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Teaching Fractions for Conceptual Understanding to Grade Iv Students in a Private School of Gilgit-Baltistan

Thesis Info

Author

Jabeen, Sitara

Department

Institute for Educational Development, Karachi

Program

MEd

Institute

Aga Khan University

Institute Type

Private

City

Karachi

Province

Sindh

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Subject

Education

Language

English

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676728030091

Similar


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.
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مولوی محمد الحسنی

مولوی محمد الحسنی
جون کا معارف طباعت کے آخری مرحلہ میں تھا کہ اچانک اطلاع ملی کہ ندوۃ العلماء کے نقیب رسالہ البعث الاسلامی کے مدیر مولوی محمد الحسنی کا انتقال ہوگیا، یہ خبر اتنی خلاف توقع تھی کہ بڑی دیر تک یقین نہیں آیا، ان کی عمر زیادہ نہیں تھی، چالیس سے تین ہی چارسال آگے بڑھے ہوں گے، صحت بھی اچھی تھی، کبھی کسی طویل یا شدید بیماری میں مبتلا نہیں ہوئے تھے، جب ملاقات ہوتی، ہشاش بشاش نظر آئے۔
یہ سچ ہے کہ جو آیا ہے، اسے ایک دن جانا ضرور ہے، کل نفس ذائقتہ الموت[ العنکبوت:۵۷] لیکن کسے معلوم تھا کہ ان کا وقت موعود اتنا قریب ہے، ہم لوگوں کے سامنے تو بچے تھے، ان کی پیدائش کل کی بات معلوم ہوتی ہے، ہم کس طرح خیال کرتے تھے کہ وہ ہم سے پہلے رخصت سفر باندھ لیں گے۔ لیکن ان کے دوستوں اور ہم سنوں کو بھی اس تیزروی کا گمان نہیں تھا، ان کی جسمانی ساخت اور صحت کی رفتار دیکھ کر سبھی عمر طویل کی پیشنگوئی کرتے تھے، لیکن ظاہر بینوں کے یہ سارے اندازے غلط ثابت ہوئے اور اﷲ کی مشیت پوری ہو کر رہی، تقدیر کے سامنے تدبیر نے سپر ڈال دی، اور انسان کی مجبوری دبے بسی ہی نہیں خام خیالی اور غلط اندیشی بھی نمایاں ہوگئی۔
مصلحت ایزدی تھی کہ وہ چھوٹی عمر ہی میں اس دنیا سے کوچ کر جائیں تقدیر الٰہی کے رازہائے سربستہ کی نقاب کشائی انسان کے بس میں نہیں ہے، اس کا علم ناقص اس کی نظر کوتاہ اور اس کا علم محدود ہے، ان حالات میں وہ حکمت الٰہی کا احاطہ کس طرح کرسکتا ہے، عالم غیب ہماری نگاہوں سے اوجھل ہے، ہم ظاہربیں باطن کے حقائق سے ناواقف ہیں، البتہ اﷲ کی مصلحت پر ہمارا ایمان ہے، اور...

Islamic World in the Global Scenario, Challenges and Strategy: A Study From the Seerat Nabawi’s Perspective

Islam is the perfect religion from every aspect and for every time which provides guidelines for all situations of human life. Islamic political system is one of these aspects which is based on the principles of Holy Quran and sayings of the prophet Muhammad (PBUH), and it supports such a civil structure which follows the directives and requirements mentioned in the afore said two main sources. In Islamic political system, the supreme authority is Almighty Allah and human being utilizes this right as His vicegerent. The present global political system and the strategy of Muslims invite the attention of the thinkers around the globe for effective international interaction between Islamic world and others. This shows that serious deliberations are direly needed to compete with the current challenges. In the present paper, the contemporary situation of global political system will be discussed in order to determine the development of western political system, suggest means to compete with the challenges of this age and to facilitate in devising a suitable strategy for it

