This study dealt with confusions in the context of teaching of algebra at the lower secondary level. A major problem in the present situation in the teaching of mathematics in Pakistan is that many students of mathematics do not have a conceptually sound understanding of algebra. That is, some students do not know how to solve certain problems, as they are not given the opportunity to develop their thinking skills. Some students want to ask questions but many teachers do not encourage them to do so. This study was conducted in one government higher secondary school, with two mathematics teachers and eight students of classes seven and eight. The specific question that guided the investigation was "How can teachers be helped in dealing with students' conceptual problems in algebra at lower secondary level”. This study consisted of three stages, the pre-intervention stage, the intervention stage, and the post intervention stag. In the pre-intervention stage I interviewed the study teachers and students, tested the students, and observed the specific mathematics lessons to explore problems which students faced during the conceptually learning of algebra, and how teachers delt with these problems. At this stage I found that students had several conceptual problems like, the use of wrong signs, smaller and greater numbers, like and unlike terms, and misconceptions about power and base. These problems may be related to the teaching methods because the teachers were using inappropriate methods of solving equation. It was further noted that teachers held limited knowledge of teaching algebra, and were emphasising the completion of the syllabus, which created a tense environment in the class, where learning without understanding and reasoning occurred. In the intervention stage, an attempt was made to try to solve some of the problems While there was a shortage of time, there was evidence to indicate that change was taking place in the teaching and understanding of basic concepts in algebra. In the post intervention stage, I co- planned lessons with teachers and found a change in attitude of the teachers. During this study, I faced many problems and constraints and sometimes felt frustrated, but slowly and gradually, I overcame these problems. The results of the study showed that while there was a slight change in teacher's attitude, any significant effect have to take place over a much longer period.
المبحث الرابع: أهم الشاعرات في اللغة الأردية بعد قيام باكستان
من أھم الشاعرات بعد التوحید لھن الدور الکبیر في إصلاح المجتمع ومنھن۔
صفية شميم مليح آبادي
وھي من أکبر الشاعرات ویأتي إسمھا في الصف الأول في مقدمۃ الشاعرات المشھورات وقد ولدت في 28 مارس 1920م ولھا مجموعات شعریۃ رائعۃ منھا نغمۃ قدس، چراغ، نشاط غم وگرائیہ ستم وغیرھا۔
رابعة نهاں
ولدت في 20 سبتمبر في عام 1920م، وھي شاعرۃ قدیمۃ ومعروفۃ ولھا خمس مجموعات شعریۃ وھي شقیقۃ الشاعرۃ۔ الکبیرۃ بلقیس جمال. ومن أشعار رابعہ نھاں:
دل و نگاہ کے ہر امتحاں سے گزرے ہیں
خموش رہ کے بھی حسن بیاں سے گزرے ہیں
الترجمۃ: لقد مررنا من کل امتحان القلب والنظر
فقد قُمنا بحسن البیان مع السکوت الدائم
آدا جعفري
ولدت الشاعرۃ ادا جعفري 1924م وقد ثم طبع مجموعتھا الشعریۃ الأولی في عام 1950م۔ ولھا أشعار مشھورۃ ومعروفۃ منھا:
تم پاس نہیں ہو تو عجب حال ہے دل کا
یوں جیسے میں کچھ رکھ کے کہیں بھول گئی ہوں
الترجمۃ: لم تکن أنت موجودٌ عندي وحالۃ قلبي عجیبٌ
ھکذا کأنني وضعتُ شیءًا ثم نسیتُہ
ومن الشاعرات المعروفات زھرہ نکاہ کشور ناھید وفھمیدہ ریاض
فهميدة رياض
وھي من أشھر شاعرات العصر الحدیث تناولت في أشعارھا المواضیع المختلفۃ ورفعت قلمھا وصوتھا ضد الظلم والاستبداد السیاسي ولھا مجموعات شعریۃ رائعۃ ومنھا پتھر کی زبان، بدن دریدہ، دھوپ، ادھورا آدمی وغیرھا من الکتب الرائعۃ والمنظومات القیمۃ ولھا أشعار رائعۃ منھا:
In this article an effort has been made to describe Hazrat ‘ishah (R. A) ’s methodology of derivation of Ahkm from Holy Quran. Holy Quran and Sunnah of Holy Prophet (S. A. W) is basic source of Islamic Shar‘ah. Hazrat ‘ishah Siddqah (R. A) was the wife of the Holy Prophet (S. A. W), and the daughter of Hazrat Ab Bakr (R. A). She spent her time in learning and acquiring knowledge of the two most important sources of Islam, the Qur'an and the Sunnah of His Prophet (S. A. W). Hazrat ‘ishah (R. A) narrated 2210 Ahdth out of which 174 Ahdth are commonly agreed upon by Bukhri and Muslim. She was an ardent and zealous student of Islamic jurisprudence. She has not only described Ahdth and reported her observations of events, but interpreted them for derivation of Ahkm. Umm Al-Mu’minn Hazrat ‘ishah (R. A) is a great scholar and interpreter of Islam, providing guidance to even the greatest of the Companions (R. A) of the Holy Prophet Muhammad (S. A. W). She has not only described Ahdth and reported her observations of events, but interpreted them for derivation of Ahkm. Whenever necessary, she corrected the views of the greatest of the Companions of the Holy Prophet (S. A. W). It is thus recognized, from the earliest times in Islam, that about one-fourth of Islamic Shar‘ah is based on reports and interpretations that have come from Hazrat ‘ishah (R. A). As a teacher she had a clear and persuasive manner of speech. Hazrat ‘ishah (R. A) is a role model for women. She taught Islam many people. She was an authority on many matters of Islamic Law, especially those concerning women.
