Associate Degree in Education (ADE) Teaching of Mathematics CODE No: 6409 UNITS: 1–9 DEPARTMENT OF SCIENCE EDUCATION FACULTY OF EDUCATION ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD i (All rights Reserved with the Publisher) First Printing .................................... 2015 Quantity ........................................... 500 Printing Coordinator ........................ Printing Press Operation Committee Printer .............................................. AIOU, Printing Press Publisher .......................................... Allama Iqbal Open University, Islamabad ii COURSE TEAM Chairman: Prof. Dr. Tanveer Uz Zaman Writers: 1. Farkhunda Rasheed Ch. 2. Muhammad Azeem 3. Dr Amjad Ali 4. Irum Naseer Reviewers: 1. Prof. Dr. Tanveer Uz Zaman 2. Farkhunda Rasheed Ch. 3. Samima Kashif 4. Dr. Iqbal Shah Course Development Coordinator: MS Saima Kashif Course Coordinator : Prof. Dr. Tanveer-Uz-Zaman Assisted in Course Development: Farkhunda Rasheed Choudhary Formatting & Layout Design: Mushtaq Hussain iii TABLE OF CONTENTS Unit # Name of Unit Page No. Unit 1: Introduction ........................................................................................3 Unit 2: Enhancing Learner Understands of Mathematics ........................55 Unit 3: Teaching and Learning of Mathematics ........................................83 Unit 4: Learning Aids and Mathematics Laboratory ..............................105 Unit 5: Teaching of Some Important Concepts ........................................121 Unit 6: Teaching of Algebra, Geometry & Trigonometry .......................171 Unit 7: Teaching of Sets, Information Handling and Financial Arithmetic .......................................................................................269 Unit 8: Assessment in Mathematics ...........................................................315 Unit 9: Planning Instructions for Mathematics Learning .......................361 iv FOREWORD Elementary education is the base of any educational system. Its quality depends upon curriculum, learning environment and competency of the teachers. Therefore, Teacher Education has become very much significant now a day than it has been half a century ago. Almost all over the world, education policies and practices are being radically transformed, and teacher education programs in institutions and universities are being in line with the latest trends in education. The rapid advancements in science and technology have influenced nearly all aspects of life. In this era, students need to become lifelong learners so that they can cope with the fast moving developments of the world. Therefore, the teaching and learning of mathematics have become very much essential than ever. Therefore there is need to ensure that learners acquire extensive mathematical knowledge and skills and enabling them meet the requirements of this century. It is also necessary to develop effective pedagogical strategies and approaches for teaching mathematics for the learners. The Associate Degree in Education program trains prospective and in service teachers. Teaching of Mathematics course has been designed to teach mathematics in an effective manner by investigative approaches, developing problem-solving skills and engaging in data analysis. It will provide extensive pedagogical knowledge to enhance motivation to learn mathematics, develop mathematical thinking, and deal with difficulties that elementary school children have while learning mathematics. This course will be helpful for pre-service as well as in service teachers. In this course teachers will learn to create a suitable learning environment and employ strategies that encourage active participation of the students. This course has been designed carefully for providing up to date pedagogical knowledge that actively involve teachers in the teaching learning process. It is hoped that teachers will find this course very useful for their teaching. Prof. Dr. Shahid Siddiqui Vice Chancellor AOIU, Islamabad v ACKNOWLEDGMENT The Allama Iqbal Open University and the author both are grateful to the scholars and publishers for using/adopting their books, web material and reports as reference materials for the development of the course of General Mathematics and Statistics. It may be pointed out for general information of all whose work has been quoted in the course that Allama Iqbal Open University is a non commercial educational organization in Pakistan which is providing educational facilities to under-privileged remote rural areas through distance education mode. Great stress has been placed in making this course to facilitate prosperous, in-service and pre-service teachers for Teaching Mathematics. There are many activities included in the course for the better