# Problem solving information

### What is a problem?

A problem is a question that motivates you to search for a solution. This implies first that you want or need to solve the problem, and second that you have to search for a way to find a solution. Whether a question is a problem or an exercise depends on the prior knowledge of the problem solver.

This website includes problems for all strands and for Levels 1 to 6.

### What is problem solving?

Problem solving was part of the Mathematical Processes Strand of the New Zealand Mathematics Curriculum (1992). While problem solving is not a category within the New Zealand Curriculum (2007), the key competency of Thinking includes problem solving.

We believe that by solving problems students get a much better feel for what mathematics is all about, what it can do and how it does it.

In this website the term ‘problem solving’ is used to mean mathematical problem solving. Mathematical problem solving is about finding solutions and not just answers to mathematical problems.

There are four steps that you need to go through in solving most mathematical problems. These are:

1. understand and explore the problem
2. find a strategy
3. use the strategy to solve the problem
4. look back and reflect on the solution.

Of course, problem solving can be more complicated than this.

### Problem solving strategies

The selection and use of strategies is a part of the process of problem solving. An understanding of specific problem solving strategies helps make problems clearer, simpler and more manageable. It also helps students develop better problem solving skills.

The main problem solving strategies explored on this site are:

• Guess (this includes guess and check, guess and improve)
• Act it Out (this includes using equipment)
• Draw (this includes drawing pictures and diagrams)
• Make a List (this includes making a table)
• Think (this includes using skills you already know)

Of course, you also need to use other problem solving skills as you solve problems. These skills include being systematic, keeping track, looking for patterns and working backwards.

### Why teach problem solving?

There are many benefits to teaching problem solving. These include:

• it bases students’ mathematical development on their current knowledge
• it is an interesting and enjoyable way to learn mathematics
• it is a way to learn new mathematics with greater understanding
• it produces positive attitudes towards mathematics
• it makes the student a junior mathematician
• it teaches thinking, flexibility and creativity
• it encourages co-operative skills
• it is a useful way to practice mathematical skills learned by other means
• it is similar to the approach used in other curriculum activities.

### Organising the teaching of problem solving

When implementing problem solving in your mathematics programme there are many factors you need to consider, including how you structure the lesson, and the types of question you will ask top scaffold students.