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- Björklund, Camilla, 1977, et al.
(författare)
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Teaching finger patterns for arithmetic development to preschoolers
- 2018
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Ingår i: Proceedings of MADIF 11The eleventh research seminar of the Swedish Society for Research in Mathematics Education, Karlstad, January 23–24, 2018. - Borås, Sweden : Stema Specialtryck AB. - 1651-3274. - 9789198402421
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Konferensbidrag (refereegranskat)
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| 7. |
- Björklund, Camilla, 1977, et al.
(författare)
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What is to be learnt? Critical aspects of elementary arithmetic skills
- 2021
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Ingår i: Educational Studies in Mathematics. - : Springer Science and Business Media LLC. - 0013-1954 .- 1573-0816. ; 107, s. 261-284
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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- Chan, S. W. Y., et al.
(författare)
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The early language gap between first- and second-language learners: acquisition of Chinese characters among preschoolers
- 2023
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Ingår i: Frontiers in Psychology. - 1664-1078. ; 14
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Tidskriftsartikel (refereegranskat)abstract
- For culturally and linguistically diverse children, early second language (L2) development is important for school achievement and social inclusion. These children face challenges in acquiring L2, especially in Hong Kong, where the dominant Chinese language contrasts strongly with their home languages. Studies that compared the language abilities of first language (L1) and L2 students in English-speaking contexts have reported young L2 learners' disadvantage in using the dominant language in oral language and comprehension at school entry. The findings raise the question of whether L2 learners who fall behind their L1 peers in language abilities will be further disadvantaged, showing a weaker development gradient. This study used the Chinese Character Acquisition Assessment (CCAA) to compare character acquisition of 491 L2 children aged from 3 to 6 years against that of 240 of their L1 peers from Hong Kong kindergartens. The CCAA is comprised of six subtests and assesses children's abilities to make associations among character written form (orthography), sound, and meaning. Results showed that L2 learners had greater development in meaning and sound associations across class levels, implying that they may first develop oral language related abilities. In addition, results indicate that diverging gaps between L1 and L2 learners' Chinese character acquisition existed across class levels for the associations involving written character form, but not in regard to associations between character meaning and sound. This study highlights the Chinese learning needs of L2 preschoolers and provides understanding of their abilities in mapping among character written forms, sounds, and meanings. The findings suggest the importance of supporting L2 children's oral language at earlier stages of Chinese learning, and the need to provide instructional support to compensate for their relative weakness in literacy at school entry.
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- Innabi, Hanan, 1962, et al.
(författare)
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Sustainable Learning of Statistics
- 2023
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Ingår i: In: Burrill, G.F., de Oliveria Souza, L., Reston, E. (eds.), Research on Reasoning with Data and Statistical Thinking: International Perspectives. - : Springer Cham. - 1869-4918 .- 1869-4926. - 9783031294587 ; , s. 279-302
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Bokkapitel (refereegranskat)abstract
- Sustainable learning is learning that persists and grows over time. It continues beyond formal instruction, and what has been learned in one situation can be expanded and also used in other situations. We address one of the fundamental questions in statistics education research: What makes learning of statistics sustainable? Our conjecture is that enabling learners to focus on variability in statistics will most likely facilitate more sustainable learning of statistics. This conjecture has two sources of support. Learning and teaching of statistics involves two lines of reasoning: (1) deterministic, oriented towards exact numbers and causal explanations, and (2) stochastic, oriented towards uncertainty and variability, where both are important. However, there seem to be a general tendency among people to reason deterministically rather than stochastically. Research shows that a focus on variability in statistics can help in learning to reason stochastically. The second source concerns variation in learners’ experience. Research drawing upon phenomenography and Variation Theory argues that experiencing differences and similarities (in this order) is a necessary condition of learning. Further, we suggest that using Variation Theory as a pedagogical tool to emphasize variability in statistics to support students’ development of stochastic reasoning will potentially increase sustainable learning of statistics.
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- Kullberg, Angelika, 1969, et al.