understanding and engagement of the students. The university and the department would like gratefully to acknowledge the expertise provided by various experts in developing and improving the outlines and course books. The Allama Iqbal University acknowledges the contribution of author and publisher for the development of this course. I am also thankful to Farkhunda Rasheed Choudhary, Mr. Fazal Karim of Editing Cell, Mr. Anwar-ul-Haq and Mr. Mushtaq Hussain of Print Production Unit (PPU) for efficiently finalizing the composing and designing the process of this course. Finally, I am indebted to all staff of Department of Science Education for helping in correspondence Prof. Dr. Tanveer-Uz-Zaman Chairman Department of Science Education vi INTRODUCTION This course will equip prospective teachers with knowledge and skills to teach math in grades I- through VIII. They will become familiar with the maths curriculum and expected student learning outcomes. Prospective teachers will learn to use a variety of instructional methods that promote active learning of math, including making and using teaching and learning materials. They will plan math lessons and activities and practice teaching math with peers. This course will deepen the mathematics education of elementary school teachers. In the course, teachers will be trained in teaching mathematics. This course will increase the pedagogical education in mathematics, particularly with regard to teaching processes, learning processes and teacher guidance, with a focus on psychological-didactic approaches to learning and teaching mathematics. Unit-1 is about the introduction. Student will learn about Nature of Mathematics, Historical Review of the Development of Mathematics Education, Contributions of Different Mathematicians, and place of Mathematics in Elementary School Curriculum, Introduction of curriculum of Mathematics at elementary level and its objectives, Educational Value of Mathematics, Use of Mathematics in Everyday Life, Aesthetic and Cultural Values of Mathematics. In unit-2 is about Enhancing Learner’s Understanding of Mathematics. In this unit students will learn about Meaningful learning, Patterns in Mathematics, Misconceptions: Using and recognizing them, Making Mathematics Meaningful, using Environment for teaching mathematics, linking mathematics learning to the real world. In Unit-3, some contextual factors of Teaching and Learning of Mathematics have been discussed. Moreover, Effective Questioning, mathematical Modelling, Hands-on, Minds-on, Mathematics, Learning Mathematics by Enquiry, Learning Mathematics by Problem Solving have also been discussed. In teaching and learning process, the Learning aids have great significance. In Unit-4, there learning Aids and Mathematics Laboratory have been discussed. In this unit following topics have been covered: learning Aids in Mathematics Teaching, Modern Learning aids for Mathematics, Mathematics Laboratory in Elementary School, Using Learning Aids in Mathematics Laboratory, Use of Low Cost Material (From local context), and Learner Cantered Activities. In this course the teaching of some important points were also discussed. It contains, Teaching of Numbers & Arithmetic Operations, Fractions and Decimals, LCM and GCD, Concept of Measurements (Length, Mass, Time & Temperature), Unitary Method and Percentages. In addition to this in unit-6, vii Teaching of Algebra, Geometry and Trigonometry have also been added in this course. In this unit student will learn how to teach Algebra, Geometry and Trigonometry. The sets are very essential concepts of mathematics learning. Therefore their teaching has also been discussed in unit-7 along with information handling and financial arithmetic. The teaching learning process is incomplete without assessment. In unit-8, assessment in mathematics has been discussed. In this unit Scope of assessment in Mathematics, Preparation of Different Type of Assessments in Mathematics, Interpretation and Use of Test Results and using Tests Results have been discussed. Lesson Planning is also very much essential for efficient delivery of content. In unit-9 planning Instructions for Mathematics Learning have been discussed. In this unit importance of Planning in Teaching of Mathematics has been discussed. Moreover, Planning for the Full Course, Scheme of Work, Lesson Planning, Qualities of Good Lesson Plan and Development of Model Lesson Plans have been added. Prof. Dr. Tanveer-Uz-Zaman Course Coordinator viii OBJECTIVES OF THIS COURSE After going through this course, the prospective teachers will be able to: Develop and use teaching aids to foster student’s learning. Use various methods of teaching mathematics effectively. Develop competencies and skills for the teaching of mathematics at elementary