problem 1:
a) Try and recall the manner you were taught multiplication of numbers. What were the strengths and weaknesses of that method?
b) Mathematics must be seen as an exploratory subject. Describe how this can be done while teaching the concept of number. (Provide a suggestive lesson plan and outlines of activities which would be suitable).
c) What is the major difference between a ‘game’ and ‘an activity that is not a game’? Use an illustration from the learning of measurement to bring out this difference.
d) Give an illustration of an algorithm for multiplication of two natural numbers that is distinct from the standard algorithm. Why is this algorithm mathematically accurate?
problem 2:
a) What are the processes included in ‘thinking mathematically’? Describe them by using an illustration related to the spatial understanding.
b) Give an illustration of a concept that a Class 5 child is made to learn by heart without understanding the full meaning of the concept. What features of this concept is the child not understanding? What will the effects be of this manner of ‘teaching’ on the child?
c) Describe the E-L-P-S series in the context of learning ‘negative number’.
d) Evaluation is the continuous sub-process of the teaching-learning processes. Give at least three different manners of assessing continuously in the context of teaching ‘angle’.
problem 3:
a) prepare 356 in base 8. In addition, give a detailed activity to help a child understand ‘place value’ in base 8.
b) Give validation for calling classification and seriation pre-number concepts.
c) Why must children first meet number names as adjectives and not as nouns?
d) Outline a sequence of three activities to introduce a child to subtraction and to help her enhance her understanding of this concept. Each of such activities must be at different ability levels.
Justify your choice of activities.
e) List out three errors children generally make when dividing one number by another.
problem 4:
a) According to you, which is the earliest class in which we should introduce children to negative numbers, and why?
b) Prepare a unit plan for teaching children negative numbers.
c) List out 2 abilities which are developed via learning algebra. Justify your choice of abilities.
d) By using the context of teaching children algebra, describe the relationship of mathematics and language.
problem 5:
a) Devise a series of at least 3 activities to describe the difference between 3/5 and 5/3, for illustration, to Class 4 children.
b) describe two distinct activities for assessing a child’s understanding of ‘angle’.
c) Repetition need not be boring. Validate this statement in the context of teaching ‘area’.
d) Give a sequence of 3 activities which can help children move ‘from particular to general’ in the context of learning decimal fractions.