غزل ۔۔۔ڈاکٹر محمد کامران
پروفیسر پنجاب یونیورسٹی لاہور
ایسا بھی نہیں تم سے مجھے پیار نہیں ہے
لیکن مجھے اس بات پہ اصرار نہیں ہے
میں نے یہ غزل موجٍ صبا تجھ پہ کہی ہے
حالانکہ مجھے تجھ سے سروکار نہیں ہے
اس شخص کی آنکھیں مجھے سونے نہیں دیتیں
دل جس کی محبت میں گرفتار نہیں ہے
میں نے بھلے وقتوں میں خریدا تھا کوئ خواب
اب اس کا کہیں کوئ خریدار نہیں ہے
ماں باپ کی عزت کا اسے خوف ہے ورنہ
اس شوخ کے انکار میں انکار نہیں ہے
Water and related issues are gaining importance in the present world politics. It is believed that water would be the source of some major future conflicts in many regions including South Asia. Water distribution between Pakistan and India has become a serious political issue since independence. The problem has its roots in the partition of the Indian Subcontinent in 1947. Although the issue was resolved amicably by the two states in 1960 and a treaty was signed, even then number of other issues developed after the treaty. One of the important aspects of the settlement route was the Indian refusal and Pakistan’s insistence on the presence and participation of any third neutral party. Despite the Indian policy of bilateralism on many regional issues, water disputes and resolution remained a classical example of multilateralism, where at least on four major occasions the settlements were reached with the involvement of a third neutral party.
Teaching and learning of fractions continues to be one of the major challenges in primary school context. Among many reasons of the challenges in understanding fractions, one dominant reason is the traditional teacher-centered teaching, which focuses more on solving algorithms based on memorized rules. This study is an attempt to investigate how learners could be facilitated in learning fractions with understanding. For this purpose, I carried out an action research based on qualitative research approach with six students of grade IV in a private school of Gilgit-Baltistan. I conducted the study in three stages; reconnaissance stage, intervention stage and post- intervention stage. In the reconnaissance stage, my focus was to examine the students’ understanding of fractions and the process of learning fractions before intervention through one to one clinical interviews, classroom observations and document analysis. In the intervention stage, I taught twelve lessons of fractions to the students with innovative teaching strategies concentrating the three representations; concrete, pictorial and symbolic and focused the process of building conceptual understanding of fractions. In the post- intervention stage my focus was to explore students’ understanding of fractions after being exposed to the instructions again through one to one clinical interviews of the participant-students.The findings revealed that the students’ understanding of the concepts of fractions i.e. equivalent, ordering, addition and subtraction of fractions was developed. The factors which contributed in building students’ conceptions were: scaffolding students of the foundational concepts (partitioning, part-whole and part-part relationship, concept of whole), promoting students’ fraction vocabulary, simultaneous use of concrete, pictorial and symbolic representation, building connections among the concepts of fractions. The findings of this study suggest mathematics teachers to teach fractions using concrete, pictorial and symbolic representations and facilitate students to explore the moves between these representations.