الفهرس 
الفصل الاوليوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
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SUMMARY OF THE RESEARCH
Introduction :
The use of mathematics in the various ways of knowledge is considered one of the main characteristics of the big cognitive progress which happened lately. Nowdays, knowledge with its different fields - is based more on mathematics than any other time, moreover, the progress of any cognitive field is measured by its use of mathematical manipulations.
No doubt that the increased cognitive revolution recognized by the world in all fields is in need of special skills for dealing with it in a quantitiative form to classify it, interpret, and show the relationships among its variables for using it in daily activities. Among these skills which should be taken into account to cope with this cognitive progress are skills of establishing, reading, and interpreting tables and different graphs which are implied in a set of skills for reading mathematics (Mathematical translation).
The subjects of mathematical functions in the secondary stage are considered among the important subjects which provide learners with full opportunities for practicing mathematical translation and indicating their effect on their academic and professional lives. Moreover. they can practise these skills and be trained on them through natural situations related to life where the function in its mathematical structure is a real translation for many life situations. Hence majority of life situations can functionally be expressed.
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Problem of the research
The problem of this research is determined in how to prepare an instructional program for developing the graphical skills of mathematical functions for secondary students, measuring the effect of this program on the achievement of secondary second year students and transfering the effect of teaching the program’s content to some other subject matters in mathematics and other subjects for those students. Therefore, the present research attempts to answer the following questions :
1-What are the most important graphical skills of mathematical functions, necessary for secondary students?
2-What is the appropriate form of a program suggested for developing these skills for secondary students?
3-What is the effect of the suggested program on developing graphical skills of mathematical functions for secondary students?
4-What is the effect of the suggested program on the achievement of the second year students of secondary school in mathematics?
5-What is the effect of the suggested program on transfering the effect of learning subjects of functions (with a real variable) to some other subjects in mathematics and other subjects for the sample of the research?
• To answer these previous questions which determined the research problem, the researcher presented some previous studies dealt with the topic of mathematical functions and concepts related to them. In addition to the previous studies which dealt with different graphs, the researcher presented a special criterion for the studies interested in learning mathematics in the secondary stage and in how transfering this learning in (and out) mathematics. Based on the results of this group of previous studies, besides the research theoretical background. hypotheses of this research can be stated in the following way :
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Hypotheses of the research :
I- ”There are statistically significant differences between the means of students’ scores of the experimental and control groups in mastery of the graphical skills in favour of the experimental group”.
2-”There are statistically significant differences between the means of students’ scores of the experimental and control groups in the achievement of the subjects of functions unit in favour of the experimental group”.
3-”There are statistically significant differences between the means of student’ performance of the experimental and control groups in the transfer of the effect of learning the subjects of the functions unit in favour of the experimental group”.
4-” There are statistically significant differences between the means of students’ scores of the experimental group on the achievement test applied to them as a pre - post test in favour of the post - one”.
5-” There is statistically a significant positive correlated relationship between mastery of graphical skills and achievement in the subjects of functions unit for the experimental group ”
6-” There is statistically a significant positive correlated relationship between mastery of graphical skills and transfering the effect of learning some other academic subjects the experimental group”.
• For checking the validity of these hypotheses, there are some procedures followed by the researcher :
Precedures of the research :
First : Theoretical background :
Preparing a theoretical study about the skills of graphs of mathematical functions needed by secondary stage students through presenting the nature of mathematical skills in general.
This includes the following steps
1-Reviewing previous studies and books in the graphs filed in different scientific specializations and especially mathematics and methods for
teaching it.
2-Analyzing the content of mathematics books in the secondary stage.
3-Writing a list of graphical skills needed for the secondary students’ mastery in reading and interprating the graphs of the functions at that stage.
4-Qiiestionairing the opinions of the jury specialized in mathematics and its teaching methods.
5-Writing the list of skills in its final form.
Second : the practical aspect :
This is represented in determining the extent of the effectiveness the suggested program on the developing graphical skills of the mathematical functions, and measuring the effect of the program on the students’ achievement, general secondary second year in the unit of functions, and also the transfer of what they have learned to other mathematical (and non mathematical) subjects. This is as follows :
1- Preparing tools of the study :
A-A test in the graphical skills of the mathematical functions which students at secondary stage learn.
B-A test in achieveing the subjects of the unit of the functions in the mathematics course for secondary second year.
C-A test for measuring transfer of the effect of learning the subjects of the suggested program for secondary second year.
2- Piloting an experimental study for the tools of research to check the validity of using each of them.
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3-Selecting the sample of research in a random way from secondary second year students schools, calubbia Govrnorate. Theschools selected are Shibin El-Kanater (boys - girls).
The sample is divided into two equal groups :
* The experimental group (N = 51) taught the subjects of the finictions unit by using geometry transformations with oriented discover),
technique.
* The control group (N = 44) taught the same subjects by the traditional technique followed in teaching.
4-The achievement test of the suggested program is administered as a pre-post test to the two groups (experimented and control).
5-The subjects of the program are taught to the experimental group through the suggested method at the same duration at which control group taught the same subjects through the traditional method.
6-The tools of this research are administered as pre-post tests to the two experimental and control groups for finding out the differences between
them.
7-Data is registered by appropriate statistical methods, presented. analysed discussed and interpreted.
Results of the research
After analysing data and treated it statistically for checking the validity of the research hypotheses and answering the questions, the results are
as follows :
I- There are statistically significant differences between the means of
students’ performance of both groups; experimental and control in the mastery of graphical skills of the mathematical functions as measured by ”Graphical skills test” - prepared by the researcher - in favour of the
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experimental group studnets. This means that the first hypothesis is valid.
2-There are statistically significant differences between the means of students’ scores of the experimental and control groups in achieving of the functions unit subjects in favour of the experimental group students. This means that the second hypothesis is valid.
3-There are statistically significant differences between the means of students’ scores of the experimental and control groups in transfering the effect of their learning of the subjects involved in the functions unit as measured by the test of transfering the effect of learning - prepared by the researcher-in favour of the experimental group students. This refers to the validity of the third hypothesis.
4-There are statistically significant differences between the means of the experimental group students’ scores in achieving the subjects included in the functions unit on the pre-post achievement test in favour of the post - test. This indicates the effectiveness of the suggested program. Thus, the fourth hypothesis is valid.
5-Among the results obtained in this study : there is statistically a significant positive correlated relationship (0.86) between the experimental group students’ mastery of graphical skills and their achievement in the functions unit. This refers to the validity of the fifth hypothesis of the research.
6-Also the results of the present research revealed that there is apositive correlated relationship (0.72) statistically significant between the experimental group students’ achievement of the functions unit and the effect of transfering their learning the subjects included in this unit to other scientific subjects. This refers to the validity of the sixth hypothesis.