The Effect of Combining Two Models on Mathematical Achievement and the Development of Procedural Fluency Among Fifth-Grade Science Students in Mathematics

This research aims to study the effect of integrating two models 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 strategies of binary analysis, synthesis, and fragmented knowledge integration, and a control group of (33) students who studied according to the traditional method. The researcher prepared an achievement test tool consisting of multiple-choice objective items and a procedural fluency scale. After conducting the necessary statistical analyses, it was administered to students in both research groups. The results showed statistically significant differences in mathematical achievement and the development of procedural fluency among students, in favor of the experimental group Based on the research results, the researcher recommends the following. 1) Focus on the use of modern teaching strategies, including the analysis and synthesis strategies and the fragmented knowledge integration strategies, in teaching mathematics. 2) Integrate the analysis and synthesis strategies and the fragmented knowledge integration strategies into the curriculum and teaching methods curriculum in colleges of education. The researcher proposed several suggestions, including: 1) Studying the impact of other types of strategies, such as analysis and synthesis and the integration of fragmented knowledge, on various dependent variables, such as attitude, information retention, cognitive preference, concept acquisition, and others. 2) Comparing the impact of analysis and synthesis and the integration of fragmented knowledge with other effective teaching strategies, such as mental description, constructivist learning, and multiple intelligences..