20771_Problem_solving_Year_6_Background_information_resources

INTRODUCTION
Problem-solving and mathematical thinking
By learning problem-solving in mathematics,
students should acquire ways of thinking,
habits of persistence and curiosity, and
confidence in unfamiliar situations that will
serve them well outside the mathematics
classroom. In everyday life and in the
workplace, being a good problem solver can
lead to great advantages.
NCTM principles and standards for school
mathematics
(2000, p. 52)
Problem-solving lies at the heart of mathematics.
New mathematical concepts and processes have
always grown out of problem situations and students’
problem-solving capabilities develop from the very
beginning of mathematics learning. A need to solve a
problem can motivate students to acquire new ways
of thinking as well as to come to terms with concepts
and processes that might not have been adequately
learned when first introduced. Even those who can
calculate efficiently and accurately are ill prepared for
a world where new and adaptable ways of thinking
are essential if they are unable to identify which
information or processes are needed.
On the other hand, students who can analyse problem
meanings, explore means to a solution and carry
out a plan to solve mathematical problems have
acquired deeper and more useful knowledge than
simply being able to complete calculations, name
shapes, use formulas to make measurements or
determine measures of chance and data. It is critical
that mathematics teaching focuses on enabling all
students to become both able and willing to engage
with and solve mathematical problems.
Well-chosen problems encourage deeper exploration
of mathematical ideas, build persistence and highlight
the need to understand thinking strategies, properties
and relationships. They also reveal the central role of
sense making in mathematical thinking—not only to
evaluate the need for assessing the reasonableness
of an answer or solution, but also the need to consider
the inter-relationships among the information provided
with a problem situation. This may take the form of
number sense, allowing numbers to be represented
in various ways and operations to be interconnected;
through spatial sense that allows the visualisation of
a problem in both its parts and whole; to a sense of
measurement across length, area, volume and chance
and data.
Problem-solving
A problem is a task or situation for which there is
no immediate or obvious solution, so that problemsolving
refers to the processes used when engaging
with this task. When problem-solving, students engage
with situations for which a solution strategy is not
immediately obvious, drawing on their understanding
of concepts and processes they have already met, and
will often develop new understandings and ways of
thinking as they move towards a solution. It follows
that a task that is a problem for one student may not
be a problem for another and that a situation that
is a problem at one level will only be an exercise or
routine application of a known means to a solution at
a later time.
A large number of tourists visited Uluru during 2007.
There were twice as many visitors in 2007 than in
2003 and 6530 more visitors in 2007 than in 2006. If
there were 298 460 visitors in 2003, how many were
there in 2006?
For a student in Year 4 or Year 5, sorting out the
information to see how the number of visitors each
year are linked is a considerable task. There is also
R.I.C. Publications ® www.ricpublications.com.au Problem-solving in mathematics
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