issues are to be the focus of future research.
We wish to thank Kate le Roux and Viki Janse van Rensburg for reading drafts of this manuscript and suggesting useful improvements.
We declare that we have no financial or personal relationships that may have inappropriately influenced us in writing this article.
P.L. and V.F. (both of University of Cape Town) contributed equally to the design of the assessment questions, analysis of student work, development of the framework, writing of the article and preparation of the manuscript for publication.
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Lamon, S.J. (2007). Rational numbers and proportional reasoning. Toward a theoretical framework for research. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–666). Charlotte, NC: Information Age Publishing.
Land, R., Meyer, J.H.F., & Baillie, C. (2010). Editors' preface. In J.H.F. Meyer, R. Land, & C. Baillie (Eds.), Threshold concepts and transformational learning (pp. ix–xlii). Rotterdam: Sense Publishers. Available from https://www.sensepublishers.com/media/1177-threshold-concepts-and-transformational-learning.pdf
Leatt, A., Meintjes, H., & Berry, L. (2006). Children's access to social assistance. In J. Monson, K. Hall, C. Smith, & M. Shung-King (Eds.), South African child gauge 2006 (pp. 70–71). Cape Town: Children's Institute, University of Cape Town. Available from http://www.ci.org.za/depts/ci/pubs/pdf/general/gauge2006/gauge2006_social.pdf
Long, C. (2009). From whole number to real number: Applying Rasch measurement to investigate threshold concepts. Pythagoras, 70, 32–42. http://dx.doi.org/10.4102/pythagoras.v0i70.37
Long, M.C. (2011). Mathematical, cognitive and didactic elements of the multiplicative conceptual field investigated within a Rasch assessment and measurement framework. Unpublished doctoral dissertation. University of Cape Town, Cape Town, South Africa. Available from http://hdl.handle.net/11180/1521
Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Lawrence Erlbaum.
Meyer, J.H.F., & Land, R. (2003) Threshold concepts and troublesome knowledge: Linkages to ways of thinking and practising within the disciplines. Enhancing Teaching-Learning Environments in Undergraduate Courses Project, Occasional Report 4. Edinburgh: University of Edinburgh. Available from http://www.etl.tla.ed.ac.uk/docs/ETLreport4.pdf
Meyer, J.H.F., & Land, R. (2005). Threshold concepts and troublesome knowledge (2): Epistemological considerations and a conceptual framework for teaching and learning. Higher Education, 49, 373−388. http://dx.doi.org/10.1007/s10734-004-6779-5
Meyer, J.H.F,. & Land, R. (2006). Threshold concepts and troublesome knowledge: An Introduction. In J. Meyer, & R. Land (Eds.), Overcoming barriers to student understanding. Threshold concepts and troublesome knowledge (pp. 3–18). London: Routledge.
Parker, M., & Leinhardt, G. (1995). Percent: A privileged proportion. Review of Educational Research, 65(4), 421–481. http://dx.doi.org/10.3102/00346543065004421
Prince, R., & Archer, A. (2008). A New Literacies approach to academic numeracy practices in higher education in South Africa. Literacy and Numeracy Studies, 16(1), 63–75. Available from http://epress.lib.uts.edu.au/journals/index.php/lnj/article/view/1948
Rational Number Project. (n.d.). The Rational Number Project. University of Minnesota. Available from http://www.cehd.umn.edu/ci/rationalnumberproject/
Ross, P.M., Taylor, C.E., Hughes, C., Kofod, M., Whitaker, N., Lutze-Mann, L., et al. (2010). Threshold concepts: Challenging the way we think, teach and learn in Biology. In J.H.F Meyer, R. Land, & C. Baillie (Eds.), Threshold concepts and transformational learning (pp. 165–177). Rotterdam: Sense Publishers. PMCid:PMC3198851
South African Institute of Race Relations. (2009). South Africa survey online 2009/2010: Employment and incomes. Johannesburg: South African Institute of Race Relations. Available from http://www.sairr.org.za/services/publications/south-africa-survey/south-africa-survey-online-2009-2010/downloads/Employment.pdf/
Steen, L.A. (2001). The case for quantitative literacy. In L.A. Steen (Ed.), Mathematics and democracy: The case for quantitative literacy (pp. 1–22). Princeton, NJ: National Council on Education and the Disciplines and Woodrow Wilson Foundation. Available from http://www.maa.org/sites/default/files/pdf/QL/MathAndDemocracy.pdf
Street, B. (2005). Applying new literacy studies to numeracy as social practice. In A Rogers (Ed.), Urban literacy. Communication, identity and learning in development contexts (pp. 87–96). Hamburg: UNESCO Institute for Education.
Street, B., & Baker, D. (2006). So, what about multimodal numeracies? In K. Pahl, & J. Rowsell (Eds.), Travel notes from the New Literacy Studies (pp. 219–233). Clevedon: Multilingual Matters.
1. Race classification in South Africa is used as a social (rather than a biological) construct in the measurement of success (or otherwise) of transformation in society.
The Child Support Grant (CSG) is a cash grant to the value of R190 per month per child as of April 2006. Children are eligible for this grant if their primary caregiver and his or her spouse jointly have R800 per month or less in income and live in an urban area and formal house. Those who live in rural areas or informal housing in urban areas must earn R1100 per month or less to qualify for this grant. In July 2006, the CSG went to over 7.4 million eligible children aged 0–13 years. Using the General Household Survey 2004, Budlender calculated that some 8.8 million children are eligible for the CSG. This is 65% of all children under the age of 14 years. Using this eligibility rate, it is estimated that 84% of all eligible children access (or take up) CSGs across the country in 2006. There is substantial evidence that grants, including the CSG, are being spent on food, education and basic goods and services.
Consider the take-up rates for Limpopo and North West provinces, as shown in the graph. Without doing any calculations, say which province experienced the larger percentage increase from 2005 to 2006 in CSG take-up rate. Explain your reasoning.
The data in the chart below is taken from the South Africa Survey, 2009/2010 (South African Institute of Race Relations, 2009). Answer the questions about this chart below.
(Disposable income refers to earnings after taxes have been paid.)
Consider the real disposable income per person for Indians and Whites. Without doing any calculations, say which race group experienced the greater percentage increase in real income per person from 1960 to 2005. Explain your answer.
1. Proportional reasoning ability of school leavers aspiring to higher education in South Africa
Vera Frith, Pam Lloyd
Pythagoras vol: 37 issue: 1 year: 2016
doi: 10.4102/pythagoras.v37i1.317
Pythagoras | ISSN: 1012-2346 (PRINT) | ISSN: 2223-7895 (ONLINE)


