The objective of this research was to diagnose mathematical abilities in preschool children aged 5 to 7 on the basis of geometry and, subject to the results obtained, to recommend targeted pedagogical interventions with respect to the preschoolers found to have deficits in knowledge and skills. The research was conducted in the Biala Podlaska Laboratory of Psycho-Motor Skills in Poland in June 2018. A SensoMotoric Instrument eye-tracking device and the i ViewX platform registering data with a frame rate of 250 Hz was used. Using a special measurement system, the device can track and record the eye movements of an analysed person in a sequence and at a specific speed. The analysis of the data was performed with the application of the BeGaze 3.4 software. To demonstrate the differences between the correctness of task performance and the age and gender of the children, a Pearson's Chi squared test was performed. To analyse the time that children from the study group needed to perform specific tasks, Student's t test was employed. In all analysed cases, the significance level p = 0.05 was assumed. The results of the research involving the studied group of children (N = 176) demonstrated differences in the level of geometric skills. Regarding biological variables, such as gender and age, statistically significant differences were observed with respect to the age of the studied group. Distinguishing between plane shapes did not cause any problems in comparison with the tasks which required analytical thinking. The most evident distinctions were observed between children aged 5 and older children (6 and 7 years old). The level of difficulty of the tasks was a factor that affected the time needed to provide answers irrespective of gender. The level of geometric performance of the majority of the studied children was normal. Nonetheless, individual targeted interventions should be considered with respect to certain children with mathematical problems in order to improve their geometric skills before they start school education. The development of pedagogical interventions should be preceded by a targeted diagnosis of unsatisfactory performance and progress with respect to elementary mathematical skill acquisition. Teachers should be inspired to use innovative methods and techniques in their didactic practise in order to motivate children to study geometry.