Аннотация
The purpose this article stems from the existing problems of insufficient adherence to the principles of interdisciplinary methodology when using mathematical methods in socio-economic research over the past ten years. The article aims to present a detailed methodology for interdisciplinary research, illustrated with a specific example of using mathematical methods in socio-economic studies within the integrative framework of scientific knowledge. A statistical analysis of the causal relationships underlying the decline in overall birth rates in Kazakhstan and the number of children born by birth order over an extended period has been conducted. Furthermore, the validity and reliability of the conclusions drawn from the statistical analysis are confirmed using a mathematical method based on statistical dependency equations. The value of the article lies in outlining the procedure of interdisciplinary research methodology applied to the study of demographic processes using mathematical methods. The importance of implementing the principles of interdisciplinary research methodology is demonstrated through a concrete demographic study, particularly when applying commonly used correlation-regression methods. Additionally, the selection of the mathematical method is considered in accordance with the research objectives, including the methodology for applying statistical dependency equations to the subject of study. For the first time, forecasts are calculated using normative computations. The study reveals that the dynamics of the total number of children born in Kazakhstan are influenced by the number of children born by birth order, including the identification of reasons for the sharp decline in the number of first- and second-born children, and their future prospects. The causes were primarily the reduction in the number of women of childbearing age. To maintain a stable generation in the near future, attention should be given to large families (with more than 4–5 children) and state support should be provided to them.