Maths Problem Solving

Problem solving is one of the four proficiency strands in the Australian Maths Curriculum. Research shows that problem solving strategies need to be explicitly taught, talked about, compared and reflected upon if students are to become adept problem solvers.

Natural Maths has been at the forefront of creating effective materials for problem solving for many years. Recently we have updated our approach to and pedagogy for maths problem solving to include interactive materials and a revised approach to the Polya model for Problem Solving which we call the STAR model. The STAR model has been well received by students who can make sense of the prompts as well as with teachers who can use the generic question starters to stimulate thinking and problem solving. See below for a full description of the STAR Model which is used throughout the new maths problem solving series.

Sort out …	Sort out the important information what you have to find out if there is missing information the meaning of new words what the answer will tell you
Think about …	Think about what you know that might help whether you have done a similar problem what strategy you could use what materials you might need
Action	Action carry out the plan you have made check that  you used all the given information estimate what the answer might be and cross-check with your answer
Reflect on …	Reflect on how effective your strategy was whether you are satisfied with your solution what other problems you might solve in the same way

 

Problem Solving Strategies

Students need to be taught the main maths problem solving strategies listed below and to be able to make decisions about which ones to use for any particular problem.

• Draw a picture/diagram
• Act it out
• Make a model
• Guess, check and improve
• Make a table
• Spot a pattern
• Identify and use a mathematical operation
• Work Backwards
• Work systematically
• Try a simpler case or break it up into manageable parts
• Use logic

The 20 problems in each of the problems solving series provide such opportunities as well as lesson plans for teachers to assist with maximising the potential learning of each problem. The problems are matched to the key topics of the Australian Curriculum as shown on the content table at the front of each book. There are mental routines and games in each book to consolidate or support the actual content and problem solving strategies required.