CERTIFICATEPROGRAMMEIN
TEACHING OF PRIMARY SCHOOL
MATHEMATICS (crPM)
Term-End Examination
December, 2006
MATHEMATICS
LIV[T-o1 LEARNING
:
Maximum Marks : 700
Time : 3 hours
Note : Answer snY ten- questions'
Further, design an
1. List five characteristics of a good activity.
3 to classify counting
activity that allows children of class
odd and even, or prime
numbers into different sets (such as
characteristic you have
and composite, etc.). For each
you have designed
listed, briefly exprain whether this activity
10
has it or not.
'assimilation' and
a* 2 . (a) Exprain what the terms
'accommodation' mean' in the context of schemes'
? Use two examples (frorn
distinct topics of
child may improve
mathematics) to illustrate how a
through these
her mathematical understanding
processes.
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(b) Prove, or disprove, each of the following
statements:
(i) If Ml and Mz are two consecutive even
numbers, then M? + M3 is the square
of an
even number.
(ii) The sum of two odd numbers is even.
3. (a) (il Give an example of a mathematicarproblem
related to fractions that has more than
one
solution.Also give two solutionsof the problem.
(ii) why is it important to expose studentsto
such
problems (see(il) ?
(b) Using an example of a concept from the
Class 3
math syllabus,explain the process of
abstractinga
concept. Further, explain how you can
help children
move from the concrete to the abstractnotion
of the
concept.
4' (a) "Girls of Class 5 are taller than
boys of Class 5.,,
Outline a series of activitiesfor children
of Class 4
to test this hypothesis.The activities -t
should require
them to go through all the stagesof data
handling. 8q
(b) Give an exampre of a prane figure that
does not
possessrotational symmetry.Also justify your choice
of example.
2
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5. (a) Give two reasons to explain why children find
mathematical notation confusing. Support your
answer with illustrations.How would you help your
studentsto becomecomfortablewith such notation ?
(b) Give three expectationsthat a constructivisthas from
her learner. Also give a learning situation that
illustratesthese expectations.
6. What is the sequence stepsusuallyfollowed in solving a
of
word problem, accordingto Davisand Mayer ? Illustrate the
steps in the context of solvingthe following problem :
"There drt) 20 children in Kusum's class. In how many
ways can she choosethree childrento act as a lion, a fox
and a rabbit, respectively,if all the children can do any
role ," 10
,
7 . (a) I-low would you help a Class 4 child realise the
advantageof representingdata in a bar diagram as
comparedto a frequencytable ?
f
(b) Relatedto the experimentof tossinga coin, describe
one outcome that is irnpossibleand another that is
'" sure to happen.
;
(c) Describe three errors that a 6-year-old child might
make in reading a picture representinga 3D-object.
How would this knowledgeabout errors be useful to
you as her teacher? Give one examplein support of
your answer.
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8. (a) Tanya was working with children of Class 4. She
divided the children into groups of 4 studentseach.
Each child was given sets of four pictures, depicting
the stagesin the life cycle of a plant, or of an insect,
or of an animal. Each child was expectedto arrange
the 4 pictures in a meaningfulorder and then discuss
the pictureswith the other group members.
(i) What are the mental abilitiesthat children could
develop through this activity ?
(ii) Why should Tanya do this activity in small
groups ?
(b)(i) to
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(ii) Describe two different activities to help children
develop the ability to estimate the sum pf two
decimal fractions. (Remember, a decimal fraction
is a number like 13'523)
9. (a) Describe an activity in detail, based on calendars, to
help your learners look for a variety of number
patterns in a given collection of numbers. 4,1
(b) Give three characteristics of assessment in the
!
programming model. . Also explain one major
difference between the views of assessment in the
banking and programming models of learning, using
an exanrple.
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10. (a) According to Piaget, what is egocentricism? What
experiment did he carry out to show that young
children are egocentric?
(b) Raman believesthat children are clean slates when
they join school. Give an example to convince him
that this is not true.
(c) why should children be encouragedto explain the
reasoningbehind the method they are using to solve
a problem ? Give two reasonsfor this.
11. Describethe steps through which you would take children
of Class5 to help them developthe ability to read the map
of a state.Give a task for each step, and justify your choice
of task.
10
12. (a) (i) What does the ability to conserve quantity
mean ? ExPlainthis with an examPle'
(ii) Why do pre-school children find it difficult to
conserve quantity ? Your explanation should
t include an examPle.
"t (b) Explain the difference between conceptual knowl edge
F and procedural knowledge. Illustrate your explanation
an
with an example related to the learning of
algorithm for division of fractions'
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