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→‎Hypotheses of the Study

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 # There is a significant statistical difference at the level of the significance (0.05) between the mean rank of the marks of the two groups of the study,  i.e. the experimental and the control groups, in favour of the experimental group on the post-test implementation.
 # The concrete manipulative materials (modified algebra tiles) are effective in enhancing the achievement level of the visually handicapped students in the unit of algebraic terms and expressions, as Blacke’s ratio exceeds whole one.
+=== Limitations of the Study ===
+The study was bound by the following limitations:
+'''Content Sample:''' The study was limited by teaching the unit of algebraic terms and expressions using the modified algebra tiles to the visually handicapped students.
+'''Population Subjects:''' The study was limited to a sample of seventh grade visually handicapped students in Al-Noor Schools in Dakahliya, Damietta, and Cairo.
+=== Variables of the Study ===
+The variables, in this study, were classified as follows:
+# Independent Variable: This is the variable whose effect is to be measured in this study. This variable is represented in the method of teaching used, and it has two levels: the first level depends on using concrete manipulative materials (modified algebra tiles) and it is used with the students of the experimental group. The second level is the traditional one, which is used with the students of the control group.
+# Dependent Variable: This is the variable whose effect on the independent variable is to be measured before and after the experimental implementation. This variable is represented in the educational achievement in mathematics as measured by the achievement test prepared by the researcher.
+=== Instrument of the Study ===
+The researcher designed an achievement test on the unit of algebraic terms and expressions.
+=== Procedures of the Study ===
+To answer the study questions and to examine the validity of its hypotheses, the researcher went through the following procedures:
+# Developing the concrete and manipulative materials (modified algebra tiles) to teach the unit of algebraic terms and expressions to the visually handicapped students.
+# Reshaping the content of the unit of algebraic terms and expressions in a way that suits/fits the nature of the visual handicap.
+# Preparing a teacher’s guide for the unit of algebraic terms and expressions including some signs and principles that would help the teacher in teaching the unit to the visually handicapped students.
+# Preparing an achievement test on the unit of algebraic terms and expressions
+# Subjecting the unit, the teacher’s guide, and the achievement test to the judgment of the experts and the educationalists to judge their suitability to the nature of the visual handicap and making the suitable modifications in the light of their suggestions.
+# Reprinting the unit and the achievement test in Braille language to be easily administrated to on the visually handicapped  students.
+# Implementing a preliminary experiment for the achievement test that aims at analysing its items, measuring its factor of constancy, and determining the time of the test.
+# Implementing a pre-achievement test on both groups i.e. the experimental and the control groups.
+# Teaching the unit of algebraic terms and expressions using concrete manipulative materials (modified algebra tiles) for the visually handicapped students of the experimental group.
+# Implementing a post-achievement test on both groups i.e. the experimental and control groups.
+# Collecting data, statistically manipulating and explaining it, and answering the questions of the study.
+# Presenting suitable suggestions and recommendations to make full use of the study results.
+=== The Study Results ===
+The results of the study are:
+# There is a significant statistical difference at the level of 0.05 between the mean ranks of marks of the two groups of the study, i.e. the experimental and the control groups, in favour of the experimental group on the post-test implementation.
+#The effectiveness of the modified concrete manipulative materials (modified algebra tiles) in enhancing the achievement level of visually handicapped students concerning the unit of algebraic terms and expressions.
+=== Structure of the thesis ===
+The Thesis was composed of 5 chapters, a list of bibliography, 12 appendices, and Arabic and English summaries
+The five chapters are described as follows:
+'''Chapter 1:''' Problem of the Study
+In this chapter, the framework of the entire thesis was presented, which includes background of the problem, problem of the study and study questions, aim of the study, significance of the study, hypotheses of the study, limitation of the study, variables of the study, instrument of the study, terms of the study, and procedures of the study.
+'''Chapter 2:''' Review of the literature
+In this chapter, prior literature related to the subject of the study was reviewed in five domains:
+* Handicapped and visually handicapped students.
+* Characteristics and needs of the visually handicapped students.
+* The visually handicapped students education.
+* Teaching and learning mathematics for the visually handicapped students.
+* Concrete manipulative materials and its significance in teaching and learning mathematics for the visually handicapped students.
+'''Chapter 3:''' Related Studies and International Projects
+In this chapter, related studies and international projects related to the subject of the study was reviewed in three domains:
+* Studies related to the use of concrete manipulative materials in teaching and learning mathematics.
+* Studies related to teaching and learning mathematics for the visually handicapped students.
+* International projects related to teaching and learning mathematics for the visually handicapped students.
+Then, the researcher presented his commentary on related studies and projects.
+'''Chapter 4:''' Procedures of the Study
+In this chapter, the researcher presented in detail how he had developed the algebra tiles to suit/fit the nature of visual handicap and how he reshaped the content of the unit of algebraic terms and expressions using the modified algebra tiles. He also presented developing procedures of both the teacher’s guide and the achievement test. Procedures of the experimental study were also presented in terms of administration of pre-test, administration of the modified unit, and administration of the post-test
+Chapter 5: Finding, Interpretation, Conclusion, and Recommendation
+The chapter presents the statistical analysis results of testing the study hypotheses as well as interpretation and implications of these results in the light of the literature review and purposes of the study. It also includes recommendations pertinent to the findings of the program and concludes with the suggestion for further research related to the use of concrete manipulative materials in mathematics education, and  the visually handicapped students education
+The 12 appendices are titled as follows:
+Appendix 1: A list of jury members who validated the instruments of the study.
+Appendix 2: Results of content analysis of the unit of algebraic terms and expressions.
+Appendix 3 : Teacher’s guide for teaching the unit of algebraic terms and expressions.
+Appendix 4: The unit of algebraic terms and expressions after reshaping it using the modified algebra tiles.
+Appendix 5: A list of references which are used in developing both the teacher’s guide and the reshaped unit.
+Appendix 6: A list of the instructional objectives which are measured by the achievement test.
+Appendix 7: The achievement test in its seeing format.
+Appendix 8: Raw data for the visually handicapped students in the pilot study of the achievement test.
+Appendix 9: Results of statistical analysis for the achievement test items.
+Appendix 10: Answers key of the achievement test.
+Appendix 11: Raw data for both groups of the visually handicapped students in the pre-test administration
+Appendix 12: Raw data for both groups of the visually handicapped students in the post-test administration
 == Discussion ==
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