الملخص الإنجليزي
This study aimed to clarify the effect of using Proof without Words on the mathematical logical thinking of Eleventh-grade students and their achievement, and tried to answer the following two specific questions:
1. What is the impact of using Proof without Words on the achievement of Eleventh-grade students in mathematics? 2. What is the impact of using Proof without Words on the mathematical logical thinking of Eleventh-grade students? To answer these questions, intentional sample of (58) female students from eleventh grade was selected and distributed into two groups: an experimental group which has (29) students, studied using Proof without Words, and a control group which has (29) students, studied by the usual way. To achieve the purposes of the study, an educational material for the unit of "Sequences and Series" to the eleventh grade in accordance with proof without words, was prepared and verified sincerity arbitration, and a Standardized mathematical logical thinking test and an achievement test which was prepared by the researcher. The results showed the presence of statistically significant differences at the level (a = 0.05) between the mean score of the experimental group and the mean score of the control group in both post mathematical logical thinking test and achievement test in favor of the experimental group who studied using proof without words. In light of these results, the study recommended the teachers to use different methods and techniques to develop the students' logical mathematical thinking, and encourage the researchers to study more about proof without words with other variables.