On Atypical Solutions of Some Typical and Atypical Problems Encountered in the School Mathematics Course

Key words: fraction, divisibility, equation, inequality, interval method, logic Due to the fact that both interdisciplinary and intradisciplinary connections are not fully reflected in school mathematics courses, with an emphasis on new forms of organizing learning, insufficient attention is currently paid to improving the content of learning and thereby increasing efficiency. This work’s scientific and pedagogical novelty lies in its identification of atypical (non-traditional) solutions to a variety of typical and atypical problems encountered in the school mathematics course. It also highlights common mistakes made when solving typical and atypical problems and suggests potential workarounds. The terms “typical problem” and “typical solution” as well as “atypical problem” and “atypical solution” will be briefly explained in this article. After that, we will emphasize the specific classes of typical problems (arithmetic problems, equations, inequalities, etc.) and provide methodological guidance on how to solve the problems' primary challenges and steer clear of common blunders. For each class of problems, we will highlight the potential successful uses of intra-subject connections in the school mathematics course. In addition, we will briefly discuss common ways used to solve these kinds of problems. We will also address a number of uncommon mixed situations at the end of the paper, for which we will provide alternative methods that deviate from the “traditional” solutions.