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The purpose of this study is to implement an a-didactical activity relating to the acquisition of the triangle inequality, prepared within the framework of the Didactic Situations Theory (TDS), and to report the experiences of the students during the implementation process. The study employs a case study method based on a qualitative approach. Six seventh-grade students in a middle-low socioeconomic secondary school in the Marmara Region of Türkiye participated in the study. The researchers prepared an a-didactical activity in which students discovered triangle inequality. Data were collected through observation, video recording, and worksheets. A descriptive analysis was performed on the data obtained. As a result of the analysis, it was concluded that students completed the activity with the correct expressions by experiencing different phases of the a-didactical situation.

This study aims to determine the effect of an instruction dealing with non-routine problem solving on fifth graders' strategy flexibility and success in problem-solving. For this aim, a quasi-experimental pre-test- post-test design without a control group was designed. The sampling method of the research is convenience sampling. There were 65 fifth graders (11–12 years of age) who came from two different classes of a public middle school located in Istanbul/Turkey. The instruction carried out by the first researcher in the students' classrooms lasted ten weeks (20 lesson hours). Pre-test and post-test consisted of eight non-routine problems which can be solved by using guess and check, make a systematic list, work backward, look for a pattern, simplify the problem, and make a drawing strategies. The results showed that instruction that focuses on non-routine problem solving could improve students' strategy flexibility in this area. Besides, non-routine problem-solving instruction was associated with a significant positive improvement in students' problem-solving achievement. Based on these results, some educational implications and suggestions for future studies were discussed.