الفهرس 
الاطار العام للدراسةيوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
The review of previous related literature revealed that there were a few studies on problem-based learning in mathematics in general and at the secondary stage in particular. The review also revealed that there is a relationship between critical thinking and the problem-based learning. Several studies recommended that the critical thinking skills should be developed in all the subject matters as well as in mathematics. The problem has been crystallized and stated in the following five questions:
1- What are the critical thinking skills appropriate to the second-grade preparatory stage pupils in mathematics education?
2- What is the effectiveness of the problem-based learning strategy in developing mathematics achievement among the second grade pupils at the prep stage?
3- What is the effectiveness of the problem-based learning strategy in developing some mathematics critical thinking skills among the second grade pupils at the prep stage?
- STUDY LIMITATIONS:
The present study limited itself to:
1- Two units from the content of Geometry course for the second grade pupils at the prep stage because they were suitable for the problem-based learning strategy.
2- Two prep schools at Benha Educational Administration, one as an experimental group (Al-Sayda Aisha Prep School for Girls) and the second as a control group (15May Prep Schools for Girls).
- STUDY PROCEDURES:
1- Reviewing the previous literature related to the problem-based learning, critical thinking skills and their relationship to mathematics education.
2- Identifying the critical thinking skills appropriate to the prep school students in mathematics education.
3- Preparing students’ handouts and teacher’s manual and judging their validity.
4- Developing the study tools: the achievement test and the critical thinking test for second-grade prep stage pupils and judging their validity.
5- Drawing the study sample from the second-grade prep stage pupils and administering the tools as a pre-application.
6- Experimenting the problem-based strategy to the study experimental group.
7- Administering the tools as a post-application in order to measure the strategy effectiveness in achievement and in developing some critical thinking skills.
8- Treating the data statistically and interpreting the findings.
9- Suggesting some recommendations.
- STUDY FINDINGS:
1) There were statistically significant differences at 0.05 significance level between the scores means of the control group female pupils in the pre-application and the post-application on the critical thinking skills test as a whole and in each sub-skill (Predicting the hypotheses – interpretation, evaluating discussions – deduction), in favour of the post-application.
2) There were no statistically significant differences at 0.05 significance level between the scores means of the control group female pupils in the pre-application and the post-application on the critical thinking test in the induction skill. Thus, the first hypothesis was not verified.
3) There were statistically significant differences at 0.01 significance level between the scores means of the experimental group female pupils in the pre-application and the post-application on the critical thinking test as a whole and in each sub-skill (Predicting the hypotheses - interpretation - evaluating discussions - deduction - induction), in favour of the post-application. Therefore, the second hypothesis was accepted.
4) There were statistically significant differences at 0.01 significance level between the scores means of the control group and the experimental group female pupils on the critical thinking test as a whole and in each sub-skill (Predicting the hypotheses - interpretation - evaluating discussions - deduction - induction), in favour of the experimental group in the post-application. Therefore, the third hypothesis was accepted.
5) There were statistically significant differences at 0.01 significance level between the scores means of the control group and the experimental group female pupils on the achievement test as a whole and in each sub-skill (knowledge – comprehension - application), in favour of the experimental group in the post-application. Therefore, the fourth hypothesis was accepted.