*Q 1 (i)* Educational value of mathematics Ans Mathematics has got many educational values which determine the need of teaching the subject in schools. These values can be studied under the following heads: 1. Practical Value 2. Cultural Value 3. Disciplinary Value. *1. Practical Value:* Mathematics has great practical value. Everyone uses some mathematics in every form of life. A common man sometimes can do without reading or writing but he cannot do without counting and calculating. Any person who is ignorant of mathematics can be easily cheated. He will always be at the mercy of others. We have to make purchases daily. We buy cloth, food items, fruit, vegetables, grocery etc. *2. Cultural Value:* Mathematics has got a great cultural value which is steadily increasing day by day. Mathematics has made a major contribution to our cultural advancement. The progress of our civilisation has been mainly due to the progress of various occupations such as agriculture, engineering, industry, medicine, navigation, rail road building etc. *3. Disciplinary Value:* Mathematics trains or disciplines the mind also. It develops thinking and reasoning power. According to Locke, "Mathematics is a way to settle in the mind a habit of reasoning." Mathematics is 'an exact and definite science'. Every student of mathematics has to reason properly without any prejudices or unnecessary biases. Reasoning in mathematics has the characteristics of simplicity, accuracy, objectivity, originality etc. Q1 (ii) Why it is necessary to teach and study mathematics? Ans: It is very necessary to teach and study mathematics due to the following reasons: 1. Mathematics develops the ability to think because to find the solutions, you have to think of a whole coherent process. It could be said that mathematics is fundamental in the education of children, since math teaches them to think. 2. Thanks to mathematics, we can explain how things work, that is, we can express our thoughts and ideas with clarity, coherence and precision. 3. Mathematics promotes wisdom. Mathematics applies to other sciences as in new technologies and it is very present in our life. 4. Mathematics quickens our minds and helps us, in general, to deepen and think when we are faced with complex problems. 5. Math will be more represented in the future. Whether we like that or not, math is becoming an increasingly important factor in a variety of industries. Future journalists and politicians will speak less and analyze more. Q2 i Linkage of mathematics to real world: Ans: Linkage of mathematic to real world In order to link Maths to real word and engage students, I always introduce a new topic showing an application of Mathematics in medicine or cancer research. For example, straight lines can be used to describe how the number of cancer cells evolves over time. Simultaneous equations can then be introduced to find the intersection point between a given cancer and a given drug (both represented as straight lines). This approach can also be adapted to different key stages by introducing the drug as a quadratic (or more complex) function. Hence, by using simple Maths topics, it is possible to build a mathematical model and describe cancer progression. Then, several treatments can be tested on the model in order to predict the different outcomes and select the best therapy. Q2 (ii) *Purpose of pattren in mathematics: A pattern is a series or sequence that repeats. ... There are two main types of math patterns: number patterns, or sequences of numbers arranged according to a rule or rules, and shape patterns, which are labeled by using letters and the way that they repeat. The ability to recognize and create patterns help us make predictions based on our observations; this is an important skill in math. Understanding patterns help prepare children for learning complex number concepts and mathematical operations. Our BC Math Curriculum, from kindergarten to grade seven, identifies and describes the big ideas behind the tasks and activities students are engaged in and working on in their classrooms. These big ideas are: 1. We use patterns to represent identified regularities and to form generalizations. 2. Patterns allow us to see relationships and develop generalizations. *Q3* Ans *PROCESS OF PROBLEM SOLVING METHOD:* The child is curious by nature. He wants to find out solutions of many problems, which sometimes are puzzling even to the adults. The problem solving method is one, which involves the use of the process of problem solving or reflective thinking or reasoning. *Definition:* Problem solving is a set of events in which human beings was rules to achieve some goals. *Procedure for Problem solving:* *1.* Identifying and defining the problem: The student should be able to identify and clearly define the problem. The problem that has been identified should be interesting challenging and motivating for the students to participate in exploring. *2.