Problems and Problem Solving - Ministry of Education

a)
b)
c)
d)
e)
f)
g)
a sample problem, solved using three different methods with helpful notes as to the thought
processes involved in exploring each method;
fully worked and explained problems showing how different strategies can be used to solve
problems;
examples and non-examples of genuine non-routine mathematical problems;
a sample rubric, applied to three examples of a solved problem, that shows how performance
on problem-solving tasks can be assessed and interpreted by teachers;
suggestions regarding the grade level and how students should be organised when asked to
solve each problem in the problem bank;
that each problem is linked to appropriate strands and concepts in the curriculum; and
a comprehensive glossary, at the end of the handbook, of important words and terms that are
highlighted in the text.
To Teachers
At times, out of utter frustration, you may be tempted to say that your ‘students can’t think’. Indeed,
there is often an absence of thought in many mathematics classrooms; however, it is quite
likely that your students will think if they are given the opportunity to or if they are exposed to a
thought-based classroom, over time. As you introduce some of these problems to your students,
you may find them becoming frustrated as they grapple with tasks that are novel and for which
they do not have worked examples, or for which they are unable to find solutions. Your response
at this stage is crucial. Do not be alarmed if they are frustrated. In time, as they come
to appreciate that there is a difference between ‘not knowing’ and ‘not having found out as yet’,
the frustration is likely to be replaced by enthusiasm. Do not give them answers or show them
worked examples; you may, however, provide useful prompts to point them in a particular direction
or you may ask open questions to encourage them to think about the problems in different
ways. Remember that your role is to help students to develop the ability to solve problems by
themselves.
Most importantly, do not decide to keep a problem from your class because you
think they cannot do it. Do not create a climate in your classroom in which right answers
are more important than strategizing, or in which students think they must be able to solve all
problems fully. When alternative solutions are presented by students, admit that you had not
6 PROBLEMS AND PROBLEM SOLVING
ProblemSolving.indd 6
8/24/12 6:55:32 PM