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You are here: Home / Movies / Pro wrestling. Action. Death. Is this the least romantic Valentine's Day at the movies?
Pro wrestling. Action. Death. Is this the least romantic Valentine's Day at the movies?
February 11, 2019 by Michael
"Happy Death Day 2U" follows college student Tree Gelbman, who again finds herself dying over and over until she can reveal her killer's identity.
Looking for love at the movie theaters this Valentine's Day weekend? That's going to be a challenge.
The "Fifty Shades of Grey" franchise, and its SM take on romance, has ended its controversial domination of mid-February date nights, a run that lasted three of the past four years.
2019's releases for Valentine's weekend include a slasher film ("Happy Death Day 2U"), a futuristic action flick with a powerful cyborg ("Alita: Battle Angel") and a family with big dreams of joining the WWE who idolize The Rock ("Fighting With My Family").
The closest thing to something like 2010's holiday lovefest "Valentine's Day" is the comedy "Isn't It Romantic," in which Rebel Wilson's rom-com loathing Natalie finds herself stuck in a romantic comedy world after taking a blow to the head. She's not happy.
Tree (Jessica Rothe, right) defends Ryan (Phi Vu, left) in "Happy Death Day 2U." (Photo: MICHELE K. SHORT)
"The weekend is no longer about this commercialized, romantic image of Valentine's Day," says Jackie van Beek, whose comedy "The Breaker Upperers," about two women who professionally end relationships, makes its debut Friday on Netflix. "It's now for all those people who are not going to be sitting down for a glass of chardonnay with their true love next to a vase of carnations."
Box office: 'Lego Movie 2' opens at No. 1 with $35M but only takes in half of original film's haul
Van Beek, who says she has zero regrets about missing V-Day with
Article source: https://www.usatoday.com/story/life/movies/2019/02/11/2019-least-romantic-valentines-day-movies-ever/2808365002/
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Q: Delete blank rows using Macro, after Row x I've found this Macro on another post:
Sub DelBlankRows()

Columns("A:A").Select
Selection.SpecialCells(xlCellTypeBlanks).Select
Selection.EntireRow.Delete

End Sub

Can this be modified so that it only deletes rows after row x (row 14 on the spreadsheet that I'm currently working on)?
Thanks!

A: this is fairly straightforward.
Rows(x & ":" & y).EntireRow.Delete

Just swap x and y for the rows you want.
As an aside, it is best to avoid selecting ranges unnecessarily as it only slows things down. Any time you select a range then do something with the selection, you can just perform that action directly on the range instead.
EDIT: Just re-read the question - so try this one:
Range("A14:A" & Cells.SpecialCells(xlCellTypeLastCell).Row).SpecialCells(xlCellTypeBlanks).EntireRow.Delete

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whilst we often shine with our particularly high working pressures, we don't need too much of a good thing here. our water-granulate blasting heads have been developed in many practical tests so that a very consistent blast result is produced with extremely little granulate consumption. the "smearing" of the surface with dirt and granulate can no longer occur. this guarantees super cleaning results with acceptable time and cost expenditure.


text:
This folder provides the code for rendering your own data. You do not need this
if you use our data available [here](https://github.com/google/nerfactor#data).

The scenes need to be specified in Blender. We use Cycles, Blender's built-in
physically-based rendering engine.

## Setup

You should use the Python bundled inside Blender, rather than that of your
system or environment.

Because of the API changes in Blender 2.8x, please run our code with
Blender 2.8x. More specifically, we used Blender 2.83.4.

