In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

Reciprocal Teaching is an interactive method that is used to improve reading comprehension. Using this teaching strategy, teachers and students take turns leading discussions regarding sections of text using the four strategies: predicting, questioning, clarifying and summarizing. This study is an attempt to investigate the effect of using reciprocal teaching on improving female college students' achievement in reading comprehension. To fulfill the aim of the study, the researcher has adopted two null hypotheses: first, there is no significant difference between the achievement of students' who practice the reciprocal teaching technique and that of students who do not practice it. Second, there is no statistically significant difference

The study aims to identify the impact of electronic games on increasing the dropout rate among students in the basic stage in Jordan from their teachers’ point of view. The study adopted a descriptive survey method. Its community consisted of all fe(male) teachers of the basic stage in public and private schools, (First Amman, Irbid, and special education in Zarqa and Amman). The electronic questionnaire was used as a tool for the study. The results have shown that the effect of electronic games on increasing the dropout rate among students in the basic stage in Jordan was high. Besides, there are statistically significant differences due to the gender variable for males. There are statistically significant differences due to the varia

         Over the last few decades, many instructors have been trying all kinds of teaching methods, but without benefit. Nevertheless, in the 1986, a new technique is appeared which called K-W-L technique, it  is specified for reading comprehension passages because reading  skill is not easy matter for students for specific purposes (ESP).therefore, the K-W-L technique is a good one for thinking and experiences. To fulfill the aims and verify the hypothesis which reads as follows" it is hypothesized that there are no significant differences between the achievements of students who are taught according to K-W-L technique and those who are taught according to the traditional method

The research aimed to identify the causal relationship between forgiveness and psychological hardness for university students, by answering the following questions: Does forgiveness cause psychological hardiness? Does psychological hardiness cause forgiveness? Is the relationship between the two variables a reciprocal relationship? The research sample consisted of (300) male and female students from the universities of Baghdad and Al-Mustansiriya University. To extract the psychometric properties of the two scales: forgiveness and psychological hardiness, a sample of (50) male and female students employed to repeat the test, making the six connections between the two research variables. To determine the causal relationship, The Pearson c

  The mind map represents a system to solve problems including design problems, because it depends on employing the complex and purposeful mental activity, which starts from a desire based on the search and investigation in order to reach integrated results of scientific thinking, utilizing the objective view of the scientific and practical aspects from various angles. This visual system can develop thinking and shorten the retrieval time of the previous information in order to employ it in the solution finding system, that it evokes past experiences and relates them to current situations, then enables the user to choose a suitable solution for the problems. This visual, educational and circulatory means, at the same time, has speci

The present study aims at empirically investigating the effect of vocabulary learning strategies on Iraqi intermediate school students’vocabulary performance and reading comprehension. The population of the present study includes all the 1^st year male students of  Al-Wark’a intermediate  school of Al-Risafa 1/ General  Directorate of Education for the first course of the academic year (2015-2016). To achieve the aim of the study ,a pre-test and post-test after (5) weeks of experiment are administrated .The sample of the present study consists of (100) subjects :(50) students as an experimental group and other (50) students as  a control group . The subj