## Analysis of Tenth Graders Errors and the Relation between their Acquisition of the Basic Skills and their Ability to Solve the Mathematical Equations in the Basic Grade

تحليل أخطاء طلبة الصف العاشر الأساسي ودراسة العلاقة بين قدرتهم في حل المعادلات الرياضية واكتسابهم للمهارات الأساسية في المرحلة الأساسية في محافظة جنين

##### Abstract

This study aimed at analyzing and classifying the errors made by the tenth graders in solving the mathematical equations, acknowledging the extent of their Acquisition of the basic skills, and knowing their ability to solve mathematical Equations, investigating the relationship between the extent of their acquisition Of the basic skills and their ability to solve the mathematical equations, and investigation the differences between the basic mathematical skills test and the mathematical equations solving test for pupils, males and females. To achieve the foregoing objectives, this study aimed at answering the following Questions:
1.To what extent do the tenth graders acquire the basic skills available in their curricula?
2.To what extent are the tenth graders able to solve the mathematical equations available in their curricula?
3.What type of errors do the tenth graders make while solving the mathematical Equations and the degree of each types availability?
4.Is there relationship between the tenth graders ability in solving the Mathematical equations and the extent of their acquisition of the basic skills Available in the basic grade curriculum?
5.Are there differences in the achievement of the tenth graders in the basic skills and mathematical questions solving tests due to the variable of sex?
6.Are there differences between the basic skill tests available in the basic grade and solving the mathematical equations among pupils?
7.Are there differences between the basic skill tests available in the basic grade and solving the mathematical equations among males?
8.Are there differences between the basic skills available in the basic grade and solving the mathematical equations among females?
The population consisted of the tenth graders in the schools of Tubas City under the ministry of education. The sample consisted of (293) pupils,(l30) males and(l63) females. The sample was intentionally selected among the tenth grader sections in the schools of Jenin directorate.
(293)pupils,(l30)males and(l63)females. The sample was intentionally selected among the tenth grader sections in the schools of Jenin directorate.
In order to answer the questions of this study, the researcher prepared two tests: one measures the extent of the pupils acquisition of the basic skills available in the curriculum of the basic grade , and another that measures the extent of their ability to solve the mathematical equations linked to that grade.
The validity of the content of the two tests was approved by a judging committee. The reliability coefficient was calculated for each test by half-split method and Spearman -Brown equation .The reliability coefficient of the basic mathematical skills was (0.92), and the reliability coefficient of the mathematical equation test was (0.83).
The results of the study showed considerable decrease in the pupils acquisition of the basic skills ,and their ability in solving the mathematical equations. And the errors that the pupils make falls into sex categories: weakness in the basic concepts and skills, weakness in solving two variables linear equations, errors in solving the squre ,fraction and triangular equations, weakness in writing solution set, errors of guessing, and others. The first category errors (weakness in the basic concepts and skills) were the most common, and there is positive relationship between the pupils, acquisition of the basic skills and their ability to solve the mathematical equations. Also, there are significant differences (α = 0.0) between the two test in favor of the basic skills test among pupils, males and females.
In the light of these results, the researcher has recommended the necessary of taking interest and disclosing the cause of the pupils, weakness in mathematical and benefiting from the tutorial classes to set a right the different aspects of weakness in acquiring the basic skills in mathematics. Also, the researcher has recommended similar further studies on other samples of populations in Palestine. This study aimed at analyzing and classifying the errors made by the tenth graders in solving the mathematical equations, acknowledging the extent of their Acquisition of the basic skills, and knowing their ability to solve mathematical Equations, investigating the relationship between the extent of their acquisition Of the basic skills and their ability to solve the mathematical equations, and investigation the differences between the basic mathematical skills test and the mathematical equations solving test for pupils, males and females. To achieve the foregoing objectives, this study aimed at answering the following Questions:
1.To what extent do the tenth graders acquire the basic skills available in their curricula?
2.To what extent are the tenth graders able to solve the mathematical equations available in their curricula?
3.What type of errors do the tenth graders make while solving the mathematical Equations and the degree of each types availability?
4.Is there relationship between the tenth graders ability in solving the Mathematical equations and the extent of their acquisition of the basic skills Available in the basic grade curriculum?
5.Are there differences in the achievement of the tenth graders in the basic skills and mathematical questions solving tests due to the variable of sex?
6.Are there differences between the basic skill tests available in the basic grade and solving the mathematical equations among pupils?
7.Are there differences between the basic skill tests available in the basic grade and solving the mathematical equations among males?
8.Are there differences between the basic skills available in the basic grade and solving the mathematical equations among females?
The population consisted of the tenth graders in the schools of Tubas City under the ministry of education. The sample consisted of (293) pupils,(l30) males and(l63) females. The sample was intentionally selected among the tenth grader sections in the schools of Jenin directorate.
(293)pupils,(l30)males and(l63)females. The sample was intentionally selected among the tenth grader sections in the schools of Jenin directorate.
In order to answer the questions of this study, the researcher prepared two tests: one measures the extent of the pupils acquisition of the basic skills available in the curriculum of the basic grade , and another that measures the extent of their ability to solve the mathematical equations linked to that grade.
The validity of the content of the two tests was approved by a judging committee. The reliability coefficient was calculated for each test by half-split method and Spearman -Brown equation .The reliability coefficient of the basic mathematical skills was (0.92), and the reliability coefficient of the mathematical equation test was (0.83).
The results of the study showed considerable decrease in the pupils acquisition of the basic skills ,and their ability in solving the mathematical equations. And the errors that the pupils make falls into sex categories: weakness in the basic concepts and skills, weakness in solving two variables linear equations, errors in solving the squre ,fraction and triangular equations, weakness in writing solution set, errors of guessing, and others. The first category errors (weakness in the basic concepts and skills) were the most common, and there is positive relationship between the pupils, acquisition of the basic skills and their ability to solve the mathematical equations. Also, there are significant differences (α = 0.0) between the two test in favor of the basic skills test among pupils, males and females.
In the light of these results, the researcher has recommended the necessary of taking interest and disclosing the cause of the pupils, weakness in mathematical and benefiting from the tutorial classes to set a right the different aspects of weakness in acquiring the basic skills in mathematics. Also, the researcher has recommended similar further studies on other samples of populations in Palestine.