Q1 a) Give an example of each, with justification, to illustrate the following statements:
i) There can be several solutions to a problem
ii) Mathematics learning is spiral in nature.
iii) Knowing the number names does not reflect the understanding of number.
b) A child may not be able to perform a task simply because of language incompetence, and not cognitive incompetence. Illustrate the difference between language incompetence and cognitive incompetence while performing a Mathematical task with suitable examples.
Q2 a) Developing an understanding of “variable” is crucial for developing anunderstanding of “algebra”. Write three major hurdles children face while learning the concept of variable. Suggest a game that can be given to a group of children which helps them to overcome any one difficulty.
b) Estimation is a difficult skill to master. Explain why it is difficulty in the context of measuring height. Suggest an activity to assess that a group of children have mastered the skill for estimation. Explain why this activity is an “assessment activit
Q3a) Explain the differences in the following processes with the help of suitable examples (apart from the examples given in the material).
i) ‘Concrete to abstract’ and ‘particular to general’.
ii) Inductive and deductive methods of proof.
b) Solve the following number puzzle:
Step 1: Take a number from 1 to 9
Step 2: Multiply the number by 3
Step 3: Subtract 6 from the result obtained in step 2
Step 4: Divide the result obtained in step 3 by 3.
Step 5: Subtract the result obtained in step 4 from the number taken in the step 1. What is the number chosen?
Is the answer same if we take any other number from 1 to 9? Justify.
Q4 Explain the 5 levels of development in geometric understanding proposed by Van Hieles. Illustrate you explanation in the context of learning the concept of “size”.
Q5 Draw pictures to represent the following:
I) Comparing two objects which look different in size but have the same volume.
ii) Measuring the area of an irregular figure.
Q 6. a) Manisha always performs the division algorithm as follows:
In which step of the Division algorithm has she made the error? What are the possible reasons for committing the error. How do you help her to apply the algorithm in the correct way.
b) “Children learn better in groups “Justify this statement with the help of two suitable examples in the context of learning the concept of “angle”.
Q8. Suppose you want to teach a unit on “data handling”. What are different lessons you would divide this unit into. For any one of these lessons create a lesson plan.
Q9Write one word problem each for comparison model and complementary addition model for subtraction and explain the difference in the two models.
Q10Which of the following statements are ‘true’ and which are ‘false’? Give justification for your answer.