1. "Install" Blender-Python (the binaries are pre-built, so just download
   and unzip):
    ```bash
    proj_root='/data/vision/billf/intrinsic/sim'
    repo_dir="$proj_root/code/nerfactor"
    # Make directory
    mkdir "$proj_root"/software
    cd "$proj_root"/software
    # Download
    wget https://download.blender.org/release/Blender2.83/blender-2.83.4-linux64.tar.xz
    # Unzip the pre-built binaries
    tar -xvf blender-2.83.4-linux64.tar.xz
    ```

1. Install the dependencies to this *Blender-bundled* Python:
    ```bash
    cd blender-2.83.4-linux64/2.83/python/bin
    # Install pip for THIS Blender-bundled Python
    curl https://bootstrap.pypa.io/get-pip.py | ./python3.7m
    # If the above fails, make sure you deactivate your Conda environment
    # Use THIS pip to install other dependencies
    ./pip install absl-py tqdm ipython numpy Pillow opencv-python
    ```

## Rendering

The following code block renders a scene lit by a given light probe from
multiple views. Besides the regular RGB images, it also renders other buffers
including albedo and surface normals. In addition, it renders several novel
lighting conditions including all light probes bundled in Blender and several
OLAT conditions; those renders serve as the relighting ground truth.

```bash
scene='hotdog'
light='2188'
proj_root='/data/vision/billf/intrinsic/sim'
blender_bin="$proj_root/software/blender-2.83.4-linux64/blender"
repo_dir="$proj_root/code/nerfactor"
scene_path="$proj_root/data/scenes/$scene.blend"
light_path="$proj_root/data/envmaps/for-render_h16/train/$light.hdr"
cam_dir="$proj_root/data/cams/nerf"
test_light_dir="$proj_root/data/envmaps/for-render_h16/test"
light_inten='3'
if [[ "$scene" == drums || "$scene" == lego ]]; then
    add_glossy_albedo='true'
else
    add_glossy_albedo='false'
fi
outdir="$proj_root/data/render_outdoor_inten${light_inten}_gi/${scene}_${light}"
REPO_DIR="$repo_dir" BLENDER_BIN="$blender_bin" "$repo_dir/data_gen/nerf_synth/render_run.sh" --scene_path="$scene_path" --light_path="$light_path" --cam_dir="$cam_dir" --test_light_dir="$test_light_dir" --light_inten="$light_inten" --add_glossy_albedo="$add_glossy_albedo" --outdir="$outdir" 1> /dev/null
# Note: We used stdout redirection to silence Blender's rendering prints
```

We modified our parallel rendering code to this current version that renders all
views sequentially for portability. If you have a cluster, consider distributing
all views across the cluster to render them in parallel. The heavylifting
function to be distributed is `render_view()` in `render.py`.