Numerical Simulation for Optimization of Canal Irrigation System

Agricultural production needs to provide food and fiber for the burgeoning global population which is expected to touch 9.25 billion mark by 2050 from the current 7 billion. Agriculture accounts for about 84% of total water use in Asia, 72% worldwide, and 87% in developing countries. The need for improving irrigation management has been figuring high in most of the under developed countries in Asia and Pacific region since beginning of 21 st century. The total actual renewable water resources decreased from 2,961 m 3 per capita in 2000 to 1,030 m 3 per capita in 2013 which puts Pakistan in the category of red zone countries. This realization has shifted the attention of the researchers and policy makers to focus on improving the performance of the irrigation systems. To achieve equity in distribution of canal water, new techniques for managing irrigation water resources and for better performance of the irrigation system is required to be given priority under water stress and constraints environment. The simulation models provide information about actual state of the flow anywhere in the canal at any time and are appropriate tools. One dimensional hydrodynamic model, Simulation of Irrigation Canal, SIC is applied for the research study to simulate the hydraulic and operational conditions of Lower Bari Doab Canal (LBDC) for better management and operation. The model was set up using observed cross sectional survey canal data of 2008-2010. The observed data of water levels, gate openings and out flows, for August 20-27, 2010 was used for calibration of the model. The steady state calibration of the hydraulic model compiles all canal reaches and structures for the actual conditions. The calibration of the model showed close agreement between observed and simulated water levels. As a whole, simulated and actual water levels represented a good calibration of the hydraulic model. The calibration results indicated that the computed water levels were within range of 20-35 cm than the observed water levels. After calibration, the model was validated using observed field data of six irrigation periods during 2006 to 2011, (May 10-17, 2006; August 24-31, 2007; November 8-15, 2008; October 07-14, 2009; February 20- 27, 2010 & July 7-14, 2011). The results indicated that the computed water levels were within range of 17-32 cm than the observed water levels. It showed that the model- computed water levels were in close agreement with the observed values for head, middle and tail reaches of the canal. The three statistical approaches i.e., Coefficient of Efficiency -E (Nash-Sutcliff coefficient), coefficient of determination -R 2 and the Student’s t- test were adopted for evaluation of model performance. The analysis indicated that the model perfromance is resaonably accepatable. Numerical Simulation of Lower Bari Doab Canal (LBDC) canal was performed to compute water levels for 100% to 40% of design discharge with and without gate operations. The results showed that without gate operations, at 80% of design discharge at head, the cross regulators need to be operated to feed 25% offtakes to their design discharges. Therefore, gate operation is required at 80% of design discharge. The simulated discharges of offtakes for 100%, 80% and 60% of design discharge at LBDC head indicated that the reduction in the discharges for tail portion offtakes is remarkably more than the offtakes at the head and middle portion when the discharge at the head of the main canal is reduced from 100% to 60%. This indicated that the reduction in discharge from 100% to 60% at the head of a main canal, adversely affects ii ABSTRACT NUMERICAL SIMULATION FOR OPTIMIZATION OF CANAL IRRIGATION SYSTEM the equity conditions along the main canal. The percent reduction varied from 3-20% from head reach to 25% to 42% in the tail portion. Based on results of this study, it is recommended to adopt normal range of operation as 80% for distribution operation instead of 70%. This study suggests new “Combined Efficiency Performance (CEP)” parameter as better representative of performance indicator to check the overall hydraulic and operational performance of canal. This indicator helps canal mangers to evaluate the operational plans. When the value of Combined Efficiency Performance (CEP) is between 0.8 to 1, the canal performance is “Good” and is graded as value equal to 1. When CEP is between 0.8 to 0.4, the performance is “Satisfactory”, the canal is graded equal to value 0.5, while when CEP is less than 0.4 and greater than 1, the canal performance is “Poor” and is graded as value equal to 0. The actual water delivery schedule for period June 15 to July 8, 2011 (Kharif season) was tested and results were compared with optimized plan for performance assessment in terms of equitable distribution of canal water. These indicators are: (a) Delivery Performance Ratio (DPR); (c) Reliability (P d ). (c) Equity (P e ) in water distribution; (d) combined efficiency performance (CEP). The simulations made with ID hydrodynamic SIC Model for LBDC provide information on canal behavior and help canal mangers to optimize operational plan for implementation. Additional modules are developed to better integrate SIC model as Support Tool in the Decision making process of the canal managers. Thus before implementing a new operational procedure in the field, the canal managers can evaluate its likely consequences on the system. The proposed distribution plan with head discharge of 220 m 3 /s of Lower Bari Doab Canal (LBDC) was simulated. The results concluded that the average daily delivery performance ratio (DPR) for actual plan (Kharif 2011) is 0.94 while for optimized plan; the average DPR value is 0.97 showing improvement by 4% on average for optimized plan. The reliability (P d ) of irrigation supply indicated that for actual plan, the P d value is 0.048, while for proposed plan, it is 0.056 indicated improvement by 16.6%. The equity (P e ) in terms of water distribution along LBDC main canal concluded that the equity slope for optimized plan is 0.02 as compared to 0.077 of actual plan. The P e for actual plan is 0.9 while for optimized plan it is 0.97 indicating 8% improvement. The evaluation of combined efficiency performance (CEP) of offtakes concluded that for actual plan, the number of offtakes graded as “Good” are 31 while for the proposed plan, the number of offtakes graded as “Good” are 46. The analysis indicated that CEP value for Optimized plan is 0.82 while for actual plan, CEP value is 0.77, showing 13% improvement. In Pakistan, computer oriented research to study hydraulic behavior of large complex network using canal simulation hydraulic models is less common and not constantly implemented. This research study uses hydrodynamic model for simulations of main canal under different operating conditions. The canal managers can optimize the operational plans and implement their decisions in more efficient way than the current practices. The findings of this research serves as a decision support tool for the canal irrigation system managers to formulate effective and responsive control operation strategies under varying flow scenarios.