The use of different pressuremeters for in-situ soil testing is now well established. The pressuremeters, which provide high quality design parameters, are affordable on high cost projects only. Small cost projects permit the use of low cost techniques only (e.g. SPT), which often yield poor quality design parameters. Usually pressuremeters are employed for soil characterization using pre-bored or self-boring or full-displacement techniques. There was a need to develop a device in Pakistan that could be used as pre-bored as well as full-displacement pressuremeter for characterizing the alluvial soil deposits of Punjab province. Moreover, the new device should be simple, robust, cost effective and still produces parameters of high quality. This thesis describes the development of such a new in-situ testing device; namely the New Pressuremeter. Certain modifications have been made to the design of Newcastle Full-Displacement Pressuremeter (NFDPM), developed earlier by Akbar (2001) that has a radial displacement measurement system. The length of the probe of NFDPM is 420 mm (length to diameter ratio of 8.4), which creates handling problems in the field. To overcome this difficulty it was decided to reduce the length of the test section and to keep the length of the probe of the new device equal to the length of SPT split spoon sampler to get benefit from the available large SPT data. On the basis of this fact, the length of the probe of the new device was taken as 305 mm giving length to diameter ratio of 6.3. The analysis of a pressuremeter test is based on the assumption that the membrane expands as a right circular cylinder. With modifications, the new pressuremeter was developed using most of the local resources. The main body of the 48.2 mm diameter (D) probe is made of high strength stainless steel. Both ends of the main body are identical. The upper end of the probe is connected to drill rods used to push the probe into place. A pressure hose and electrical cable pass through the drill rods and are connected to the probe by a re-usable hydraulic fitting. A 45° stainless steel cone having a maximum diameter of 50.8 mm (surface area 28.5 cm 2 ) is screwed onto the base of the probe. The cone creates a cavity, which is 5% larger than the diameter of the probe. The oversize cavity helps in such a way that during installation, the friction between the membrane and the soil is almost eliminated thus ivpreventing the ends of the membrane from being pulled out of the clamping rings. This eliminates the need for a protective sheath (e.g. Chinese lantern) reducing the cost and making its assembly simpler. This device is robust and can be used in a greater variety of soil types. This device has displacement and applied pressure measurement systems and can produce stress-strain curves and unload-reload cycles. Using the new device following calibrations were carried out: • Calibration of pressure transducer • Calibration of the displacement transducer (Hall effect transducer) • Calibration for the system stiffness In situ testing was carried out at three locations of alluvial soil deposits of province of Punjab ranging from very soft to very stiff clays and loose to medium dense sands using the new device by full-displacement and pre-bored techniques. A total of 65 full scale pressuremeter tests [40 at Site-1(20 each using full-displacement and pre-bored techniques), 7 at Site-2 (all using pre-bored technique), 18 at Site-3 (9 each using full- displacement and pre-bored techniques)] were performed during this research. In situ testing with the SPT and CPT (CPT was not carried out at Site-1) was also carried out along with laboratory testing on disturbed and undisturbed samples to compare the results and validate the performance of the new pressuremeter. It is found that the soil parameters obtained using the new device as full-displacement and pre-bored pressuremeter compare well with those determined by laboratory and other in- situ testing devices. New correlations have also been proposed on the basis of test results obtained during this research work. The comparison of soil parameters determined from different sources proves the validity of the performance of the new device. However, more in-situ testing is recommended to build more confidence in the new device.