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text:
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Thimphu Bhutan History, Weather 2018 - 2019 Sightseeing
Bhutan's capital city, Thimphu (pronounced "tim-poo"), is a must-visit destination for many travellers coming the country for the first time. Below, you get a taste of what one of the most modern city in Bhutan is like and see the difference between life rights here versus life in other components of the vast country.
The Himalayan kingdom of Bhutan produces the ideal vacation in the hills. The location is not only magical however mystical, filled with history and distinctive Buddhist society. Its capital city of Thimphu thus becomesevery tourist's dream to witness the Bhutanese ways of life. Situated in the western part of the country, Thimphu occupies a valley. The city projects as the administrative seat of the King, with a lengthy list of numerous Buddhist sites, monasteries, museums and various other areas to check out in Thimphu.
History of Thimphu
Before 1960, Thimphu consisted of a group of hamlets scattered across the valley including Motithang, Changangkha, Changlimithang, Langchupakha, and also Taba, a few of which constitute areas of the city today (see below for district details). In 1885, a battle was held at what are currently the Changlimithang sporting activities ground in Thimphu. The decisive triumph opened the way for Ugyen Wangchuck, the first King of Bhutan to basically regulate the entire country. Because this moment the sporting activities ground has been of major relevance to the city; football, cricket matches as well as archery competitions occur there. The modern-day Changlimithang Stadium was improved the website in 1974. Under the Wangchu Dynasty, the country appreciated peace as well as progress under successive reformist queens. The third king, Jigme Dorji Wangchuck, changed the old pseudo-feudal systems by abolishing serfdom, redistributing land, and also changing taxation. He likewise presented numerous executive, legislative, as well as judiciary reforms. Reforms proceeded and in 1952 the choice was made to shift the capital from the ancient capital of Punakha to Thimphu. The 4th king, Jigme Singye Wangchuck, opened the country for advancement and India supplied the needed incentive in this procedure with economic and also various other kinds helpful. In 1961, Thimphu officially became came to be the capital of Bhutan.
5th King of your house of Wangchuck of Bhutan- Jigme KhesarNamgyel Wangchuck.The fourth king, who had actually developed the National Setting up in 1953, developed all executive powers to a council of ministers chosen by the individuals in 1998. He presented a system of voting no self-confidence in the king, which encouraged the parliament to remove the king. The National Constitution Committee in Thimphu began drafting the Constitution of the Kingdom of Bhutan in 2001. In 2005, the 4th king of Bhutan announced his choice to turn over the reins of his kingdom to his boy Prince Jigme Khesar Namgyal Wangchuk. The coronation of the king was kept in Thimphu at the refurbished Changlimithang Arena as well as accompanied the centenary of the establishment of the House of Wangchuck. In 2008, this paved way for the change from absolute monarchic policy to a parliamentary autonomous constitutional monarchy, with Thimphu as the headquarters of the brand-new government, with the countrywide defined purpose of achieving "Gross NationalHappiness" (GNH) concomitant with the growth of Gross NationalProduct (GNP).
Below are some interesting facts concerning the THIMPHU you never ever knew:
1. It Is the 5th Highest Capital City by Altitude
At 2,334 meters above sea level, Thimphu is the 5th greatest capital city by altitude, after La Paz in Bolivia (3,640 m), Quito in Ecuador (2,850 m), Bogota in Colombia (2,625), as well as Addis Ababa in Ethiopia (2,355). And no, you will not get altitude sickness here, although you may experience slight breathlessness while walking uphill.
2. NO TRAFFIC SIGNAL, No Worry
Thimphu is one the few capitals in the world that does not have a single traffic light. One might wonder how website traffic works below then. Well, it's feasible, because who needs traffic signal when you can have a HUMAN traffic signal?
While a lot of us are familiar with traffic cops at junctions in times when the lights aren't working or when there's a crash, over here in Thimphu, the human traffic control is the main landmark and tourist attraction of the town.
3. Thimphu Is Home To One of the Largest Buddha Statues on the World
Coming here as a tourist, this tourist attraction is a must-visit while in Thimphu. Buddha Dordenma Statue is the biggest Shakyamuni Buddha statue to be constructed as well as beings in the mountains in within the funding. Measuring 51.5 m, this statue - which was finished in 2015 - ignores the southerly entry to Thimphu and also can be seen by lots of within the valley.
When you look at the statue, which is constructed from bronze and also gilded in gold, you're not looking at one Buddha. As a matter of fact, you're checking out 125,000 more that are positioned within the Buddha Dordenma statue.
Weather in Thimphu, Bhutan
Thimphu has a temperate highland climate, influenced by the south-west monsoon, determining 1.427 mm on average. Winters are cold with an average January temperature level of 4.9 °C( 40.8 ° F), with evening temperatures below cold and also great days, normally over 10 ° C( 50 ° F) as well as rather big diurnal temperature variation. Snowfalls might happen overnight, yet accumulation does not last lengthy. On the coldest nights temperature levels can lower -10 ° C but seldom fall to -15 ° C. The most affordable temperature level ever videotaped is -21 ° C( -5 ° F). Summers are pleasantly cozy as well as very rainy, with a typical August temperature of 20.4 ° C (68.7 ° F). The highest possible temperature ever taped is 30 ° C (86 ° F). The most effective times to see are from mid-September to the end of October as well as from March to May.
Demographics of Thimphu
According to the census of 31 May 2005, the population of the city was 79,185 with a density of 3,029 per square kilometer (7,850/ sq mi), with 92,929 over a location of 1,843 square kilometres (712 sq mi) in the entire area; the matching figure predicted in 2010 for the area was 104,200. In 2011, the city's population was about 91,000.
How to Reach Thimphu
