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result(s) for
"Variation theory"
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Teachers' learning in a learning study
The point of departure in this study is the question: do teachers who develop theoretical knowledge of the variation theory change the way(s) they offer their pupils the object of learning due to the theoretical framework. The aim of the study is to describe this development, i.e. to find if and how teachers developed theoretical knowledge when planning instruction, and in what way(s) this has an impact on the pupils' learning outcome when using contrasts in the instruction. The theoretical framework is strongly content related, and by analysing the learning object's critical aspects the teachers are guided to focus on the content in this particular way. The question \"what does it take to develop knowledge about the object of learning?\" has to be answered by the teachers before choice of teaching method is made. The research method used is Learning Study, a fusion between lesson study and design experiment. The teachers (6) have carried out nine research lessons in three Learning Study cycles (containing three lessons each). The pupils belong to three different classes and are between 9 and 11 years old. The result shows how the teachers gradually use the variation theory when planning instruction and how the learning outcomes shown by the pupils improve. The developed theoretical insight seems to affect the teachers' ways of seeing the object of learning, such as subtle changes of how to organize the critical features of the learning object, are discerned. In every learning study cycle contrasts are used in one lesson, and in the analysis of the effect of the contrasts, the two remaining lessons are used as control groups. The results show the impact of contrasts in the pupils' learning outcomes. The need to complement a lesson study with a theoretical perspective on learning is that the teachers are then given the opportunity to make use of the theory when planning instruction individually, not only in a lesson study. There again, the Learning Study model seems to be a powerful model with which to develop teachers' understanding of the theoretical framework.
Journal Article
A social semiotic approach to identifying critical aspects
Purpose
– The purpose of this paper is to propose a social semiotic approach to analysing objects of learning in terms of their critical aspects.
Design/methodology/approach
– The design for this paper focuses on how the semiotic resources – including language, equations, and diagrams – that are commonly used in physics teaching realise the critical aspects of a common physics object of learning. A social semiotic approach to the analysis of a canonical text extract from optics is presented to illustrate how critical aspects can be identified.
Findings
– Implications for university teaching and learning of physics stemming from this social semiotic approach are suggested.
Originality/value
– Hitherto under-explored similarities between the Variation Theory of Learning, which underpins learning studies, and a social semiotic approach to meaning-making are identified. These similarities are used to propose a new, potentially very powerful approach to identifying critical aspects of objects of learning.
Journal Article
A complete classification of the isolated singularities for nonlinear elliptic equations with inverse square potentials
In this paper, the author considers semilinear elliptic equations of the form $-\\Delta u- \\frac{\\lambda}{|x|^2}u +b(x)\\,h(u)=0$ in $\\Omega\\setminus\\{0\\}$, where $\\lambda$ is a parameter with $-\\infty0$. The author completely classifies the behaviour near zero of all positive solutions of equation (0.1) when $h$ is regularly varying at $\\infty$ with index $q$ greater than $1$ (that is, $\\lim_{t\\to \\infty} h(\\xi t)/h(t)=\\xi^q$ for every $\\xi>0$). In particular, the author's results apply to equation (0.1) with $h(t)=t^q (\\log t)^{\\alpha_1}$ as $t\\to \\infty$ and $b(x)=|x|^\\theta (-\\log |x|)^{\\alpha_2}$ as $|x|\\to 0$, where $\\alpha_1$ and $\\alpha_2$ are any real numbers.
eBook
Learning about the numerator and denominator in teacher-designed lessons
This study concerns pupils’ experience of unit and non-unit fractions of a discrete quantity during specially designed lessons. The aim was to explore pupils’ understanding of operations such as
b/c of a
in lessons where the teachers were aware of some pupils’ difficulties beforehand and what needed special attention. Five classes were involved in the study and 10 video-recorded lessons and written pre- and post-tests were analysed. Even though the lessons were designed for learning how to operate with both unit and non-unit fractions, we found that more pupils could solve items with unit fractions than with non-unit fractions. We found that few pupils in this study had difficulties with equal partitioning. Instead, it seemed difficult for some pupils to understand the role of the numerator and denominator and to differentiate between the
amount of parts and the amount of objects in each part
, and some pupils did not differentiate between
the numbers of units and the amount of objects within a unit
. This study identified some critical aspects that the pupils need to discern in order to learn how to operate with unit and non-unit fractions of a discrete quantity.