(författare)
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Teaching one thing at a time or several things together? : Teachers changing their way of handling the object of learning by being engaged in a theory-based professional learning community in mathematics and science
- 2016
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Ingår i: Teachers and Teaching. - Abingdon : Routledge. - 1354-0602 .- 1470-1278. ; 22:6
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Tidskriftsartikel (refereegranskat)abstract
- Twelve lower secondary schoolteachers in mathematics and science were asked to teach a topic of their choice during a lesson that was video-recorded. We were able to analyse 10 of the cases and we found that all of them were similar in one respect: concepts and principles were introduced one at a time, each one followed by examples of the concept or principle in question, apparently to highlight its essential meaning. All the teachers participated in three modified lesson studies with three cycles in four different groups during three semesters. The modified lesson studies were built on a theoretical idea supported by a large number of recent studies. The theory states that new meanings (of concepts and principles, for instance) are learned through engaging with instances of contrasting concepts and principles. The core idea is that new meanings derive from differences, not from sameness. After the three modified lesson studies, the teachers were asked to once again teach the same topic as in the recorded lessons before the lesson studies. The new lessons were also recorded and the analysis showed that there was one thing in common in all cases: all of the 10 teachers dealt with the relevant concepts and principles in relation to each other (i.e. simultaneously) and not one at a time. By thus bringing out the differences between them, their meaning was made possible to grasp for the students. The study lends support to the conjecture that the modified lesson study is a powerful tool for enabling teachers to structure the content of their teaching in accordance with a principle that is more powerful in making learning possible, even if this contradicts their taken-for-granted practice.
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| 16. |
- Kullberg, Angelika, 1969, et al.
(författare)
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What is made possible to learn when using the variation theory of learning in teaching mathematics?
- 2017
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Ingår i: ZDM - the International Journal on Mathematics Education. - : Springer. - 1863-9690 .- 1863-9704. ; 49:4, s. 559-569
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Tidskriftsartikel (refereegranskat)abstract
- The variation theory of learning emphasizes variation as a necessary condition for learners to be able to discern new aspects of an object of learning. In a substantial number of studies, the theory has been used to analyze teaching and students’ learning in classrooms. In mathematics education, variation theory has also been used to explore variation in sets of instructional examples. For example, it has been reported how teachers, by using variation and invariance within and between examples, can help learners to engage with mathematical structure. In this paper, we describe the variation theory of learning, its underlying principles, and how it might be appropriated by teachers. We illustrate this by an analysis of one teacher’s teaching before and after he participated in three lesson studies based on variation theory. Both the theory and the empirical illustration focus on ‘what is made possible to learn’ in different learning situations. We show that in the two analyzed lessons, different things were made possible to learn.
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- Marton, Ference, 1939, et al.
(författare)
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On the Unit of Description in Phenomenography
- 2005
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Ingår i: Higher Education Research and Development. - : Informa UK Limited. - 0729-4360 .- 1469-8366. ; 24:4, s. 335-348
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Tidskriftsartikel (refereegranskat)
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| 28. |
- Marton, Ference, 1939, et al.
(författare)
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Teaching through Variation: A European Perspective
- 2017
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Ingår i: R. Huang & Y. Li (Eds.), Teaching and Learning Mathematics through Variation – Confucian Heritage Meets Western Theories. - Rotterdam : Sense Publishers. - 9789463007818 ; , s. 389-406
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Bokkapitel (refereegranskat)abstract
- This book is about variation and invariance in the teaching of mathematics, that is, about what instances, examples, tasks are used and in which order, to make it possible for students to make concepts, principles, methods their own. Although we can find cases of individual teachers and individual textbook authors paying special attention to such aspects of the teaching of mathematics in different places in the world and at different points in time, such focused attention on the pattern of similarities and differences-especially on the latter-between tasks, instances, examples seems have been particularly common in China for a long time. Moreover, this character of Chinese practice of teaching mathematics has been made explicit by Gu (1991) who called it Bianshi (i.e. teaching with variation) and who tried to relate it to theoretical and empirical research on the learning and teaching of mathematics (in the following the acronym “BS” is used to widely refer to the Chinese tradition of systematically using variation and invariance in the teaching of mathematics). This is the major impetus of most chapters of the present book. We also find another influence, not quite comparable in importance, with the former. It is our own research specialization, called the Variation theory of learning. This research specialization originates from a phenomenological interest in differences in how various phenomena appear to people, i.e., an interest in which different meanings the same phenomenon might have for different people. The reason for this interest is the assumption that people act in relation to things as they appear to them. Hence learning to handle situations in powerful ways takes learning to see them in powerful ways. As one particular contrast between Bianshi (BS) and the Variation theory of learning (VTL) is our focus in the present chapter, and as the former is elaborated in other chapters, we will deal with the latter at some length in the present chapter. There are shorter, but by no means less accurate, introductions to the theory in other chapters. First, when we have established the contrasts between BS and VTL, will we use it very briefly in the very last section as a perspective on the previous chapters. Doing so may appear odd, unconventional, and even disappointing. We have, however, found a problem that – we believe – has to be addressed for the field (the teaching of mathematics through variation) to move forward. Being the authors of one of the last chapters of the book, we were eager to make it pertinent beyond itself.