FLIGHT - Bhutan's only international airport remains in Paro, about two hours far from Thimphu by road. There are normal flights from New Delhi and also Mumbai to Paro city by Drukair- Royal Bhutan Airlines, which is the flag provider of the Kingdom of Bhutan.
ROAD - Thimphu is linked to a lot of components of Bhutan. It has a city bus terminal where inter-district buses depart and arrive. From Paro airport terminal, Thimphu-bound taxis are readily available as well as can set you back as much as Nu 800. Self-driving from Phuentsholing is a scenic and also pleasurable journey that takes about five hours (172 kilometres)
BUS - You can catch a bus plying from one end of the city to the various others. The neighborhood bus terminal is located simply east of the arena on Chang Lam.
Taxi - To travel around, you can hire a taxi, which can be a little costly. These visitor taxis cab charge regarding NU 15 per kilometer, with a minimal charge of regarding Nu 1,400 daily (which includes driver's food, accommodation as well as fees).
On-Foot - Many shops and areas of interest are within walking distance of Thimphu's major hotels. There are chances of obtaining lost in Thimphu as there are no street names. There is only one main street, Narzim Lam, which is lined with shops of all kinds. It would certainly be best to get a map or ask for instructions to your final destination.
Self-Drive -Bhutan is not a part of 1949 and also 1968 Conventions of road traffic, but an InterNational driving permit is honored by the country. Indians can bring their own cars as well as travel in Bhutan. For a travel permit you will certainly need to relate to the Road Safety Department for a minimal payment of regarding INR 400 for a one week travel in Bhutan. For the vehicle travel permit you will need to generate all valid files of the lorry together with the driving license of the vehicle driver. Driving gets on the left site of the road. Around, speed limits are from 8 km/h to 20 km/h. The optimum rate limitation in urban locations is 30 km/h as well as 50 km/h is the optimal rate limit in the country. For more details about driving in Bhutan or applying a permit.
Car Rental/Car Hire Options
Public transport is available in Thimphu however the frequency is restricted to few times in a day. Rentingcars is a great option. Nevertheless the roads are mountainous and also if you are not accustomed to driving in such terrain, it is a good idea to rent a taxicab or utilize the one arranged by your guide.
Bhutan is one-of-a-kind in even more ways than one. Apart from being home to impressive valleys as well as the most attractive of hills, it likewise has a very interesting cuisine to provide. Particular regions additionally have certain foods they are recognized for. What the Bhutanese are essentially crazy with is flavor which comes across so boldly in a variety of their dishes.
Vegan tourists could breathe a sigh of relief regarding their food choices. What is interesting to note is that regardless of the existence of lots of popular meat-based dishes, a significant number of Bhutanese people are vegetarians. A lot of Indian and also Chinese food is additionally available throughout the country.
The following is a listing of the Bhutan foods that a person has to not miss out on their journey to this Himalayan Kingdom:
1. Ema Datshi- (Chillies as well as Cheese) - 'Datshi' in the Bhutanese language of Dzongkha means 'cheese', which is what they utilize in a variety of meals, the most popular being Ema Datshi which resembles a stew made from chilies as well as cheese ('Em a' implies chilies) and may show to be as well hot for some. Being the countrywide dish of Bhutan, it is unarguably one of the most prominent recipes in the country, and any discussion about Bhutanese food cannotgo without the reference of Ema Datshi.
2. Red Rice - Besides the Bumthang area where buckwheat food things are a lot more popular, red rice is among the staple foods of the Bhutanese people. It is a medium-grain selection of rice that is grown in the Kingdom in the Eastern Himalayas. It has been expanded for a number of years in the abundant dirt of the Paro Valley which obtains the advantage of mineral-rich glacier water.
3. Jasha Maroo or Maru (Spicy chicken) - Another dish worth tasting would be the Jasha Maroo which is like a spicy stew or curry which is made with diced chicken, onion, garlic, chillies, tomato, ginger and coriander leaves. Ginger gives this dish its essence. It may be served with a generous portion of chicken broth. Beef may likewise be utilized instead of chicken. This is usually served with red rice as it is in case of most Bhutanese dishes.
Best Places to Browse Through in Thimphu, Bhutan
While there is a great deal of areas to check out in Thimphu, here's a list of 10 best which you should see on your next trip there. Have a look!
1. Trashi Chho Dzong
Also known as Tashichho Dzong, or simply, Thimphu Dzong, this is surely among one of the most interesting place to see in Thimphu. This grand ft additionally offers the place for country's biggest yearly event tsechu. The dzong is not the original Thimphu Dzong as the palace has been destroyed in fires practically five times till day. Last refurbished in 1962 by the then King Jigme Dorji Wangchuck, the fort has the secretariat, offices of the King as well as other officials as well as ministers as well as the throne room.
2. Changangkha Lhakhang
A popular Buddhist temple, this location was very first built in the 12th century under the guidance of Lama PhajoDrukgomShigpo from Tibet. The location is specifically visited by parents to obtain true blessings for their newborn children. The white fortress-like structure makes it one of one of the most popular visitor places in Thimphu.
3. Tango Goemba
Originallybuilt in the 15th century by Lama Drukpa Kunley, Tango is one more Buddhist site in the city. Renovated in 2016, the place serves as a centre for Buddhist studies. You would certainly have to hike uphill for concerning forty-five mins to get to the place. The chapels, meditation cave, living quarters at Tango are among the most fascinating areas to see in Thimphu. You can also witness a crystal right here brought in from Tibet which is used especially for meditation.
4. National Memorial Chorten
Probably among the most popular Thimphu points of interest, this Chortenfeatures as a daily place of worship in many natives lives. Built in the Tibetan style as a memorial to the 3rd Bhutanese King Jigme Dorji Wangchuck, the location is known for its whitewashed walls and golden tiered roofs. Among the most popular areas to see in Thimphu, this Memorial Chorten is visited out every day by elderlies, kids and also other people on their way to workplaces, institutions as back home.
