Home > Developing Students Conceptual Understanding and Reasoning Skills of Geometrical Proofs Through Integrating Geogebra Software in Grade 10 in a Private Higher Secondary School Situated in Chitral, Pakistan
Developing Students Conceptual Understanding and Reasoning Skills of Geometrical Proofs Through Integrating Geogebra Software in Grade 10 in a Private Higher Secondary School Situated in Chitral, Pakistan
Mathematics is one of the compulsory subjects taught from kindergarten to matriculation level in the schools of Pakistan. Teaching mathematics remained a challenge generally and geometry, particularly due to the abstract nature of the topics. The board and chalk method of teaching is not enough to develop the conceptual understanding and the reasoning skills of students. For this purpose, the integration of the Dynamic Geometry Software's (DGS) are introduced to enrich and enhance the learning of students in classroom teaching, along with the traditional instructional methods. Geogebra is one of the Dynamic Geometry software, which is famous for its freeware, offline use and versatile features to construct analyse and visualize the geometrical objects. An action research based on qualitative approach has been conducted on grade 10 students to develop their understanding of geometrical proofs through integrating the Geogebra software in a private secondary school, Chitral. The data has been collected in two phases and comprises 12 lessons on circle theorems taken from the National Curriculum of Mathematics i.e., NCM (2006). The data collection tools includes focused group discussion of six research participants, interviews of mathematics teacher, feedback from critical friend, students 'work on the software and their written reflections after each phase. The findings revealed that the integration of the software enhanced the understanding of geometrical proofs and their reasoning skills in the students. The students found the software friendly, interactive, and helpful in understanding the abstract topics. The use of the Van Hiele's geometrical thinking model enhanced the understanding of the students in the systematic using of Geogebra. For example, the students visualized the geometrical objects, analysed the properties through dragging and flipping and then informally deduced the relative changes in the figures to formally provide arguments or reasons for their geometrical works in solving problems related to circle theorems. Furthermore, this software helped the teachers to utilize the teaching time effectively through engaging the students individually in the learning process. In addition, the integration of the software filled the gap of conversation between the students and teacher while teaching abstract topics in geometry, making them tangible and visible. Finally, the success of the integration of software in teaching depends on the motivational power and skills of teachers in designing the tasks to scaffold the students' learning vividly.
ایمان اسلام کو جزو لاینفک ہے اس کے بغیر اسلام قابل قبول نہیں کوئی بھی شخص مکمل ایمان لائے بغیر دائرہ اسلام میں داخل نہیں ہو سکتا ۔ فصل اول میں ایمانیات کے بارے میں قرآن مجید کی درج ذیل سورتوں کی ۲۰ آیات سے وضاحت کی گئی ہے۔
سورة آل عمران آیت نمبر ۱۶۰، سورة النساء آیت نمبر۸۲، سورة الاعراف آیت نمبر۱۸۵، سورة يونس آیت نمبر۳۴، سورة بنى اسرائیل آیت نمبر ۹۹، سورة الانبياء آیت نمبر ۴۲، سورة الحج آیت نمبر۷۰، سورة المؤمنون آیت نمبر ۸۵،۸۶،۸۷،۸۸،۸۹، سورة النور آیت نمبر ۵۰، سورة الروم آیت نمبر ۳۵،۳۷ ،سورةالزمر آیت نمبر ۴۳، سورة المؤمن آیت نمبر ۸۱،۸۲، سورة المرسلات آیت نمبر۲۰،۲۵، اس فصل میں ان آیات میں اللہ تبارک وتعالیٰ نے اپنے بندوں سے سوال فرمایا ہے۔
اس فصل میں ہر آیت کو بیان کرنے کے بعد اس کی تفسیر پر روشنی ڈالی گئی ہے اور اس آیت میں استفہام کے استعمال کی وضاحت کی گئی ہے کہ ہر آیت میں اللہ تبارک و تعالیٰ کا سوال کرنے کے پیشِ نظر جو مقصد کارفرما تھا اس کو واضح کیا گیا ہے۔
Education is a very important aspect of human life. Muslims were strongly believed on Religious Education. It was considered mandatory for spiritually life here in this world and here after. This article “Research Study of Religious Education Trends in the Prophet (PBUH) Era” introduces the concept of “education” with its definition from Oxford Dictionary and by Muslims philosophers. The “Education System” is also defined with its main components and its objectives in the light of sayings by various Muslim intellectuals. Then, the education system in the Prophet (PBUH) Era is discussed in detail. The role of Prophet (PBUH) and his companions and their effects are also discussed. It also studies the main objectives of Religious Education, its curriculum, the role of Mosque and the relation between teacher and student. Lastly, the current education system of Pakistan is analyzed critically and a few suggestions are given to make it a better one.