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| 29. |
- Marton, Ference, 1939, et al.
(författare)
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The idea and practice of learning study
- 2015
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Ingår i: Chapter 6 in Realising learning. Teachers professional development through lesson and learning study, K Wood and S Sithamparam (editors). - London : Routledge. - 9780415844321 - 9781315814216 ; , s. 103-121
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 31. |
- Marton, Ference, 1939, et al.
(författare)
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The object of learning in action research and learning study
- 2019
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Ingår i: Educational Action Research. - : Informa UK Limited. - 0965-0792 .- 1747-5074. ; 27:4, s. 481-495
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Tidskriftsartikel (refereegranskat)abstract
- The Learning study and the Educational Action Research approaches to educational research are compared, not from a third, neutral point of view, but from the perspective of the former. Hence, the comparison is carried out in terms of how the main point of departure of the Learning study (LS), the question of 'What is to be learned?', is addressed in the two approaches. Both represent critical stances to Educational objectives, the frequently taken-for-granted answer to the question. Educational objectives communicate, however, what the students are expected to become able to do, but not what they need to learn in order to get there. Hence, what is to be learned cannot be stated in advance, prior to the teacher learning what her students need to learn. The two approaches to educational research agree on the principle that what is to be learned has to be found in the interaction between students and teachers; however, there is an important difference between the two concerning the very point of departure. Educational objectives are too wide and imprecise according to LS, the teachers have to find the critical aspects (necessary to appropriate, but not appropriated as yet by the students) of the object of learning. According to Action research, as formulated by Lawrence Stenhouse, educational objectives are too narrow, too limited and limiting. We shall start looking for what is to be learned amongst inherent aspects of the content itself.
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| 32. |
- Marton, Ference, 1939
(författare)
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Towards a pedagogical theory of learning
- 2007
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Ingår i: In N. Entwistle & Tomlinson, P. (Eds.) Student learning and university teaching. - Leicester, England : British Psychological Society. - 9781854334442 ; , s. 19-30
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- (From the chapter) This chapter describes the early stages of developing a theory of learning, which offers an alternative perspective to those currently underpinning teaching and learning. It is not specific to higher education; indeed, it has been developed mainly from work at school level. However, the ideas are sufficiently general to apply to teaching and learning at university level, and there are already some examples of research in universities based on the theory. As it is still being developed, the status of 'theory' has yet to be attained: what is offered is better thought of as a 'framework', a way of thinking about learning within educational contexts. Its importance lies in directing the teacher's attention to the specific object of learning--the actual content of what the student is expected to learn. The theory also suggests in general terms what is needed to make learning possible, and so is a pedagogical theory which has generally been referred to as variation theory, for reasons which will become clear.
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| 33. |
- Marton, Ference, 1939
(författare)
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Towards a pedagogical theory of learning
- 2017
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Ingår i: Deep Active Learning, Matsushita K. (eds). - Singapore : Springer. - 9789811056604 ; , s. 59-77
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter describes the early stages of developing a theory of learning, which offers an alternative perspective to those currently underpinning teaching and learning. It is not specific to higher education; indeed, it has been developed mainly from work at school level. However, the ideas are sufficiently general to apply to teaching and learning at university level, and there are already some examples of research in universities based on the theory. As it is still being developed, the status of ‘theory’ has yet to be attained: what is offered is better thought of as a ‘framework,’ a way of thinking about learning within educational contexts. Its importance lies in directing the teacher’s attention to the specific object of learning —the actual content of what the student is expected to learn. The theory also suggests in general terms what is needed to make learning possible, and so is a pedagogical theory which has generally been referred to as variation theory , for reasons which will become clear.
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| 34. |
- Marton, Ference, 1939, et al.
(författare)
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Utveckling är inlärning är utveckling
- 1976
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Ingår i: Forskning om utbildning. - 0345-3588. ; 3, s. 2-14
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 35. |
- Pang, M. F., et al.