5. Dechen Phodrang
Ranking high on the Thimphu places to go to listings, this is the site of the original Thimphu Dzong. Built in the 12th century, the dzong here was destroyed in a fire. Dechen Phodrang is currently a state college, which instructs around 250 students. The main church right here contains murals and paintings going back 800 years.
6. NationalLibrary of Bhutan
The answer to the usual what to see in Thimphu is hands down this NationalLibrary. The place was built in 1967 with the single function of maintaining ancient texts. This is the one location which houses most informing as well as interesting things to see in Thimphu. The architecture here is stunning in common Bhutanese tradition. Most Booksright here gets on hand-made paper, protected in between wooden pieces or wrapped in silk. You can also spot various blocks used in printing.
Timings: 9:00 AM-- 5:00 PM (Mon- Fri).
Entry cost: No Charge.
7. Duer Hot Springs Trek
Among the most challenging treks in the land of Bhutan is the Duer Hot Springs trek, which partly crosses roads with Snowman trek which is ideally one of the hardest travelling tracks in the entire world. Duer Hot Springs is the destination of this trek which has a spectacular charm worth the arduous difficulties on the route. Ranging from 3000 meters to 4700 meters, the track relocates via numerous difficulties, steep elevations and low descents.
8. Thimphu Chorten
Memorial Chorten is one the most important spiritual place for Bhutanese people where they worship daily. Throughout the day people walk round the perimeter of the Chorten as a holyritual. Constructed in 1974, it is an impressive illustration of Buddhist culture and architecture.
The whitewashed structure is crowned by a gold spire and also is carved with detailed patterns. The apex emanates with the golden radiance with the initial ray of morning sunlight. The Chorten homes comprehensive paintings and numerous Buddha statutes.
9. Jomolhari Trek
Jomolhari Trek is the longer version of the Jomolhari loop travelling route that put up the travelers against marvelous heights, unfathomable valleys, and challenging trekking routes. It also offer the travelers to experience the breathtaking sight of Himalayan Mountains, flourishing valleys, lush environment-friendly yak pasturelands, lakes, rivers, thick woodlands and also fruit orchards and also the stunning views of Mountain JichuDrakey, Tshering Gang as well as JhoDrakey await you. It provides a superb possibility to experience Bhutanese town life very closely as well as admire the ancient architecture.
10. Deer Park
Deer Park of Thimphu is a Center for Art as well as Reflection. It was established in the year 2007 under the auspices of DzongsarJamyangKhyentse Rinpoche.
Highlights: The Park commemorates the revered event in Sarnath, India. During this event, Buddha turned the Dharna wheel for the benefit of all the view beings. This name aids one review the significant value of all the priceless mentors as well as acts which are a tip of the spirit of compassion as well as visibility in which these presented.
11. Dochula Pass
The Dochula Pass is a mountain come on the snow covered Himalayas within Bhutan when traveling from Thimphu to Punakha where 108 memorial Chortens or stupas called "Druk Wangyal Chortens" have actually been developed by Ashi Dorji Wangmo Wangchuk, the oldest Queen Mommy.
Top Things to do in Thimphu
Get an amazing experience to explore because there are several spectacular places to visit in Thimphu. The remarkable TrashiChhoeDzon gives a monastic view to the place and also it is also an area which is a host of several vivid tsechu celebrations. You can also take a stroll by the weekend markets which permit you to taste some of the finest dried fishes in addition to pork and also various other fish and other seafood items too.
Thimphu is an ideal place for journey like hiking, trekking, rappelling as well as whitewater rafting. The hiking Bhutan tour takes visitors to two of the largest cities of the country namely Paro and Thimphu besides other locations. The nine mile trek starts at Paro as well as after a sightseeing tour at the NationalMuseum and also the carvings of Buddhism's background at Tshogshing Lhakhang; it relocates to the viewpoint of Taktsang monastery. The trip after that proceeds to Thimphu for in-depth exploration of its attractions like Memorial Chorten, national library, Simtokha Dzong as well as the ZorigChusum or PaintingSchool.
1. Shop at the weekend market
This is anenormous event in the day-to-day life of people in Thimphu and one of one of the most fun things to do in Thimphu. Sellers flock to the city right from Thursday evening as well as only leave late Sunday. You can find all kinds of Bhutanese delicacies here, as well as homemade cheese and also dried fish is something that you have to attempt if you are major about regional food. Shopping in Thimphu does not improve than this with the different rlocal incense sticks as well as large dices of excellent saffron made use of for pilgrims.
If you're seeking something a little more extreme, rock climbing is for you. Exciting rock climbing scenic tours is conducted by the Vertical Bhutan Climbing Club. Climb 'The Nose', a climbing rock near Thimphu that provides thirteen amazing climbing routes for all levels.
3. Watch A Game Of Archery At The Archery Stadium.
Archery - The National Sports of Bhutan.
Bhutan's National sport is quite a gala event. The game of archery played in a fashion similar to soccer, their traditional dances on hitting bull's eye and the large exclamations of the gamers create a terrific spectacle. Get yourself a wide overflowed hat, a pair of sunglasses, some knick knacks to chew as well as a bottle of water to enjoy a full archery game.
Sightseeing Places in Thimphu
Tashichho Dzong Fortress
Buddha Dordenma Statue
(10:00 AM – 7:00 PM. Monday – Saturday)
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Home Astronomy & Space ExoMars spots unique green glow at the Red Planet
ExoMars spots unique green glow at the Red Planet
ESA's ExoMars Trace Gas Orbiter has detected glowing green oxygen in Mars' atmosphere—the first time that this emission has been seen around a planet other than Earth.
