This research delves the impact of implementing a didactic sequence on the appropriation and diversification of mental calculation strategies among 5th-grade students (aged 10-11 years). The study moves beyond traditional approaches to investigate how structured and interactive learning experiences can enhance mathematical reasoning and flexibility in calculation methods. Building upon theoretical perspectives that emphasize the importance of mental calculation in mathematics education, Beishuizen (1997) highlights numerical decomposition as a key technique. Kamii and Dominic (1998) argue that algorithmic dependence may hinder children's mathematical reasoning, reinforcing the necessity of promoting flexible strategies. Mendes (2013) underlines the relationship between multiplication and division in developing mathematical understanding, a crucial aspect of this study. Additionally, Sowder (1992) emphasizes the role of mental computation in fostering number sense, and Verschaffel et al. (2009) highlight the importance of flexible arithmetic strategies for problem-solving. This research employs a mixed-methods approach, involving 19 students from the same 5th-grade class. Data collection includes participant observation and pre-post-test assessments. The didactic sequence comprised eight formative sessions, the aim of which was to encourage problem-solving through mental calculation strategies, fostering collaborative learning and strategy sharing. The study aligns with Threlfall (2002), who asserts that exposure to multiple problem-solving strategies enhances mathematical reasoning and adaptability. The findings indicate a significant improvement in students' performance post-intervention, with the students exhibiting increased calculation speed and greater strategic diversity, favouring numerical decomposition in addition and subtraction. Initial difficulties in multiplication and division were mitigated as students engaged in targeted activities and peer discussions, supporting the premise that structured exposure to diverse strategies enhances mathematical fluency (Kilpatrick et al., 2001; Swafford & Findell, 2001). These results align with Baroody's (2003) suggestion that the ability to switch between strategies is key to arithmetic proficiency.

The present study underscores the importance of establishing mental calculation routines and promoting interactive learning, as encouraging students to articulate and compare different approaches fosters mathematical thinking and problem-solving (Siegler & Lortie-Forgues, 2015). The findings of Kilpatrick, Swafford, and Findell (2001) accentuate the interconnectedness of conceptual understanding, procedural fluency, and adaptive reasoning in mathematical proficiency, while Siegler and Lortie-Forgues (2015) further argue that numerical flexibility is critical for long-term mathematical success.

In conclusion, this research highlights the need for structured yet flexible instructional strategies to enhance mental calculation proficiency. By promoting a range of strategies, facilitating discussion, and encouraging active engagement, educators can assist students in developing a more adaptable mathematical understanding and enhancing their problem-solving skills.

Keywords: Mental Calculation, Mathematics Education, Didactic Sequence, Numerical Decomposition, Problem-Solving Strategies, Arithmetic Proficiency, Flexible Strategies.