الفهرس 
الاطار العام للبحثيوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
The problem of the current study is the low level of the preparatory stage students performance at mathematical Proof skills .to confront this problem the current study tries to answer the following main question :
How could the mathematical proof skills The preparatory stage students be improved? these questions branched out of the main question
1- What are the mathematical proof skills that suitable for the second preparatory class students ?
2- What is the extent of the second preparatory class students proficiency of these skills ?
3- What is the efficiency of constructivist Learning Model ”Five Es ” to improve mathematical proof skills of the second preparatory class students?
4- What is the efficiency of constructivist Learning Model ”five Es” for the second preparatory class students learning ?
The Limits of the Study :
The limits of the study:
1- A group of the second preparatory Stage students :
Because the students of the second preparatoryStage are medium siege between the first and the third preparatory stages .the improvement of the mathematical proof skills will qualify them to use these skills in the following stages and classes .besides the third preparatory class is a finished one .
2- The two units of ”Areas and projections”:
from the geometry book of the second preparatory class are the most suitable ones for the mathematical proof skills .
Determination of the Study idioms
1- Constructivist Learning Model ”five Es”
It is a constructive Learning Model based on five stages beginning with the letter ”E”
These five stages are :
1- Engagement. 2- Exploring.
3- Explanation. 4- Elaboration.
5- Evaluation.
This study will adopt this definition .
2- Mathematical proof:
It is a proof of the correctness of a sentence .this proof includes a series of mathematical sentences that every sentence is deduced from itprevious one by logic, conclusion ’and acceptable mathematical justidentification (information- theory - axiom- or.....).
This study will adopt this definition .
3- Mathematical proof Skills:
It is a series of logical performance that the individual did them accurately when proving or solving a mathematical problem by deduction, logic and presenting the Proof according to a previous mathematical theory or an action or a fact or ....etc . this skills improve as result of practicing this study will adopt this definition .
The procedures of the Study:
The procedures of the study move according to the following steps:
First :Determining mathematical Proof skills which aresuitable for the second preparatory class - stage? this is through the following :
1- Studying the previous researches and studies .
2- Review the educational morals that are existed in the field .
3- Studying the nature, the skills and the importance of Mathematical proof.
4- Studying the characteristics and the nature of the preparatory stage students .
5- Analyzing the goals and the content of mathematics books of the preparatory stagestudents to know itsmathematical proof skills .
6- Preparing a list of attained mathematical proof skills ”then represent if to the experts and specialists in this field to adjust this list to obtain a Ionia list of mathematical proof skills which is suitable for these students
Second:Determining the extent of proficiency of the second preparatory stage from the achieved mathematical proof skills in (first) and this is through :
1- Preparing a test to measure the mathematical proof skills of the second preparatory class students and make sure of its validity and stability lor measuring its purpose .
2- Selecting a sample of the second preparatory class students then applying the test .
3- Registering the results of the test then determining the extent of proficiency of these students of these skills .
Third : Determining the efficiency of the constructivistLearning Model ”five Es ” to improve the mathematical proof skills of the second preparatory class students and this is through :-
1- Preparing the lessons of the two units ”Areas and projections” according to the model .
2- Preparing a guidebook for the teacher about teaching these two units in the light of the model .
3- Selecting the sample of the study from the students of the second preparatory class and divided them into two groups :.the Experimental group and control group .
4- Applying the mathematical proof skills test on the two groups : the Experimental group and control group (anterior).
5- Teaching the two units by using the model for the Experimental group and by using the usual method for the control group .
6- Applying the test posterior on the two groups: the Experimental group and the control group .
7- Analyzing the results statistical and explaining them .
Fourth : Determining the extent of efficiency of the Constructivist Learning Model ”five Es ” in the learning level of the second preparatory class students and this through :-
1- Preparing an acquisition of knowledge-test in mathematics for the students of the second preparatory stage .
2- Calculate the validity and the stability of the test.
3- Applying the test anterior and posterior .
4-Analyzing the results statistical and explaining them .
Fifth : Presenting the results of the study and its recommendations and suggestions .
The importance of the Study :
The importance of the study is taken from what it could offer to First : to the learner:
Improving mathematical proof skills of the preparatory stage students by using the Constructivist Learning Model ”Five Es” .
Providing the learner with opportunities for the positive participation in the teaching situation .
Second : To the teacher:
Helping teachers by providing them with the Constructivist Learning Model for the enrichment of the educational situation and for increasing interaction among itselements.
Helping mathematical teachers by providing them with a list of mathematical proof skills and its relative weights to be as a guide for the teachers in their planning and teaching Mathematics.
Third : To the authors of curricula:
Helping the curricula planners by providing them with the Constructivist Learning Model that the mathematics curricula of the preparatory stage students could include it to improve mathematical proof skills of these students.
Fourth: Opening new horizons for other researches about usual the Constructivist Learning Model ”Five Es” to improve different mathematical skills during the different educational stages.
Results of the Study:
1- there are statistically significant differences at( 0,01) between the meanscores of the experimental group and the control group students in Proof analysis skillin the post – assessment, in favor of the experimental group.
2- there are statistically significant differences at( 0,01) between the meanscores of the experimental group and the control group students in proof planning skillin the post – assessment, in favor of the experimental group.
3- there are statistically significant differences at( 0,01) between the mean scores of the experimental group and the control group students in proof writing skillin the post – assessment, in favor of the experimental group.
4- there are statistically significant differences at( 0,01) between the mean scores of the experimental group and the control group students in proof ProofEvaluation skill in the post – assessment, in favor of the experimental group .
5- there are statistically significant differences at( 0,01) between the mean scores of the experimental group and the control group students in Proof skillsas a whole in the post – assessment, in favor of the experimental group.
6- there are statistically significant differences at( 0,01) between the mean scores of the experimental group and the control group studentsin the post – assessment of the achievement test as a whole and its cognitive levels ,in favorof the experimental group.
7- Using theConstructivist Learning Model ”Fives” in Teaching tothe experimental group students achieved an appropriate level of effectiveness in developing proof skills as a whole and its sub - skills.