(författare)
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Chinese lesson study, Learning study and keys to learning
- 2017
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Ingår i: International Journal for Lesson and Learning Studies. - : Emerald. - 2046-8253. ; 6:4, s. 336-347
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Tidskriftsartikel (refereegranskat)abstract
- Purpose - The purpose of this paper is threefold. First, the authors set out to advance the thesis that lesson study should be considered as the signature pedagogy of teachers. Second, the authors want to argue that combining the core attributes of Chinese lesson study and Learning study will improve the practice of lesson study. Third, the authors attempt to demonstrate how teachers discover necessary aspects of the object of learning (here called "keys to learning") through their engagement in Learning studies. Design/methodology/approach - The paper conducted a contrastive analysis of two varieties of lesson studies: the Chinese lesson study and the Learning study. Findings - Lesson studies form a field of varieties, but the commonality among them (i.e. the focus on the lesson) makes the lesson study a strong candidate for being "the signature pedagogy" of teachers. The most important attribute of the Chinese lesson study is its close connection to the daily work of teachers through its embeddedness in teacher research group (arguably the core organisational principle of the Chinese educational system). The most important attribute of the Learning study is its theoretical grounding which helps teachers create an environment for the students to discern and appropriate necessary aspects of the object of learning. Practical implications - Different varieties may be enriched by including the two core attributes found in the Chinese lesson study and the Learning study. Originality/value - Two empirical studies are used to exemplify how teacher might discover previously unknown necessary aspects of the object of learning (here called "keys to leaning").
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| 36. |
- Pang, M. F., et al.
(författare)
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Interaction between the learners' initial grasp of the object of learning and the learning resource afforded
- 2013
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Ingår i: Instructional Science. - : Springer Science and Business Media LLC. - 0020-4277 .- 1573-1952. ; 41:6, s. 1065-1082
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Tidskriftsartikel (refereegranskat)abstract
- Two studies are reported in this paper. The object of learning in both is the economic principle of changes in price as a function of changes in the relative magnitude of changes in demand and supply. The patterns of variation and invariance, defining the conditions compared were built into pedagogical tools (text, graphs, and worksheets). The first study is the latest in a series of studies aiming to test the fundamental conjecture of the Variation Theory of Learning that new meanings are acquired from experiencing differences against a background of sameness, rather than experiencing sameness against a background of differences. The study compares the learning outcomes under conditions consistent with the basic conjecture with the learning outcomes under conditions not consistent with the theory. The results support the conjecture. The second study shows, however, that the conditions that are consistent with the theory cannot be decided unless the learners' pre-requisites for the task in question are taken into consideration. One set of the pedagogical tools was found to be highly effective for learners with a better initial grasp of the object of learning, while another set was found to be equally effective for learners with a weaker initial grasp of the object of learning. The two sets were equally ineffective when used for the "wrong" group of learners.
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- Pang, M. F., et al.
(författare)
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Teaching to add three-digit numbers in Hong Kong and Shanghai: illustration of differences in the systematic use of variation and invariance
- 2016
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Ingår i: Zdm-the International Journal on Mathematics Education. - : Springer Science and Business Media LLC. - 1863-9690. ; 48:4, s. 455-470
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Tidskriftsartikel (refereegranskat)abstract
- In this study, the systematic use of variation and invariance in the teaching of mathematics is examined in accordance with two different but compatible explicit frameworks. We consider the following: (1) differences in tasks that follow on from each other can significantly change what can be learned; (2) Chinese teachers (and probably those in other high achieving countries in South-East Asia) pay considerable attention to the differences between tasks that follow on from each other; and (3) nonetheless, experienced teachers inspired by the two frameworks both of which pay attention to how tasks that follow on from each other can differ, while teaching the same mathematical topic, may still generate very different patterns of tasks and thereby make very different kinds of learning possible. Two experienced Hong Kong teachers devised and planned a series of lessons on the addition and subtraction of three-digit numbers, together with an expert on an explicit framework for systematic use of variation and invariance. Two Shanghai teachers did the same, together with an expert on a different, but compatible, framework. This paper focuses on the analysis of two lessons, one in Hong Kong and one in Shanghai, both being the first of their respective series. The video-recorded lessons were analysed with the aim of illustrating similarities and differences in terms of the systematic use of variation and invariance. These were not intended to be model lessons illustrating the respective frameworks of variation, but rather were examples of the ways teachers consciously and systematically make use of variation and invariance, as inspired by the two frameworks.
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Stochastic and Deterministic Views of Statistics: A Pedagogical Perspective
- 2022
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Proceedings (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract
- Learning and teaching statistics is a juxtaposition of two lines of reasoning—deterministic and stochastic. Research has shown that the deterministic line of reasoning is in a superior position to stochastic reasoning. Hence, the stochastic line of reasoning must be strengthened to create a better balance between the two lines in order to work toward better statistics learning and teaching. By placing greater emphasis on variability in the data, we will contribute to better stochastic reasoning. This paper adopts the variation theory of learning approach as a pedagogical tool to emphasize variability in statistics and to help students develop their stochastic reasoning. This, we claim, might lead to the sustainable learning of statistics.
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