“Less is More – Mathematical Manipulatives in Early Child Education”.

This study examines how early childhood educators in Swedish kindergartens organise goal-oriented learning within mathematics, including how different activities can contribute to children's development of conceptual understanding of mathematical phenomena. The study includes in particular the concepts of "half" and "double". The study is part of a larger development and research project conducted from 2011-2013 at Swedish kindergartens. The purpose of the research project is to examine the preconditions for mathematical learning.

The study concludes that children's experience of a meaningful goal (with the activity) seems to be the key to good teaching in a kindergarten practice, and that teaching strategies with a playful approach are important in early childhood education.

Through the empirical analysis of the ten learning activities, the study results in three different pedagogical contexts for learning. The first context is characterised by focusing on the actual learning objective. The children's attention is directed towards the intended object for learning through planned and individual assignments. The learning object (half and twice as many/much) is the focal point and is studied through the use of different items (e.g. toy animals or toy cars). In this context, the community is only involved to a limited extent in collective strategies for problem-solving, as focus is more on the child doing specific actions to carry out the assignment (e.g. taking additional animal toys to get twice as many) than on the numerical relations between items as indicated by the concepts "half" and "twice as many”. The study finds that the interaction between the children in which they observe each other's problem-solving does not, by definition, facilitate the individual child's understanding of the mathematical phenomenon being studied.

The second learning context is characterised by an indirect focus on the learning object. This context organises the problem-solving activities in which the learning object is handled as a tool or as a means to carry out the primary assignment (e.g. sharing fruit or making play dough, where the recipe is "halved" or "doubled"). The purpose of this approach is to apply mathematical concepts meaningful to the children. Here, the study finds that it is not clear to the children why the mathematical concept (half/double) is important to carry out the assignment. Instead the children often perceive the concept as an inconvenient distraction in relation to the primary objective (e.g. eating fruit or playing with play dough). Thus learning "between the lines" does not seem to be perceived as meaningful by all children.

The third and final pedagogical context is characterised by embedding the learning object in a narrative game. This could be a play or storytelling in which the children are to help the characters in the story to carry out different assignments, and where the mathematical concepts of "half" and "double" are the permeating solution. The study finds that this pedagogical context can constitute a very strong learning strategy, as it involves the children in a meaningful and stimulating activity in which they take part on their own terms and where their ideas are valued as important contributions to collective learning.

The research project includes early childhood educators in small working groups who discuss learning and teaching practices in their own kindergarten. The working groups choose the objects for learning (in the form of mathematical concepts and terms) with which they want to work, and develop and test the learning activities in their own practice. The specific study is based on learning activities conducted within one of these working groups. The group consisting of three early childhood educators worked with the mathematical concept of "half" (as many) and "twice" (as many). Each of the early childhood educators had designed and conducted activities in their own practice in this context. The activities were planned so that the children could recognise them as ordinary play situations and they were conducted with a familiar adult and group of children. All learning activities were recorded on video and subsequently used for discussion in the working group. The data material consisted of video documentation from a total of ten of these learning sessions carried out by the three teachers. The sessions lasted between 7-49 minutes (a total of 192 minutes) and involved children aged 4-5 years. Between three to five children took part in each session. The empirical analysis focuses on the pedagogical context for learning created by the early childhood educators through their choice of design and organisation of the activities and it focuses on the challenges involved.

Björklund, C. (2014). “Less is More – Mathematical Manipulatives in Early Child Education”. Early Child Development and Care, 184 (3), 469-485.