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The relevance of the presented research is conditioned by the necessity of continuous formation of a competitive personality. The competitiveness of the state in the world market is caused by the level of transport and energy infrastructure, the level of training and qualification of the country's engineers. These have determined the task currently being decided by educational organizations to find new resources for training of highly qualified specialists for the diverse industries to develop. Analyzing the multicomponent training of future engineers, experts note the pedagogical potential of mathematical disciplines in the formation of professional competence of engineers. The potential of the cyber-information approach in the training of engineers at university is disclosed and justified in the article, the potential is represented by a combination of the following resources: motivational-adaptive, subjective, integrative, managerial. The authors developed the author's method of training of future engineers in mathematics at university on the basis of the information-cybernetic approach, represented by successively implemented modules: "I get to know myself." "Intellectual puzzle", "Entertaining modeling", "Creative laboratory". The effectiveness of the developed methodology was proved in the course of the experimental research carried out from 2012 to the present time and the experimental training in mathematics at university using the didactic potential of the information cybernetic approach. The materials of the article can be useful in practical terms for university teachers of mathematics striving to significantly improve the level of mathematical training of future engineers.

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This interpretive cross-case study examined the U.S. and Russian teachers' topic-specific knowledge of lower secondary mathematics. In total, N=16 teachers (8 from the U.S., and 8 from Russia) were selected for the study using non-probability purposive sampling technique. Teachers completed the Teacher Content Knowledge Survey (TCKS) as part of the purposive selection. The survey consisted of multiple-choice items measuring teachers' content knowledge at the cognitive levels of knowing, applying, and reasoning. Teachers were also interviewed on the topic of fraction division using questions addressing their content and pedagogical content knowledge. In order to analyze the qualitative data, we conducted meaning coding and linguistic analysis of teacher narratives as primary methods of analysis. The study revealed that there are explicit similarities and differences in teachers' content knowledge as well as its cognitive types. The results are reflected in meanings expressed and language used by teachers while responding to topic-specific questions on the division of fractions. The results of the study suggest that in the cross-national context teachers' knowledge could vary depending on curricular as well as socio-cultural priorities placed on teaching and learning of mathematics. The study's main findings contribute to the body of literature in the field of cross-national research on teacher knowledge with a narrow focus on a topic-specific knowledge. It suggests close comparison and learning about issues related to teacher knowledge in the U.S. and Russia with a potential focus on reexamining practices in teacher preparation and professional development.