Alexander Karney Die Fähigkeit des arithmetisch-mentalen Operierens und die Steigerung des räumlichen Vorstellungsvermögens

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In the empirical study with 59 first-grade children, the approach of a direct relationship between arithmetic-mental operations and the enhancement of spatial visualization skills is pursued.

While previous studies in this subject area have investigated the influence of various factors of spatial imagination on mathematical competencies, this study uses a textbook analysis to record the underlying geometric competencies for dealing with arithmetic visual material. On the basis of the above, it will be analysed whether it is possible to achieve an increase in the ability to operate mentally in the arithmetic area through support exclusively in the area of space and shape.

The research interest relates to the question whether there is a connection between competencies in spatial imagination and arithmetic mental operation and whether an increase in the ability to operate mentally in the arithmetic area can be achieved through the intervention of support in the area of space and shape.

In order to answer the research question, both a quantitative analysis of the data and qualitative analysis are used. The methodological research approach can therefore be classified as mixed methods. The data are obtained through two procedures: The Hamburg arithmetic test for second grade and the point-image-interview developed by the author himself.

The correlation and regression analysis of the connection between spatial competencies from the Hamburg arithmetic test and mental operation skills, which are assessed in the interview, shows a high Pearson correlation (r=0.56) of the two areas and a high predictive power of spatial competencies on mental operation skills (r2 =0.32). The qualitative individual case analyses of the statistical outliers support the assumption that the development of spatial imagination is the necessary basis for mental operating in the arithmetic area. Using the t-test as a comparison of means for both the intervention group and the control group, it was possible to prove that the support in the geometric area had a positive influence on the ability to perform mental operations in the arithmetic area. The effect size is in a high impact range. The qualitative case analyses, which focus on a comparison of the interviews before and after the support, point to a distinctive feature: children who do not yet use a dominant arithmetic strategy are better able to apply the acquired geometric skills to arithmetic questions, while children with dominant arithmetic strategies rarely deviate from them.

The study provided empirical evidence that the areas of space and shape and number and operation are closely intertwined which in turn highlights the importance of children’s geometric understandings in primary school.