On Earth, glowing oxygen is produced during polar auroras when energetic electrons from interplanetary space hit the upper atmosphere. This oxygen-driven emission of light gives polar auroras their beautiful and characteristic green hue.
The aurora, however, is just one way in which planetary atmospheres light up. The atmospheres of planets including Earth and Mars glow constantly during both day and night as sunlight interacts with atoms and molecules within the atmosphere. Day and night glow are caused by slightly different mechanisms: night glow occurs as broken-apart molecules recombine, whereas day glow arises when the sun's light directly excites atoms and molecules such as nitrogen and oxygen.
On Earth, green night glow is quite faint, and so is best seen by looking from an 'edge on' perspective—as portrayed in many spectacular images taken by astronauts aboard the International Space Station (ISS). This faintness can be an issue when hunting for it around other planets, as their bright surfaces can drown it out.
This green glow has now been detected for the first time at Mars by the ExoMars Trace Gas Orbiter (TGO), which has been orbiting Mars since October 2016.
"One of the brightest emissions seen on Earth stems from night glow. More specifically, from oxygen atoms emitting a particular wavelength of light that has never been seen around another planet," says Jean-Claude Gérard of the Université de Liège, Belgium, and lead author of the new study published in Nature Astronomy.
"However, this emission has been predicted to exist at Mars for around 40 years—and, thanks to TGO, we've found it."
Jean-Claude and colleagues were able to spot this emission using a special observing mode of the TGO. One of the orbiter's advanced suite of instruments, known as NOMAD (Nadir and Occultation for Mars Discovery) and including the ultraviolet and visible spectrometer (UVIS), can observe in various configurations, one of which positions its instruments to point directly down at the martian surface—also referred to as the 'nadir' channel.
"Previous observations hadn't captured any kind of green glow at Mars, so we decided to reorient the UVIS nadir channel to point at the 'edge' of Mars, similar to the perspective you see in images of Earth taken from the ISS," adds co-author Ann Carine Vandaele of the Institut Royal d'Aéronomie Spatiale de Belgique, Belgium, and Principal Investigator of NOMAD.
Between 24 April and 1 December 2019, Jean-Claude, Ann Carine and colleagues used NOMAD-UVIS to scan altitudes ranging from 20 to 400 kilometers from the martian surface twice per orbit. When they analyzed these datasets, they found the green oxygen emission in all of them.
"The emission was strongest at an altitude of around 80 kilometers and varied depending on the changing distance between Mars and the sun," adds Ann Carine.
Studying the glow of planetary atmospheres can provide a wealth of information about the composition and dynamics of an atmosphere, and reveal how energy is deposited by both the sun's light and the solar wind—the stream of charged particles emanating from our star.
To better understand this green glow at Mars, and compare it to what we see around our own planet, Jean-Claude and colleagues dug further into how it was formed.
"We modeled this emission and found that it's mostly produced as carbon dioxide, or CO2, is broken up into its constituent parts: carbon monoxide and oxygen," says Jean-Claude. "We saw the resulting oxygen atoms glowing in both visible and ultraviolet light."
Simultaneously comparing these two kinds of emission showed that the visible emission was 16.5 times more intense than the ultraviolet.
"The observations at Mars agree with previous theoretical models but not with the actual glowing we've spotted around Earth, where the visible emission is far weaker," adds Jean-Claude. "This suggests we have more to learn about how oxygen atoms behave, which is hugely important for our understanding of atomic and quantum physics."
This understanding is key to characterizing planetary atmospheres and related phenomena—such as auroras. By deciphering the structure and behavior of this green glowing layer of Mars' atmosphere, scientists can gain insight into an altitude range that has remained largely unexplored, and monitor how it changes as the sun's activity varies and Mars travels along its orbit around our star.
"This is the first time this important emission has ever been observed around another planet beyond Earth, and marks the first scientific publication based on observations from the UVIS channel of the NOMAD instrument on the ExoMars Trace Gas Orbiter," highlights Håkan Svedhem, ESA's TGO Project Scientist.
"It demonstrates the remarkably high sensitivity and optical quality of the NOMAD instrument. This is especially true given that this study explored the dayside of Mars, which is much brighter than the nightside, thus making it even more difficult to spot this faint emission."
Understanding the properties of Mars' atmosphere is not only interesting scientifically, but is also key to operate the missions we send to the Red Planet. Atmospheric density, for example, directly affects the drag experienced by orbiting satellites and by the parachutes used to deliver probes to the martian surface.
"This type of remote-sensing observation, coupled with in situ measurements at higher altitudes, helps us to predict how the martian atmosphere will respond to seasonal changes and variations in solar activity," adds Håkan. "Predicting changes in atmospheric density is especially important for forthcoming missions, including the ExoMars 2022 mission that will send a rover and surface science platform to explore the surface of the Red Planet."
Provided by: European Space Agency
More information: J.-C. Gérard et al. Detection of green line emission in the dayside atmosphere of Mars from NOMAD-TGO observations. Nature Astronomy (2020). DOI: 10.1038/s41550-020-1123-2
Image: Artist's impression of ESA's ExoMars Trace Gas Orbiter detecting the green glow of oxygen in the martian atmosphere. This emission, spotted on the dayside of Mars, is similar to the night glow seen around Earth's atmosphere from space.
Credit: European Space Agency
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Oyster Bay es un lugar designado por el censo (o aldea) ubicado en el condado de Nassau en el estado estadounidense de Nueva York. En el año 2000 tenía una población de 6.826 habitantes y una densidad poblacional de 2,142.7 personas por km². Oyster Bay se encuentra dentro del pueblo de Oyster Bay.

