The effect of the enhanced cluster learning strategy on formal thinking in mathematics among middle school female students

The current research aims to investigate the effect of the enhanced cluster learning strategy on formal thinking in mathematics among middle school female students. To achieve this objective, the experimental method was employed, and the study was conducted during the first semester of the 2024/2025 academic year on a stratified random sample. The sample consisted of 80 second-grade female students from Al-Muruj Al-Khadraa Secondary School, affiliated with the Baghdad Al-Rusafa II Directorate of Education. The sample was divided equally into two groups: 40 students in the experimental group and 40 in the control group. The equivalence of the two groups was verified using an intelligence test and a prior knowledge test. The researcher employed a post-formal thinking test, which included 20 multiple-choice items. The validity and reliability of the test were confirmed. The students' responses were analyzed using an independent samples t-test. The results indicated that the mean score of the experimental group was 12.90 with a standard deviation of 3.801, while the control group had a mean score of 6.93 with a standard deviation of 3.504. The calculated t-value was 7.310, which is higher than the critical t-value of 2 at a significance level of 0.05 and a degree of freedom of 78. The result indicates that the experimental group significantly outperformed the control group in the post-test of formal thinking skills. The researcher suggested using the improved cluster learning strategy for teaching mathematics to students of all ages, helping them learn formal thinking skills and how to use them, emphasizing methods that build formal thinking, and taking into account the number of students when creating math programs.