IGNOU AMT-01 - Teaching of Primary School Mathematics

1. a) Explain why use of concrete material and hands on experiences, in teaching learning of mathematics at primary level are more effective. Illustrate with the help of one example each. b) Jaya solved the division problem as shown below: i) What is the mistake she committed? ii) What is the probable reason for her mistake? iii) Devise a strategy to overcome her misconception. 2. a) Enlist two situations each from our daily life in which we use i) Geometry ii) Integers iii) Algebra b) What is an ‘open-ended’ question? Give two examples of such questions, one pertaining to single digit addition and one to multiplication. 3. a) Rinku, 8 years old has her birthday in December and Sonal (6 years old) has her birthday in April. Rinku says Sonal is older than her. What is the misconception Rinku has? Derive a detailed strategy to help Rinku overcome this misconception. b) Represent pictorially 4. a) Explain how mathematics is a language. Further give two distinct activities to help assess how comfortable a child is with her language. b) Give an example each, with justification, of a situation in which a child uses deductive reasoning. i) While playing ii) In Mathematics. c) Explain the relationship of arithmetic and algebra with the help of a suitable example. 5. a) Suman plays basketball. State two different mathematical concepts she used for this. Justify your answer. b) ‘Mathematics is hierarchical in nature’. Justify this statement with help of an example. c) Suggest two activities of different kinds that would help children arrive at a formula that relates centimeters to meters. 6. a) Evaluation at every step, through immediate feedback, should form part of teaching – learning process. Explain this statement in the context of each, teaching and learning of place-value. Further give three distinct multiple assessment techniques for evaluation in the context given. b) How would you convince a child that any number multiplied by 0 is 0, using a teaching aid. 7. a) Illustrate the use of each of the following in learning the concept of “fraction”. i) an outdoor activity ii) newspapers and magazines b) What could be the logic behind the following subtraction done by a child: Does this shows that the child has not understood the process of subtraction of numbers? Give reasons for your answer. How will you help her to correct her mistake. 8. a) i) What is an equation? Does all the equation involve a variable. Give an example of an equation with a variable in it and which does not have a variable in it. ii) Here is a think of a number game: ‘Think of a number, then double it, add six to the sum, divide the sum by half and then subtract 3 from it the number’. Did you receive the same number you had started with? Why? Justify. b) Prove that the sum of the first n even numbers is an even number. Is the kind of logic used in proving this is inductive, deductive or both? Justify your answer. 9. a) What is a magic square? Complete entries in the following and make it a magic square. Illustrate the methods used for filling the entries. Also explain why the method work? b) Much of Mathematics teaching is actually about encouraging children to become more aware about patterns they find and to use them in their thinking. Illustrate this in the case of the situation given below by answering the questions given in questions (i), (ii) and (iii), below. “A mathematics teacher in class 5 showed the following pattern in the class. 46×44=2024 63×67=4221 71×79=4909 She gave some time for the students to identify the pattern. After some time she asked the students to find the answer of “84 × 86” in one second. One student answered 7224. Based on this situation, answer the following question. i) What is the pattern used by the student? ii) Explain why it works? iii) Describe how it helps to encourage mathematical thinking. 10. Which of the following statements are true or false? Give reasons for your answer. i) ‘Today is a bright day’ is an unambiguous statement. ii) The sum of the interior angles of a Pentagon is 450o. iii) Pre-operational thinking is the characteristic of a two year old child. iv) If the capacity of a 3D-objects increases, then the volume also increases. v) Each mathematical problem have a unique solution.

1. Which of the following statements are true? Give reasons for your answers. a) Usually the first experience of subtraction that a child has is in Class I. b) Primary school children of any age continue to feel the need to use concrete aids for learning. c) Learning algebra helps the child to develop mathematical thinking. d) Children don’t get an opportunity to apply their knowledge of negative numbers till they reach class 10. e) The language of mathematics is made up of the terminology and symbols used in mathematics. 2. a) List at least 5 ways in which a farmer uses mathematics while farming, clearly mentioning what are areas of mathematics involved are. b) What are the advantages of using algorithms? What are the dangers that we must watch out for while illustrates them in the context of multiplication algorithm for multiplying two decimal fractions. 3. In the block you have read that cognitive development is continuous and there are phases within each stage. Give two examples, one from the unit and one new example, to explain what this means. You should justify and explain both your examples in about 150 words each. 4. a) What is the difference between repetition and rote-learning? Illustrate your answer by giving an example from addition of natural numbers. b) Give an example each (apart from the ones in the blocks) to show i) the difference in the meaning of ‘angles’ in English and in mathematics, ii) how the language of algebra helps us to express statements briefly and concisely. 5. Write down an activity each, different from those given in the blocks, to help children realise that i) − (−n) = n, for any number n? ii) division by zero is not meaningless? 6. When a child was asked to solve 5/3 X 10, she wrote i) Why do you think she made this error? ii) How would you help her to apply the operation correctly? 7. a) Suggest one game in which the children are simultaneously asked to estimate the measure the size of an object and an angle. Justify your choice of the game. b) “Children learn by experiencing things”. Justify this statement by giving two examples, one pertaining to learning fractions and the other pertaining to learning about shapes. 8. a) Do you think that the number-line is a useful tool in teaching the operation of addition and subtraction of fractions? Justify your answer. b) Suggest a teaching method or an activity to bring out the difference between volume and capacity? 9. Write down a details plan (See Unit 4) for teaching children of class 6 the concept of variable. 10. a) Write “11” in base 2. Show the steps you used for doing this. b) Explain E-L-P-S sequence of learning. Illustrate it in the context of learning the concept of “Time”. c) Give two distinct that are equivalent to 3/7. Pictorially explain how they are different.