الفهرس 
الفصل الأوليوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
Problem of the Research:
The problem of the current research is represented in the low level of geometric thinking and engagement in learning of mathematics. so the current study addressed this problem by using Problem Posing Strategy. This problem has raised the following question:What is the effect of using Problem Posing Strategy in developing geometric thinking and engagement in Learning among second preparatory stage students?
The previous question was branched into two questions :
1- What is the effect of using Problem Posing Strategy in developing geometrical thinking among second preparatory stage students ?
2- What is the effect of using Problem Posing Strategy in developing engagement in learning among second preparatory stage students ?
Objectives of the Research:
the current Research aims to study the effect of Problem Posing Strategy in teaching geometry in developing geometric thinking levels and developing Engagement in Learning among Preparatory Stage Students.
Limitations of the Research:
The current Research is limited to:
1- the units of ”medians of triangle” and ”variance” in Geometry course of second preparatory grade for the first semester of 2021-2022.
2- the study sample from Nasser preparatory school for girls at Sohag governorate .
Materials and Tools of the Research:
Firstly: Materials of the Research: which are:
1- pupil ’s book after being reformulated by using Problem Posing Strategy.
2- pupil ’s worksheets .
3- A teacher’s guide for teaching geometric by using Problem Posing Strategy.
Secondly :Tools of the Research:
1- Test of geometric thinking of ”Van Hiele”.
2- A scale of engagement in learning(prepared by the researcher).
Hypotheses of the Research:
To answer the questions of the research the two following hypotheses were tested :
1- There is a statistically significant difference between the mean scores of the experimental group (which studied by using the Problem Posing Strategy) and the control group (which studied by the usual way) in the post application of geometric thinking and in each level in favor of the experimental group.
2- There is a statistically significant difference between the mean scores of the experimental group (which studied by using the Problem Posing Strategy) and the control group (which studied by the usual way) in the post application of -Engagement in Learning as whole and in each dimension in favor of the experimental group.
Method of the Research:
Because of the nature of the current research, the quasi-experimental research method was used in the application side of the research and to identify the effect of teaching geometric using the problem Posing strategy in developing geometric thinking and Engagement in Learning among Preparatory Stage Students.
Research variables included the followings:
1- The independent variable:Teaching geometry using problem posing strategy.
2- The dependent variables: geometric thinking and Engagement in Learning among Preparatory Stage Students
Procedures of the Research:
To achieve the objectives of the research, answer its questions and test the validity of its hypotheses, the following procedures were followed:
1- Surveying and analyzing the previous literature, research and studies related to the topic of research (problem posing strategy, geometric thinking, engagement in learning) in order to benefit from them in preparing research materials and tools.
2- Analyzing of the geometry course from the mathematics book of the second grade of preparatory school in order to determine the concepts, generalizations, and skills included in them.
3- Preparing materials of the Research: which are:
- pupil ’s book after being reformulated by using Problem Posing Strategy.
- pupil ’s worksheets .
- A teacher’s guide for teaching geometric by using Problem Posing Strategy.
4- Preparing Tools of the Research: which are (Test of geometric thinking of ”Van Hiele - A scale of engagement in learning).
5- Presenting research materials and tools to a group of arbitrators to judge their validity and make the suggested modifications.
6- setting the tools and process them statistically.
7- Choosing the sample randomly and dividing it into two equivalent groups, one experimental and the other control.
8- pre- application of the research tools to the two groups.
9- Teaching the units of ”medians of triangle” and ”variance” in the geometry course using the problem Posing strategy for the experimental group, and in the usual way for the control group.
10- post - application of the research tools to the two groups.
11- Monitoring the results, statistically processing them, analyzing and interpreting them, answering research questions and choosing the validity of their imposition.
11- Providing some recommendations and proposals in light of the results of the research.
Results of the Research:
The Research reached the following results:
1- the effect of using Problem Posing Strategy in teaching ”medians of the Triangle and the Variance” units in developing the geometric thinking Levels and every level separately for second- grade preparatory students (the experimental group) compared with their counterparts who study the same units (the control group) by using the usual way.
2- the effect of using Problem Posing Strategy in ”medians of the Triangle and the Variance” units in developing engagement in learning as whole and every dimension separately for second- grade preparatory students (the experimental group) compared with their counterparts who study the same units (the control group) by using the usual way.
3- The percentage of the students (in the experimental group) who reached the mastery level in levels of visualization and analysis was 100%, while the percentage of the students who reached the mastery level in the level of deduction was 87.5%, and the level of formal deduction was 45.8%, and in Rigor Level was 25, for students of the control group The percentage of the students who reached mastery in level of visualization was 72.9 %, in the level of analysis was 47.9 %, in level of informal deduction was 18.75 %, in level of formal deduction was 0%, and in the level of Rigor was 0 % , that indicates the excellence of the members of experimental group over the members of the control group in the geometric thinking levels, This is due to the use of the problem Posing strategy with the experimental group.