How spatial structuring abilities support the development of long term effective mental calculation strategies

This paper concerns an on-going research, developed from 2013, aimed to support the development of effective mental calculation strategies along the time. This research is developed with a group of thirty teachers, both of kindergarten and primary school, and a researcher (the author). For this, it’s a research starting with the development of numerical abilities (such as decomposing the number into parts) through spatial structuring abilities (such as spatial visualization of objects) already in kindergarten, in order to support effective strategies in mental calculation, in primary school. We present the analysis of results of a pilot study, carried out with children attending grade 1, and a survey, carried out with children attending the grade 3. The educational activities, which reveal a multimodal approach to numbers and arithmetical, have been presented in others research reports and they'll not discussed in this paper ( Robotti, 2018). Findings of the pilot study and the survey show that the effectiveness of the calculation strategies (in terms of response time, adequacy and of correctness) seems depending on the kind of activities developed in kindergarten and primary school. Our findings indicate that the calculation strategies can be considered stable over the time and, therefore, the acquisition of adequate skills for mental calculation in kindergarten and first class of primary school (for instance decomposing numbers into parts and memorizing arithmetical facts) can be considered a sort of "heritage" for students because it can be exploited to effective calculation even after the grade 1.