| 1. |
|
|
| 2. |
- Björklund, Camilla, et al.
(författare)
-
Teaching finger patterns for arithmetic development to preschoolers
- 2018
-
Konferensbidrag (refereegranskat)abstract
- In this paper we describe the empirical and theoretical meaning behind how finger patterns are taught to facilitate the development of preschool children’s perception of the first ten natural numbers. An intervention programme, informed by Variation theory of learning, included 65 five-year-olds and teachers at seven preschool departments in Sweden. The programme aimed at developing teaching activities and artefacts to promote children discerning necessary aspects of the first ten numbers. The design of the programme is significant to describe and evaluate as basis for forthcoming analyses of the learning outcomes, as a pedagogical approach that stands in contrast to common preschool teaching practice in Sweden is adopted.
|
|
| 3. |
- Björklund, Camilla, 1977, et al.
(författare)
-
Teaching finger patterns for arithmetic development to preschoolers
- 2018
-
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
-
Konferensbidrag (refereegranskat)
|
|
| 4. |
- Kullberg, Angelika, 1969, et al.
(författare)
-
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
-
Ingår i: Teachers and Teaching. - Abingdon : Routledge. - 1354-0602 .- 1470-1278. ; 22:6
-
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.
|
|
| 5. |
- Kullberg, Angelika, 1969, et al.
(författare)
-
What is made possible to learn when using the variation theory of learning in teaching mathematics?
- 2017
-
Ingår i: ZDM - the International Journal on Mathematics Education. - : Springer. - 1863-9690 .- 1863-9704. ; 49:4, s. 559-569
-
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.
|
|
| 6. |
- Marton, Ference, 1939, et al.
(författare)
-
Teaching through Variation: A European Perspective
- 2017
-
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
-
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.
|
|
| 7. |
- Marton, Ference, 1939, et al.
(författare)
-
The idea and practice of learning study
- 2015
-
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
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)
|
|
| 8. |
- Marton, Ference, 1939, et al.
(författare)
-
The object of learning in action research and learning study
- 2019
-
Ingår i: Educational Action Research. - : Informa UK Limited. - 0965-0792 .- 1747-5074. ; 27:4, s. 481-495
-
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.
|
|
| 9. |
- Marton, Ference, 1939
(författare)
-
Towards a pedagogical theory of learning
- 2017
-
Ingår i: Deep Active Learning, Matsushita K. (eds). - Singapore : Springer. - 9789811056604 ; , s. 59-77
-
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.
|
|
| 10. |
- Mårtensson, Pernilla
(författare)
-
Att få syn på avgörande skillnader : Lärares kunskap om lärandeobjektet
- 2015
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Lärare som undervisar i matematik förväntas kunna mer avancerad matematik än vad de undervisar om. Men formell matematikkunskap anses inte vara tillräckligt för att lärare ska kunna undervisa så att ämnesinnehållet blir begripligt för eleverna, de behöver även pedagogical content knowledge (PCK). Begreppet belyser en speciell form av ämneskunskap för undervisning och skiljer sig från den matematikkunskap som används av andra välutbildade vuxna. Det har föreslagits att olika arrangemang av kollegialt och praktikbaserat lärande kan utveckla lärares PCK. Ett exempel på ett sådant arrangemang är learning study. Den här avhandlingen handlar om den kunskap om lärande och undervisning i matematik som studiens lärare utvecklar då de deltar i learning studies och utforskar sin praktik utifrån ett variationsteoretiskt perspektiv. Det yttersta syftet med en learning study är att utveckla elevernas lärande om specifika lärandeobjekt, genom att undersöka vad som kan vara kritiskt för elevernas lärande. I ett samarbetsprojekt med fyra högstadielärare genomfördes två learning studies i matematik, under ett år. Lärargruppen undersökte vad eleverna behöver lära för att de ska förstå i) varför en kvot kan vara större än talet i täljaren och ii) olika representationer av konstanterna k och m i räta linjens ekvation. Under learning study-arrangemangets olika steg samlades studiens empiri in och denna består av filmade lektioner, inspelade möten där lärargruppen planerade och analyserade undervisning och elevers lärande, skriftliga elevtest samt elevintervjuer. Studien har en variationsteoretisk utgångspunkt, vilket innebär att lärande förklaras ske när en person ser något på ett nytt och mer kvalitativt sätt, genom att personen urskiljer aspekter som han/hon inte tidigare har urskilt. Studien visar de två lärandeobjektens kritiska aspekter samt hur de kritiska aspekterna gradvis förändrades och specificerades. Förändringen var ett resultat av att lärargruppen fick syn på avgörande detaljer om på vilket sätt eleverna förstod ämnesinnehållet samt hur skilda sätt att förstå kunde användas i undervisningen för att utveckla elevernas lärande. Där av titeln att få syn på avgörande skillnader. Denna form av utvecklad kunskap om lärandeobjektet kan ses som ett bidrag om PCK och vad det kan vara.
|
|
