Linguistic Engagement with Spatial Reasoning in Primary School, Daycare and the Family

Project leader

Dep.-Prof. Dr. Marcus Schütte

Institution

Universität Hamburg

Duration

01.01.2012 – 31.12.2013

Funding volume

37,000 € (Universität Hamburg)

Research question and state of research

The development of spatial reasoning is of great importance in the spatial world that surrounds us. Not only do nearly all actions of individuals take place in the spatial world, but cognitive abilities such as intelligence or mathematical skills are now also seen in connection with spatial imagery. Importantly, broadly based early competencies in spatial imagination not only have positive effects on later spatial thinking, but also on mathematical performance in other subdomains (cf. Lüthje 2010, p. 17; Stern, Felbrich and Schneider 2006). In addition, spatial conceptions shape our thinking and language. In a multitude of metaphors, "spatial" terms are used in everyday speech, e.g. "elated mood" (Hochstimmung), "to be on top" (obenauf sein), "something takes up a lot of room" (etwas nimmt viel Raum ein). The aim is to use concrete concepts or terms from the field of spatial reasoning to describe abstract issues or feelings precisely.

"This function of metaphors – the structuring of thinking – is also of importance for mathematical thinking. Less concrete mathematical objects – numerical quantities, relations between sets, temporal relations – are described with the help of spatial metaphors, e.g. in expressions such as 'a great number', 'numbers above 1000', or the prepositions 'before' and 'after', which originate from the spatial domain but also denote temporal relations." (Fthenakis et al. 2009, emphases in the original, p. 77; cf. also Lakoff and Johnson 1980).

Spatial abilities are thus indispensable for children's development; nevertheless, geometric content related to space still receives little attention in school. Due to a lack of systematicity and an underestimation of their importance, they are apparently avoided by teachers. For a long time, school geometry teaching focused almost exclusively on a study of shapes and on viewing the environment from a two-dimensional perspective (cf. Winter 1976, p. 15; Lüthje 2010, p. 18 f.). However, if one takes the importance of spatial reasoning skills for the cognitive development of children seriously, the question arises about the conditions for the conveyance of spatial reasoning skills. In this context, an incidental finding from a study by Anderson (1997) appears relevant. Anderson examined parent-child interactions of 21 four-year-old children and their parents in mathematics-related situations. To this end, she provided the families with building blocks, white paper, preschool worksheets and interlocking cubes, and audio-recorded the first 15 minutes of each family's joint solution-finding. She was able to find that there was a wide range of differently deep mathematical approaches in the parent-child interactions, with counting at the core of mathematics. Interestingly, however, she could find almost no explicit verbalisations of spatial-position designations in the parent-child interactions in her recordings. This suggests that these verbalisations of spatial-position designations were compensated for by deictic pointing gestures. A neglect of spatial reasoning in everyday interaction in the family context is also indicated by a finding of Acar (2011). Using play situations, Acar shows that parents reinterpret building situations, which from a mathematics-education perspective are to be assigned to the field of spatial reasoning, in arithmetic terms and place a focus of their support on counting wooden blocks, while the spatial-geometric implementation remains flawed. If, however, one assumes with Newcombe and Huttenlocher (2006) that the linguistic encoding of space is a central competency with regard to spatial reasoning skills, then the "indications" presented point to a research need for mathematics education: although great importance is attached to the linguistic engagement with spatial reasoning, this is apparently barely supported within the family. In the present pilot study, these so far only suggested findings are to be examined further with regard to their validity:

What linguistic ways of dealing with spatial reasoning can be reconstructed in everyday situations within the family?

If, however, one examines the mathematical development of children, it is, according to Fthenakis et al. (2009, p. 38f.), fundamentally necessary to include all of the child's learning environments:

"For effective learning depends on strengthening all of the child's educational and learning environments." (Fthenakis et al. 2009, p. 38f.)

If one takes this statement seriously, it must be considered that the linguistic engagement with spatial reasoning takes place not only in the family, but also, among other things, in daycare and primary school. Therefore, the treatment of the above research question, which focuses on a verification and refinement of previous results, is to be combined with an innovation of perspective. Not only families, but also daycare centres and primary schools are to be examined at the same time. The modified research question is therefore:

How do the different learning environments – family, daycare and primary school – differ with regard to the linguistic engagement with spatial reasoning?

A comparison of different learning environments with regard to the linguistic engagement with spatial reasoning takes account of the holistic development of children and is, at the same time, an opportunity to place support concepts for the development of spatial reasoning skills on a comprehensive foundation. The long-term aim of our joint research is to identify, from a holistic view of the linguistic engagement with spatial reasoning, opportunities and risks, and from this to develop a further training concept that advances the networking of the three learning environments and supports parents, daycare educators and primary school teachers in jointly fostering the development of spatial reasoning skills.