Journal Article
Cross-language differences in Arabic–English translation of Surat Quraysh: a variation theory approach
This study explores the cross-language variation in the English translation of Surat Quraysh in the context of Variation Theory with linguistic, cultural, and aesthetic considerations. It adopts a qualitative descriptive design and applies the ethnographic analytical procedures proposed by Spradley to analyze differences across the translations. The study centers on three major translations by Pickthall, Yusuf Ali, and Abdel Haleem. The results show that linguistic variation in the translated text takes the form of explicitation and modulation in meaning, with cultural variation arising from the handling of the embedded religious meaning in the Arabic text and the various cultural allusions in the source text. Aesthetic variation takes the form of variation in the emphasis on rhythm, brevity, and intensity in language usage, with the three inherent in the distance that exists in the translation of the Arabic to the English. Variation in the Qur’anic translation grants the process of translation a meaning of cultural mediation as opposed to meaning deviation in the context of the translation of the holy text.
Journal Article
What is to be learnt? Critical aspects of elementary arithmetic skills
In this paper, we present a way of describing variation in young children’s learning of elementary arithmetic within the number range 1–10. Our aim is to reveal what is to be learnt and how it might be learnt by means of discerning particular aspects of numbers. The Variation theory of learning informs the analysis of 2184 observations of 4- to 7-year-olds solving arithmetic tasks, placing the focus on what constitutes the ways of experiencing numbers that were observed among these children. The aspects found to be necessary to discern in order to develop powerful arithmetic skills were as follows: modes of number representations, ordinality, cardinality, and part-whole relation (the latter has four subcategories: differentiating parts and whole, decomposing numbers, commutativity, and inverse relationship between addition and subtraction). In the paper, we discuss particularly how the discernment of the aspects opens up for more powerful ways of perceiving numbers. Our way of describing arithmetic skills, in terms of discerned aspects of numbers, makes it possible to explain why children cannot use certain strategies and how they learn to solve tasks they could not previously solve, which has significant implications for the teaching of elementary arithmetic.
Journal Article
Cross-Language Variation in Chinese and English Translations of Dostoevsky’s Crime and Punishment : A Study Through Variation Theory
ABSTRACT Grounded in Variation Theory, this study examines cross-language variation through a comparative analysis of English and Chinese translations of Dostoevsky’s Crime and Punishment. The Theory of Variation explores phenomena arising from cultural heterogeneity during the dissemination of literary works, offering a new perspective and method for the research of literary translation. Since the early twentieth century, more than forty Chinese and over ten English translations of Crime and Punishment have been published. This analysis focuses on four influential translations: the Chinese versions by Yue Lin and Zeng Siyi, and the English versions by Constance Garnett and Oliver Ready. It reveals specific phenomena of variation, identifying the dominant variation at the linguistic level as addition, at the cultural level as the loss of cultural meaning, and at the aesthetic level as a downgrading of aesthetic feeling. Investigating the underlying causes of these variations offers insights into the countries’ linguistic and cultural peculiarities and their profound influence on the translator’s approach to literary translation.
Journal Article
Why Variation Theory Marks an Important Stage in the Study of Comparative Literature
Since its official proposal in 2005, Variation Theory has received significant attention and high praise from academic circles both domestically and abroad. Theo D’haen, editor-in-chief of The European Review, and Professor of English Comparative Literature at the University of Leuven in Belgium, also spoke highly of it. Theo D’haen said, “Professor Cao Shunqing’s Variation Theory of Comparative Literature marks a constitutive phase in Chinese comparative literature’s relationship to the discipline of comparative literature in general.” Therefore, the author interviewed Professor Theo D’haen on the topic of “Why Variation Theory Marks an Important Stage in the Study of Comparative Literature.” In Theo D’haen’s view, “Cao’s variation theory contributes to the greater acceptance of translated literature….it also fosters worldwide cultural and literary dialogue. “Cao’s variation theory is an original and important contribution to international comparative literature studies and a decisive step on the road to a specifically Chinese variant of comparative literature studies.”
Journal Article
Effects of learning addition and subtraction in preschool by making the first ten numbers and their relations visible with finger patterns
In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report is based on an analysis of assessments with 103 children (intervention group n = 65 and control group n = 38) before and after the intervention and a follow-up assessment 1 year after the intervention. Our findings show that the learning outcomes of the intervention group were significantly higher compared to those of the control group after the intervention and that differences between the groups remained even 1 year after the intervention. In particular, the results show that children participating in the intervention group learned to recognize and use part-part-whole relations in novel arithmetic tasks.
Journal Article