The Internet of Things (IoT) has abundant non-trivial applications and Smart Grid is one of them. The IoT capacitate effortless and adept adoption of Smart Grid. Currently, it is anticipated as the mostprevalentmanifestationoftheIoT.SmartGridisemergingasthenextgenerationpowergrid due to its reliability, flexibility, and efficiency. It is a state-of-the-art distributed power generation and supply infrastructure with significant auxiliary traits of intelligence and two-way communication. The utility can monitor and control power consumption of the consumer for load balancing, in real time. Similarly, the consumer can keep a trail of his power usage to plan it as per his affordability or budget. The Smart Grid also furnishes an adequacy to integrate renewable energy sources. Despite the ample amelioration, Smart Grid faces some critical security challenges such as the denial-of-service, message injection, man-in-the-middle and replay attacks etc. Moreover, provision of an IP-based communication system in this very grid has made it more vulnerable to stern securityattacks. Iftheseattacksarenotproperlyaddressed,anadversarycanmaliciouslycompromise the user/device to degrade the performance of the Smart Grid. Itisstrenuoustoemployclassicaltechniquesinordertopreventabove-mentionedsecurityattacks due to soaring communication and computation overhead. Since the Smart Grid is delay sensitive and traffic intensive environment, it is therefore inevitable to concoct and realize security techniquesinsuchawaysothattheydonotpersuadedelayduetocomplexandcomputationintensive cryptographic operations. Theperplexingarchitectureandassortedsecuritydesideratumisthemajorhindrancetoofferaprevailing solution for Smart Grid security. This research work has undertaken to design and develop lightweight authentication protocols for insuring the Smart Grid. The optimal authentication protocolsforSmartGriddelaycriticalenvironmentnotonlywithstandpotentialsecurityattacksbutit also experiences scanty communication and computation overhead due to primitive cryptographic operations. In this research, we have embellished lightweight authentication protocols for endowing secure andreliableenvironmentattheexpenseofinsignificantcommunicationandcomputationoverhead. These protocols are capable of impeding well-nigh all sorts of trivial and non-trivial attacks. The first authentication protocol is based on a hybrid Diffie-Hellman algorithm. This lightweight protocol exploits typical cryptosystems of Advanced Encryption Standard (AES) and Rivest, Shamir and Adleman (RSA) to engender a session key. Additionally, Hash-based Message Authentication Code (HMAC) is also employed in it to perpetuate data integrity. Moreover, this authentication protocol promises to commence mutual authentication by averting major attacks such as man-inthe-middle and replay attack. The second authentication protocol is an Elliptic Curve Cryptography (ECC)-based solution for retaining Smart Grid security. Since ECC promises to offer analogous security clout with significantly reduced key size as compared to other cryptographic security solutions e.g. Diffie-Hellman (D-H), Digital Signature Algorithm (DSA) and RSA. This proposed protocol realizes mutual authentication with meager resource utilization. It is also verified that the proposed scheme can relentless the security attacks. Keeping in mind the complex and delay sensitive nature of the Smart Grid, a lightweight ECC-based authentication scheme is proposed. This ECC-based protocol not only provides mutual authentication with low computation and communication cost but also withstand absolute familiar security attacks. The third security solution is realized through bilinear pairing. This protocol enables the smart meters to get connected with utility control anonymously to avail the services provided by them. The smart meters realize this objective with the private key in the absence of trusted authority. The trusted authority is involved only during the registration phase. Thereafter, the fourth scheme presented in this research work is actually an enhanced identity-based key establishment protocol. This enhanced scheme is introduced after identifying the weaknesses in the protocol presented by Mohammadali et al. (published in IEEE Trans on Smart Grid, 2018). The formal and informal security analysis is carried out under predefined adversarial threat model to verify the robustness of the proposed authentication protocols against stern attacks. BurrowsAbadi-Needham logic (BAN logic) is utilized to evaluate the integrity of the exchanged information. In the end, the performance of the proposed authentication protocols is compared with recently presented related protocols in the literature. Performance comparisons reveal the computation and communication requirements of the proposed protocols as compared to homologous protocols.