problem 1:
a) Give two real-life situations, with justification, in which a person would need to use the ability to estimate the difference or sum of two fractions.
b) Describe the differences in the given processes included in the growth in mathematical understanding. As well give an illustration of each, pertaining to ‘data handling’.
i) Known to unknown;
ii) Particular to general.
c) Describe how the E – L – P – S sequence can be applied to help children understand the concept of angle.
d) Is there any difference in the manner you would plan a unit and a lesson? Describe your answer, with illustrations in its support.
problem 2:
a) Describe why the three pre-number concepts require to be developed by a learner for him/her to be able to count. Your description requires including specific exs.
b)
i) Outline a series of three activities (each needing a different level of learner’s ability) to help a learner develop an understanding of ‘place value’. (Note that giving a ‘series’ signifies that the links between the different activities must as well be brought out).
ii) How would you modify such activities if you were doing them with a class of 30 learners?
c) There are broadly five different real-life situations that require multiplication. Give a word problem each for such situations, in the context of children playing in a field.
problem 3:
a) Children have some misconceptions regarding negative numbers. List four of them. Also, for any one of such misconceptions, give a detailed strategy for helping the children correct it.
b) The diversity in any classroom has main implications for teaching mathematics. Describe this statement, with illustrations from teaching algebra to support your description.
c) Consider a classroom condition in which a teacher is introducing Class 6 children to operations on negative numbers. In this context, describe the various levels at which mathematics and language are related.
problem 4:
a) Devise a game to help children improve their understanding of subtraction and addition of fractions. Also give two distinct activities you would use for assessing the efficiency of this game.
b) Describe the given statements, giving illustrations from the context of operations on decimal fractions (that is, numbers like x y z r, where x, y, z, r are digits between 0 and 9):
i) Mathematics permeates every aspect of your life.
ii) In mathematics, truth is a matter of consistency and logic.
iii) Articulating reasons and constructing arguments helps children learn mathematical processes.
problem 5:
a)
i) Describe the 5 levels of development in geometric understanding proposed by the Van Hieles. Describe your description in the context of learning the concept of volume.
ii) Further, do you agree that children in Class 6 generally think at Level 2? Give reasons for your answer.
b) Can you think of a planar figure with precisely two axes of symmetry? Can this figure be a triangle? Give reasons to support your answers.
c) Describe what inductive and deductive logic are and demonstrate them in the context of measuring time.
d) Give two reasons why children generally find mathematical notations confusing. Support your answer with exs pertaining to representing and reading time. How would you help your learners become comfortable with the notation?