Modern schoolchildren are the new digital generation and their preferences for working with information are based on of the dominant sensory modality which can be visual, auditory, and tactile/ kinesthetic. Therefore, to organize effective mathematics teaching it is necessary to use a personalized system of teaching techniques, instructional methods, and educational technologies taking into account the way students process information from the outside world. In light of neuropedagogy achievements and the idea of the dynamic balance, the purpose of the article is to provide evidence for the current need for taking into account the students' perceptual learning styles which reflect the nature of interhemispheric interaction in the process of cognitive learning development in mathematics learning. The article is also aimed at establishing a scientific rationale for a classification of teaching methods for development of general learning skills, logical operations, and problem solving skills in mathematics learning based on the criteria of "dominant hemisphere" and "learning style". The research methods are content analysis of scientific, educational and methodological literature to review the methods for cognitive skill development; testing the students' level of general learning skills and the level of verbal reasoning; modeling method, Google questioning of teachers from different regions of the Russian Federation, qualitative analysis of the empirical data. The scientific novelty of the study is the obtained results: empirical data in respect to personalized learning technologies used by Russian teachers; identifying the stages of cognitive skill development in mathematics learning based on the perceptual learning styles of students; establishing a scientific rationale for a classification of techniques for development of general learning skills according to the criteria of "type of learning in accordance with the dominant hemisphere"; developing the criteria for assessing cognitive skills on the basis of the students' learning styles. The theoretical significance of the study lies in its contribution to the mathematics methodology in regard to personalized learning technologies, the techniques for developing cognitive skills in mathematics learning taking into account students' learning styles and applying the ideas of neuropedagogy and the idea of the dynamic balance in teaching mathematics..