20771_Problem_solving_Year_6_Background_information_resources

INTRODUCTION
the need to use multiplication and subtraction with
large numbers. For a student in later primary years,
an ability to see how the problem is structured and
familiarity with computation could lead them to use
a calculator, key in the numbers and operation in an
appropriate order and readily obtain the answer:
298460 x 2 – 6530 = 590390
590 390 tourists visited Uluru in 2006
As the world in which we live becomes ever more
complex, the level of mathematical thinking and
problem-solving needed in life and in the workplace
has increased considerably. Those who understand
and can use the mathematics they have learned will
have opportunities opened to them that those who do
not develop these ways of thinking will not. To enable
students to thrive in this changing world, attitudes
and ways of knowing that enable them to deal with
new or unfamiliar tasks are now as essential as the
procedures that have always been used to handle
familiar operations readily and efficiently. Such
an attitude needs to develop from the beginning of
mathematics learning as students form beliefs about
meaning, the notion of taking control over the activities
they engage with and the results they obtain, and as
they build an inclination to try different approaches.
In other words, students need to see mathematics as
a way of thinking rather than a means of providing
answers to be judged right or wrong by a teacher,
textbook or some other external authority. They need
to be led to focus on means of solving problems rather
than on particular answers so that they understand
the need to determine the meaning of a problem
before beginning to work on a solution.
In order to solve this problem, it is not enough to simply
use the numbers that are given. Rather, an analysis of
the situation is needed first to see how the number
sold at the second market relates to the number sold
at the first market and the 170 eggs sold altogether.
Putting the information onto a diagram can help:
Half number sold
at first market
First market
Half number sold
at first market
Second market
10 less than half
number sold at
first market
The sum of the numbers in the three sections of the
diagram is 170; half + half + (half – 10) = 170, so 3 x
half = 180. Half number sold at first market. A diagram
or use of materials are needed first to interpret the
situation and then see how a solution can be obtained.
However, many students feel inadequate when they
encounter problem-solving questions. They seem to
have no idea of how to go about finding a solution and
are unable to draw on the competencies they have
learned in number, space and measurement. Often
these difficulties stem from underdeveloped concepts
for the operations, spatial thinking and measurement
processes. They may also involve an underdeveloped
capacity to read problems for meaning and a tendency
to be led astray by the wording or numbers in a
problem situation. Their approach may then simply
be to try a series of guesses or calculations rather
than consider using a diagram or materials to come
to terms with what the problem is asking and using a
systematic approach to organise the information given
and required in the task. It is this ability to analyse
problems that is the key to problem-solving, enabling
decisions to be made about which mathematical
processes to use, which information is needed and
which ways of proceeding are likely to lead to a
solution.
Making sense in mathematics
Lindsay sold 170 eggs at two different markets. She
noticed that the number she sold at the second
market was 10 less than half the number she sold
at the first market. How many eggs did she sell at
each market?
Making sense of the mathematics being developed
and used needs be seen as the central concern of
learning. This is important, not only in coming to
terms with problems and means to solutions, but
also in terms of putting meanings, representations
and relationships in mathematical ideas to the
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Problem-solving in mathematics www.ricpublications.com.au R.I.C. Publications ®