Number line estimation tasks: Ein fachdidaktischer Blick auf einen in den kognitiven Neurowissenschaften prominenten Aufgabentyp

Number lines and related representations are central working tools in mathematics teaching from primary school onwards. Therefore, according to a broad consensus within mathematics education literature, children initially need to learn how to understand number lines before number lines may become conducive to their further learning. In current subject didactic publications in the German-speaking world, there are clearly different and sometimes contradictory recommendations on how to understand and, depending on this, how to teach number lines. There is a lack of research on which of these recommendations are implemented in the classroom how often, in which way, and how successfully.

On the other hand, there are numerous mostly neuropsychological and cognitive psychological-oriented studies on a particular type of task, the so-called number line estimation task. The task is to draw the appropriate marker for a third number on otherwise empty number lines between two given numbers—in most of the studies between 0 and 100 or 0 and 1000—or, conversely, to indicate the appropriate number for a given marker.

This article attempts to provide a didactic analysis of the prerequisites for the successful completion of number line estimation tasks and a well-founded assessment of the didactic value of such tasks for the development of mathematical competence in primary school. The subsequent review of the extensive empirical research on number line estimation tasks makes clear that the results of the didactic analysis at least do not contradict the empirical findings, but that a number of questions, the answers to which are central to the planning of teaching measures, make further empirical research urgently necessary. Some of these desiderata are finally formulated and put up for discussion.