Geografía
Oyster Bay se encuentra ubicada en las coordenadas . Según la Oficina del Censo, la ciudad tiene un área total de , de la cual  es tierra y  (23.60%) es agua.

Demografía
Según la Oficina del Censo en 2000 los ingresos medios por hogar en la localidad eran de $57,993, y los ingresos medios por familia eran $73,500. Los hombres tenían unos ingresos medios de $51,968 frente a los $41,926 para las mujeres. La renta per cápita para la localidad era de $34,730. Alrededor del 7.8% de la población estaban por debajo del umbral de pobreza.

Referencias

Enlaces externos

 Oyster Bay Historical Society
 Oyster Bay Main Street Association
 Oyster Bay - East Norwich Central School District
 Enterprise Pilot - Local Oyster Bay Newspaper

Localidades del condado de Nassau
Lugares designados por el censo en Nueva York

redpajama_set_name: RedPajamaWikipedia


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The Mixed Economic Progress of Immigrants
by Robert F. Schoeni, Kevin F. McCarthy, Georges Vernez
In the midst of large increases in immigration, a relative deterioration in the level of education of immigrants, and slow employment growth, the question of how immigrants perform and progress economically in the United States has once more become salient. This report addresses this question in several unique ways. First, it examines in detail the differences in the rate of economic progress of immigrants from different countries of origin (rather than for all immigrants as a whole) and identifies the reasons for these differences. Second, and for the first time, it assesses whether the economic progress of recent immigrants is slower than that of previous generations of immigrants. Finally, it assesses the economic progress of immigrants in California separately from that of those in the rest of the nation, because, at 26 percent, the share of immigrants in California's labor force is more than three times higher than that in the rest of the United States. Japanese, Korean, and Chinese immigrants enter with wages much lower than native-born workers', their wages increase rapidly, reaching parity within 10 to 15 years. Europeans enter with wages similar to natives' and continue to earn comparable wages. In contrast, Mexican immigrants enter with very low wages and experience a persistent wage gap. Although education is a powerful predictor of earnings and explains some of the disparities in earnings, a substantial difference still exists in earnings profiles between certain immigrant groups and those of native-born workers after differences in education have been adjusted for. Whereas educational attainment may influence the level of earnings at a particular point in time, and it may also enhance the rate of growth of earnings over an immigrant's lifetime, the findings from the study were mixed. Finally, the rate of wage growth has not accelerated for any immigrant groups. Although not problematic for some groups, this finding suggests that the persistent wage gap experienced by, for example, Mexicans and Central Americans, may not diminish in the foreseeable future.
Immigration in a Changing Economy: California's Experience — Questions and Answers
The Costs of Immigration to Taxpayers: Analytical and Policy Issues
Data and Country-Of-Origin Groupings
Native-Born and Immigrant Workers: 20 Years of Change
Earnings of Immigrants over Their Lifetime
Empirical Model, Data, and Results
Document Number: MR-763-IF/FF
Schoeni, Robert F., Kevin F. McCarthy, and Georges Vernez, The Mixed Economic Progress of Immigrants. Santa Monica, CA: RAND Corporation, 1996. https://www.rand.org/pubs/monograph_reports/MR763.html. Also available in print form.
Schoeni, Robert F., Kevin F. McCarthy, and Georges Vernez, The Mixed Economic Progress of Immigrants, Santa Monica, Calif.: RAND Corporation, MR-763-IF/FF, 1996. As of January 22, 2020: https://www.rand.org/pubs/monograph_reports/MR763.html


Oman's average annual demand for refined petroleum products is projected at 10 per cent for another 15 year time span, until 2030, according to an estimate by the state-owned refinery company.
The country's fuel (petrol, diesel and aviation fuel) demand will surge to a hefty 582,000 barrels per day (bpd) by the year 2030 from 124,000bpd in 2014 and an estimated 126,000bpd in 2015.
Of the estimated 126,000bpd demand this year, 65,000bpd is for petrol, 50,000bpd for diesel and 11,000bpd for aviation fuel, according to demand estimate of Oman Oil Refineries and Petroleum Industries Company (Orpic), which owns the country's Sohar and Mina Al Fahal refineries.
Driving the growth in demand for fuel is mainly petrol and diesel, which again depends on the growth in vehicle usage and overall business activities.
However, the fuel demand growth projection for the current year is marginal at 1.61 per cent to 126,000bpd, mainly due to a 2.61 per cent fall in new vehicle registration in the first half. The total number of vehicles registered till the end of June 2015 stood at 50,802 as compared to 68,700 for the same period in 2014, apparently due to a slowdown in economic activity. The recent plunge in oil prices caused a slowdown in investment as well as overall economic activity in the country.
However, demand for aviation fuel is expected to surge once the new airport with a passenger handling capacity of 12 million passengers per year starts operation, probably by the end of next year.
The compounded annual growth rate of fuel demand in the last nine years was 10.4 per cent from merely 56,000 bpd to 124,000 bpd in 2014.
Presently, Sohar and Mina Al Fahal refineries have a combined refining capacity of 222,000 bpd. Once Sohar Refinery's multi-billion-dollar improvement project goes on stream by the end of 2016, total crude oil processing capacity of the country will touch 314,000 bpd. The expansion will substantially increase production of liquefied petroleum gas (LPG), naptha, kerosene, gasoline, diesel and will reduce environmental emissions. The project will help Oman to reduce dependence on imported naphtha, while the product range will increase substantially. With Duqm refinery also taking concrete shape, crude oil processing capacity will jump once the third refinery starts operation.
Orpic is also developing a new distribution infrastructure, which is called a multiproduct pipeline, for 290-kms between Muscat and Sohar. It will not only meet local demand for refined petroleum products, but also reduce truck traffic by 70 per cent, which in turn will improve road safety and environment.
Also, transportation costs of tankers are projected to come down substantially once the new pipeline and world-class storage terminal facilities are in place. The whole facility will be commissioned by the second quarter of 2017.


Hello darlings, Lately I've been on this making cocktails kick. With the temps warming up and the sun shining a little more, this white dry cider cocktail recipe is the perfect refreshing companion for a warm spring day and less sugary than a sangria.
Hello lovelies! For those of you who didn't know I LOVE rosé. It's my go-to if I'm at brunch or on a Sunday when I'm having a girls day with some friends.