The epistemological commitments of modes: opportunities and challenges for science learning

Meaning making in science is supported by different modes, such as spoken and written language, images and gestures, all of which have different affordances. The epistemological commitments of modes are affordances that cannot be avoided. This article investigates how the epistemological commitments of modes affect possibilities for learning. Video data was collected from a learning activity where upper secondary students drew and explained an experiment representing the greenhouse effect. The analysis uses the variation theory of learning, which assumes that students learn when they notice new aspects of objects of learning by experiencing variation against an invariant background. Such variation can be created through the representations used. Findings show that, in the learning activity, variation was created in a range of modes. Some of the variation, particularly with regards to radiation, was due to the epistemological commitments of drawing. However, these aspects of radiation went unnoticed by the students, possibly because several aspects varied simultaneously. The teacher then helped the students to become aware of certain variation. Implications for the teaching and learning of science when taking the epistemological commitment of different modes into consideration include both challenges, such as when unintended variation is created, and opportunities, such as when spontaneously occurring variation can be taken up for discussion.

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.

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.

Enhancing the generative learning of young people in the domain of financial literacy through learning study

Purpose The purpose of this paper is to collect new evidence about the efficacy of the pedagogical principles derived from our earlier study on boosting students’ financial literacy, with the aim of providing a theoretically and practically powerful account of how generative learning in the domain of financial literacy can be enhanced. Design/methodology/approach This is an example of learning study consisting of a design experiment, which aims to test the conjectures of the variation theory of learning. A total of 156 students who were aged from 14 to 16 years were taught under the three learning conditions which embedded the test criteria, and a total of seven lessons were used by the two participating teachers for each of the classes. To assess students’ appropriation of the object of learning, four tests were conducted, i.e. a pre-test, post-test immediately after the lessons, delayed post-test after six weeks and second delayed post-test after six months. Findings This study shows that a systematic use of the pattern of “contrast-fusion-generalization” to deal with the individual core economic concepts identified can help students lay a solid conceptual foundation for developing financial literacy. Furthermore, with the use of the meta-level pattern of “contrast-fusion-generalization” through complex everyday financial problems or situations which transcend the specific concepts, students can make effective use of the core economic concepts learned and transform them organically into one’s analytical framework. This enables students to discern and focus upon the critical aspects of novel financial situations and have a greater likelihood of making well-reasoned and sound financial decisions. Originality/value This paper sheds light on the ways in which students’ generative learning in the domain of financial literacy can be enhanced through the conceptual approach grounded in the variation theory of learning.