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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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| 3. |
- Kullberg, Angelika, 1969, et al.
(författare)
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Mechanisms enabling knowledge production in learning study
- 2020
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Ingår i: International Journal for Lesson and Learning Studies. - : Emerald Group Publishing Limited. - 2046-8253 .- 2046-8261. ; 9:1, s. 78-91
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Tidskriftsartikel (refereegranskat)abstract
- PurposeThe purpose of this paper is to add to the discussion about practitioner research in schools – by addressing mechanisms and systematic strategies based on theory in a research model, which enables the creation of knowledge products that enhance student learning and are sharable between teachers.Design/methodology/approachThe research question is the following: Can a specific form of teachers’ research produce practice-based knowledge relevant beyond the borders of the local school context? This question is addressed through empirical examples from previously published papers on learning studies in natural sciences, mathematics and language.FindingsThis paper promotes the view that teachers in learning studies can create practical public knowledge relevant beyond their local context. The authors suggest that learning studies and variation theory can offer teachers mechanisms to create such public knowledge.Originality/valueThe paper proposes that teachers’ collaboration in professional learning communities, as in a learning study, not only has the capacity to increase students’ and teachers’ learning, but it can also be used to create practical public knowledge.
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| 4. |
- 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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| 6. |
- Kullberg, Angelika, 1969, et al.
(författare)
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Effects of learning addition and subtraction in preschool by making the first ten numbers and their relations visible with finger patterns
- 2020
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Ingår i: Educational Studies in Mathematics. - : Springer. - 0013-1954 .- 1573-0816. ; 103:2, s. 157-172
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Kullberg, Angelika, 1969, et al.
(författare)
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Improvements in learning addition and subtraction when using a structural approach in first grade
- 2024
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Ingår i: Educational Studies in Mathematics. - : Springer. - 0013-1954 .- 1573-0816.
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Tidskriftsartikel (refereegranskat)abstract
- Learning to calculate with natural numbers by structuring seems promising but how this can be taught in a sustainable manner remains an open question. An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in four Swedish first-grade classes. One goal was that by the end of first grade, students would be able to solve tasks such as subtracting 8 from 15 by using part-whole number relations. In this paper, we report on learning outcomes from task-based interviews with intervention and control groups before, immediately after, and one year after the intervention, in order to investigate long-term effects and whether students used a structural approach when solving tasks in a higher number range in the second grade. In comparison to controls, students in the intervention group showed higher increases in their learning outcomes. Moreover, the intervention group used a structural approach to a larger extent when solving tasks in higher number ranges, whereas students in the control group more commonly used single-unit counting to solve such tasks. These findings have implications both for teaching and for research on students' development of arithmetic skills.
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