1. Which of the following are correct, and which are not? Give reasons for your answers.
Children know nothing when they start formal schooling. When children are taught a new concept, they must be made to solve many questions related to the concept of exactly the same type in exactly the same manner. Problems involving estimation are confusing for the learners. A negative integer is a rational number. Any regular polygon can be used for regular tiling of a floor.

2. What do each of the following terms mean? Explain them, and give an example of each Scheme
Accommodation
Process diagram
Legends in a map
Mathematical conjecture

3.(a) Give two distinct ways in which classrooms can be organised. Explain how each of these affect students learning, in the context of learning about 'chance'.
Give two essential differences between the programming model and the constructivist model of learning. Explain these differences using examples from introducing algebra to Class VI children.

4. Which of the following are characteristics of a good mathematics classroom activity for children of Class VII? Give an example, in each case to support your answer.
It must involve a lot of repetition and memorisation.
It should give children a reasonable challenge.
It must require children talking in small groups.
It must require a lot of physical activity.
It could have several different objectives.

5.(a) Give four essential features of a map. Which of these features is not properly developed in a child of Class IV usually? Give reasons for your answer.
Explain the difference between procedural and conceptual knowledge, using an example from multiplication of fractions.

6.(a) What is the shape of a curve representing normally distributed data? Give an example of data that is represented by such a curve, with explanation. How many modes does your data have Use the principle of mathematical induction to prove that the sum of the first n odd natural numbers is for all natural numbers n.

7.(a) When is a 6-digit number divisible by 8 Give the mathematical logic behind your answer.
Children's play is a part of their process of learning'. Do you agree with this Give two examples in support of your answer, pertaining to distinct areas of mathematics. Which is the smallest prime number? Give reason for your answer.

8.(a) Give an example, with justification, of a 2D-figure having only two axes of reflection symmetry.

(b) Explain the following processes in the context of decimal fractions moving from general to particular;
moving from particular to general.
Explain the concept of 'assimilation' using an example of a pre -school child making sense of pictures.

9. Consider the following solution:

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Here E denote distinct digits from o to 9 and F denotes an arithmetic operation. Find E and F. While doing so, give all the steps you used, with reasons for applying them.

10.(a) What is meant by 'taking another person's perspective' for building spatial understanding? Explain this with an example. Further, give two distinct activities to help children develop this ability.
Anima, a primary school teacher, says that she always makes the children in Class learn tables upto the 20 -times table. Zorawar, another primary school teacher, says that he does not feel the need for the children to learn the tables beyond the 10 -times table. Which of these teachers do you agree with, and why
11.(a) A teacher says that she looks at errors made by children very carefully to improve her teaching. Do you agree with this approach? Give reasons for your answer. Including an example from 'place value'.
List the processes involved in 'data handling'. Explain each of them through an example pertaining to elections.