Implementing a structural approach in preschool number activities. Principles of an intervention program reflected in learning

ABSTRACT

We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The research question is how teaching grounded on a structural approach and designed based on principles of variation theory is reflected in children’s learning of numbers. To answer this, three analyses were conducted, addressing: i) how the children’s ways of experiencing numbers changed after participating in the intervention, ii) how the theoretical ideas were afforded in the intervention program, and iii) synthesizing how the affordance was associated with the children’s arithmetic learning. One group of eight children participating in the intervention program was chosen for thorough analysis. Progression was observed in how the children changed their ways of experiencing numbers during the intervention that allowed them to enact more advanced arithmetic strategies, which was associated with the structural approach in teaching. The results also show how analysis focusing on aspects discerned in learning and aspects afforded in teaching provides a way of describing arithmetic learning with significant implications for teaching practices.

KEYWORDS:

• Arithmetic skills
• early childhood education
• intervention
• variation theory of learning

Notes

1. The third assessment is not included in this particular analysis since teaching activities between Assessment 2 and 3 are not recorded. The year after the intervention, the children were enrolled in preschool classes at different schools, with different peers and teachers.

2. Examples of children’s responses are from the target group data set.

Additional information

Funding

This work was supported by the Swedish Research Council under Grant [721-2014-1791].

Notes on contributors

Camilla Björklund

Camilla Björklund is Professor in Education at the University of Gothenburg, Sweden. Björklund is involved in research projects within the field of mathematics learning and teaching in early childhood education, which are characterized by practice-oriented research questions and designs. Research areas of interest are mathematics learning and teaching in the early years of preschool and primary school, and teachers’ professional pedagogical development. She has frequently published scientific reports and books for teacher students and practicing teachers, particularly within the field of teaching about numbers and arithmetic in the early years.

Anna-Lena Ekdahl

Anna-Lena Ekdahl is Lecturer, PhD in Didactics, at Jönköping University, Sweden and visiting associate at WITS School of Education, University of the Witwatersrand, Johannesburg, South Africa. Ekdahl is particularly interested in teaching and learning numbers and additive relations in preschool and early primary years. She is involved in intervention projects in Sweden and in South Africa. Projects are characterized by practice-oriented research questions and close collaboration with teachers. Results from projects have been published in scientific papers.

Ulla Runesson Kempe

Ulla Runesson Kempe is Senior Professor in Education at Jönköping University, Sweden and visiting professor at WITS School of Education, University of the Witwatersrand, Johannesburg, South Africa. Her research interests are learning and teaching, particularly in mathematics and the teaching profession in general. She was involved in introducing Learning study – a theory-informed version of lesson study – in Sweden. Over the years she has been responsible for several research projects involving teachers as researchers, funded by the Swedish Research Council. Her PhD was the first one where variation theory of learning was used as an analytical framework and has been engaged with the development of the theory since then. She has been involved in several international research projects studying and comparing classrooms in different countries.