Training and retraining of teachers have become a central issue in Iraq recently especially in-service training of English teachers on the new curricula (Iraq opportunities). English teachers should be objectively evaluated and assessed.
A sample of (40) trained teachers of English is included in the study and a questionnaire is used as the main instrument of the study.
The main findings of the study were the following:
1. The trainees were serious in training on the new course (item 6) the programme helped increase their information (item 4) and motivate them towards better teaching (item 3). The aims of the programme were clear (item1). The programme helped develop their teaching skills (item 2) and was comprehensive (item 5).
2. Most of the trainees benefit from the subject of testing (item12). The programme helped most of them train on teaching methods (item7).
3. Teachers' trainers were vocational and led training sessions perfectly (items 14 and 13). They fairly used lecture formats and discussion in delivering lectures (item 15 and 16).there administration and using other combined methods were not successful (items 18 and 17).
4. Items in the table of training methods showed great shortage. (table3)
5. In the field of using training aids, whiteboard was over used (item29).
6. In table (5) duration of the course was suitable to most of the trainees (item33) but its period interfered with school timetable of the trainees (item 35). Other items showed different degrees of defect in this field.
7. In the field of evaluation. Class oral discussion was used (item 24) and a post-test at the end of the course (item 39). Other procedures of evaluation were neglected.
8. In the field of trainees needs. trainees got advantage in teaching English in the classroom (item 48) and lesson planning of different period (item 47). They were trained how to be adequate with the objective of teaching English in Iraq (item 47). They were also trained on teaching different skills (item46) and established relationship between the objectives and content of the textbooks (item 43). (Items 50, 49, 51 and 44) did not meet trainees needs' in group (A).
9. In group (B) trainees preferred printing the lectures (item 54) and discussing them in the classroom (item 53). In group (C) trainees showed that using the whiteboard was efficient (item 55). Teaching aids were not appropriate (item 56).
A conclusion and some recommendations were mentioned at the end of the research based on the findings of the study in order to improve the quality of in-service training programmes in Iraq.
An edge dominating set of a graph is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G. The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domin
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