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            <title xml:lang="en">Slow down, you move too fast!</title>
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                <forename type="first">Jorryt</forename>
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            <idno type="halRefHtml">&lt;i&gt;CERME 10&lt;/i&gt;, Feb 2017, Dublin, Ireland</idno>
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                <title xml:lang="en">Slow down, you move too fast!</title>
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                    <forename type="first">Jorryt</forename>
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                <term xml:lang="en">pre-school</term>
                <term xml:lang="en">representations</term>
                <term xml:lang="en">combinatorics</term>
                <term xml:lang="en">Abstraction</term>
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              <p>Short description of the research topic and theoretical framework The focus of this poster is on the links between representations and solutions when 6-year-olds work on combinatorial tasks. The task can be explained as follows: In how many ways can three bears sit on a sofa? Studies of young children's representations often focus on informal and formal representations. Abstraction is often perceived as a goal and teachers often value when young children use abstract representations. Heddens (1986) introduced semi-concrete and semi-abstract as connections between concrete (objects) and abstract (signs) representations. He referred to representations of real situations, for example, pictures of real items, as semi-concrete, whereas he referred to symbolic representations of concrete items, where the symbols or pictures do not look like the objects they represent, as semi-abstract. Connected to the task presented above, concrete implies real bears and a sofa, semi-concrete implies images of (resembling) bears, semi-abstract implies a symbolic, not resembling, representation of the bears and abstract implies the use of formal signs. As for the concrete level, the 'real' bears can be replaced by three play-bears, or by engaging in a role-play, enacting the situation. In both semi-concrete and semi-abstract representations, the colours of the bears and their symbols are often kept identical. When conducting the combinatorial task in 13 preschool classes in Sweden (125 children, age 6), children showed different levels of abstraction in their solutions of the problem. In a previous paper we problematized the apparent relation between the level of abstraction and the number of duplicate solutions. Surprisingly we found that the children who used semi-concrete representations in their documentations were more systematic in the process of finding solutions with less duplication than the children who used semi-abstract representations. We argued that a more abstract level seemed to reduce the problem from bears on a sofa to putting three coloured dots on a paper. It seemed that children moved too fast to the next level of abstraction. Internalisation of the problem had not occurred yet which led to a reduction of the problem as described above. Simultaneously, we also concluded that documentation within the semi-concrete level was very time-consuming for children, as it takes a lot of time for the children to draw bears (Palmér &amp; van Bommel, 2017).</p>
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