The effectiveness of integrating the dual analysis and synthesis strategies and the integration of fragmented knowledge.m and their impact on mathematical achievement and the development of procedural fluency among fifth-grade science students in mathe

This research aims to examine the effectiveness of combining the two strategies of analysis and synthesis and the integration of fragmented knowledge, and their impact on mathematical achievement and the development of procedural fluency among fifth-grade science students in mathematics. The research sample consisted of two groups: an experimental group of (31) students who studied according to the dual analysis and synthesis strategies and the integration of fragmented knowledge, and a control group of (33) students who studied according to the traditional method. The researcher prepared an achievement test tool consisting of objective multiple-choice items and a procedural fluency scale. The researcher relied on a scale that includes groups, where each group contains (5) items, and each item includes three alternatives. The researcher compared the two research groups in the following variables (chronological age calculated in months, intelligence test scores, mathematics score for the academic year (2024-2025). After conducting the necessary statistical analyses, they were applied to the students of the two research groups. The results showed the presence of statistically significant differences in the students’ mathematical achievement and the development of procedural fluency, in favor of the experimental group. In light of the research results, the researcher recommended several recommendations, the most important of which is the necessity of adopting the dual analysis and synthesis strategies and the integration of fragmented knowledge in teaching mathematics for the primary, intermediate and preparatory stages in our schools. The researcher presented several proposals, the most important of which was the effect of the dual analysis-synthesis and fragmented knowledge integration strategies on fifth-grade students' acquisition of mathematical concepts and the development of their numerical intelligence.