* Analysing the problem: The problem should be carefully analysed as to what is given and what is to be find out. Given facts must be identified and expressed, if necessary in symbolic form. *3.* Formulating tentative hypothesis Formulating of hypothesis means preparation of a list of possible reasons of the occurrence of the problem. Formulating of hypothesis develops thinking and reasoning powers of the child. The focus at this stage is on hypothesizing – searching for the tentative solution to the problem. *4.* Testing the hypothesis: Appropriate methods should be selected to test the validity of the tentative hypothesis as a solution to the problem. If it is not proved to be the solution, the students are asked to formulate alternate hypothesis and proceed. *5.* Verifying of the result or checking the result: No conclusion should be accepted without being properly verified. At this step the students are asked to determine their results and substantiate the expected solution. The students should be able to make generalisations and apply it to their daily life. Q 4. (i) *Learning Aids used in Maths lab:* The use of sensory aids in teaching mathematics is of recent origin. In fact, all teaching has always involved the communication of ideas through the senses either orally through the medium of speech, or visually by the use of written or printed material. Text –books, writing materials, geometrical instruments and the blackboard (all these are sensory aids) have been long regarded as indispensible equipments for mathematics classes. For many years resourceful teachers have used models, instruments, drawings, and other devices to stimulate interest and facilitate learning. *MODELS* Models are very useful as an aid; because they can be handled and manipulated .Their main merit is that they afford pleasure in their making. *EXCURSIONS* Visits to places of mathematical interest can be of some use. *FILMSTRIPS* Various filmstrips can be used to give a new colour and attraction to different ideas of mathematics. *TV and RADIO* Broadcasting stations can also help, if the school possesses a radio set and the stations broadcast programmes of mathematical interest. *COMPUTER* Our high school books now contain a chapter on computer. *Q4. (ii)* Ans *Low cost no cost materials* These are the teaching aids which require no cost or available cheaply, and developed by locally available resources and expedite the process of learning in the classroom. Low cost no cost materials are developed from the waste and help the teachers in making the teaching intresting and concrete. These material can be used in nursery, primary medel, high and Higher secondary schools. *Q8 (i)* Ans *Characteristics of a Good Lesson-Plan* 1. Example quoted to teach and explain the subject matter should be related to the everyday life of the child. 2. Lesson-plan should be child-centred. 3. In the lesson-plan these should be provision of summary of whole subject matter. 4. In the lesson-plan there should be proper provision of recapitulation to have view of evaluation of the subject-matter taught to the students. 5. In the lesson plan these should be proper provision of the teaching aids and good illustrations. 6. It should provide maximum participation of the child in the teaching and learning process. 7. Provision of home work related to the subject- matter taught should be these. 8. Subject matter in the lesson-plan should be according to the time for teaching at the disposal of the teacher. *Q8 (ii)* Ans: *Importance of planning in mathematics:* Planning is a significant element of teaching-learning system. It is a step-by-step guide that provides a structure for an essential learning. Before planning a lesson, it is essential to classify the learning outcomes for the class. It is important because it helps the teacher in maintaining a standard teaching pattern and does not let the class deviate from the topic. Pre-planning helps the teacher to be better equipped in answering questions asked by the students during the lecture. An effective lesson plan has three basic components; aims and objectives of the course, teaching and learning activities and, assessments to check student understanding of the topic. Some forther importance are *1*. In order to begin with lesson planning, it is important to know the aims and objectives of the course being taught to students. *2.* Once the aims and objectives are in place, it is important to make sure that the planned lesson is understandable by the students. *3.* Assessments to check student understanding of the topic *4.* A lesson plan does not necessarily have to be a detailed script that contains the plan of every interaction with students in the classroom. It should preferably have the general overview of the aims and objectives of the course, the plan of teaching and learning activities of the course and the activities planned to check the students’ understanding. Mind Ability WhatsApp
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