One of the main component of “heuristic” methods is to visualize.   In fact, we use visualisation to solve simple and complex problems in our daily live, which require spatial imagination or the ability to make assumption or prediction based on the presented and remembered facts. Visualisation is a powerful method, which can be applied to mathematics to increase students’ ability to solve math problems.

Before coming to any conclusion how to resolve the problem, it is essential to understand the questions and how the mathematical concepts and tools can come in to fix the problem.  There is a proverb says “a picture is worth a thousand word”. 

One of the method to help student to visualize a problem is to draw a diagram. Visualisation however is not limited to drawing visual representations of the objects, but it can be used at every step of solving math problems.

So why visualisation is applied in the first place?  Firstly, it is applied to understand and define the scope of the problem.  Without visualisation, it is impossible to estimate the scale and its mathematical relationship.  A lot of students fail at solving complex math problem is because they fail to visualise the problem in the first place resulting they are not able to choose the right means to solve the problem or taking long time to realise what the question is asking for? 

Secondly, for advance math like modeling (e.g. 3D or 2 dimensional geometry question).  It is very difficult for anyone can resolve such calculation without mastering the visualisation skill in the early stage. 

Finally, it is a tool to estimate and projection (predicting).  This skill is crucial for solving complex math problems which require multiple operations on the equations performed in a correct order.  Student who are able to visualise can predict the outcome if they are apply certain rules of math.  Student who are trained in visualise problem in their early stage will tend to resolve problem accurately if not faster than those who purely using memorising the formulae (though most of time they can resolve at a greater speed).  That is because when the problem being modified or alter being different from the norm, student who master visualisation will able to detect the different and being versatile in tackle the problem whereas student who depend on memorize the steps will having difficulty understand the problem even though the solution is almost similar.